thesis.bib

@incollection{redner_8_2001,
	address = {Cambridge},
	title = {8. {Applications} to {Simple} {Reactions}},
	isbn = {978-0-521-65248-3},
	url = {https://www.cambridge.org/core/books/guide-to-firstpassage-processes/59066FD9754B42D22B028E33726D1F07},
	abstract = {First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems and the kinetics of diffusion-controlled reactions. First-passage processes provide an appealing way for graduate students and researchers in physics, chemistry, theoretical biology, electrical engineering, chemical engineering, operations research and finance to understand all of these systems.},
	urldate = {2021-01-04},
	booktitle = {A {Guide} to {First}-{Passage} {Processes}},
	publisher = {Cambridge University Press},
	author = {Redner, Sidney},
	year = {2001},
	doi = {10.1017/CBO9780511606014},
	pages = {252--294},
}

@article{zhang_first-passage_2016,
	title = {First-{Passage} {Processes} in the {Genome}},
	volume = {45},
	issn = {1936-1238},
	doi = {10.1146/annurev-biophys-062215-010925},
	abstract = {Many essential processes in biology share a common fundamental step-establishing physical contact between distant segments of DNA. How fast this step is accomplished sets the "speed limit" for the larger-scale processes it enables, whether the process is antibody production by the immune system or tissue differentiation in a developing embryo. This naturally leads us to ask, How long does it take for DNA segments that are strung out over millions of base pairs along the chromatin fiber to find each other in the crowded cell? This question, fundamental to biology, can be recognized as the physics problem of the first-passage time, or the waiting time for the first encounter. Here, we review a number of approaches to revealing the physical principles by which cells solve, with astonishing efficiency, the first-passage problem for remote genomic interactions.},
	language = {eng},
	journal = {Annual Review of Biophysics},
	author = {Zhang, Yaojun and Dudko, Olga K.},
	month = jul,
	year = {2016},
	pmid = {27391924},
	keywords = {Animals, Computer Simulation, Cell Nucleus, DNA, first-passage time, fractional Langevin motion, Genome, genomic interaction, Humans, Motion, viscoelasticity},
	pages = {117--134},
}

@article{liu_anchoring_2017,
	title = {Anchoring effect on first passage process in {Taiwan} financial market},
	volume = {477},
	issn = {0378-4371},
	url = {http://www.sciencedirect.com/science/article/pii/S0378437117301978},
	doi = {10.1016/j.physa.2017.02.043},
	abstract = {Empirical analysis of the price fluctuations of financial markets has received extensive attention because a substantial amount of financial market data has been collected and because of advances in data-mining techniques. Price fluctuation trends can help investors to make informed trading decisions, but such decisions may also be affected by a psychological factors—the anchoring effect. This study explores the intraday price time series of Taiwan futures, and applies diffusion model and quantitative methods to analyze the relationship between the anchoring effect and price fluctuations during first passage process. Our results indicate that power-law scaling and anomalous diffusion for stock price fluctuations are related to the anchoring effect. Moreover, microscopic price fluctuations before switching point in first passage process correspond with long-term price fluctuations of Taiwan’s stock market. We find that microscopic trends could provide useful information for understanding macroscopic trends in stock markets.},
	language = {en},
	urldate = {2021-01-06},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Liu, Hsing and Liao, Chi-Yo and Ko, Jing-Yuan and Lih, Jiann-Shing},
	month = jul,
	year = {2017},
	keywords = {Anchoring effect, Anomalous diffusion, First passage process, First return time, Switching point},
	pages = {114--127},
	file = {ScienceDirect Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\ARVMQX4L\\Liu et al. - 2017 - Anchoring effect on first passage process in Taiwa.pdf:application/pdf;ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\CP63RJ6N\\S0378437117301978.html:text/html},
}

@article{ursino_mathematical_1989,
	title = {A mathematical model of cerebral blood flow chemical regulation. {I}. {Diffusion} processes},
	volume = {36},
	issn = {1558-2531},
	doi = {10.1109/10.16465},
	abstract = {A mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat is presented. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. The model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel contains equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen and their diffusion towards pial perivascular space. The equations have been used to simulate the time dynamics of mean tissue P/sub O2/, perivascular adenosine concentration, and perivascular pH following changes in CBF. The simulation shows that the time delay introduced by diffusion processes is negligible compared with the other time constants of the system under study.{\textless}{\textgreater}},
	number = {2},
	journal = {IEEE Transactions on Biomedical Engineering},
	author = {Ursino, M. and Giammarco, P. Di and Belardinelli, E.},
	month = feb,
	year = {1989},
	note = {Conference Name: IEEE Transactions on Biomedical Engineering},
	keywords = {Animals, biodiffusion, Blood flow, Brain Ischemia, brain models, capillary blood, cerebral blood flow chemical regulation, Cerebrovascular Circulation, Chemical products, Delay effects, Differential equations, Diffusion, diffusion processes, Diffusion processes, haemodynamics, hyperbolic functions, Laplace equations, Laplace transform domain, mathematical model, Mathematical model, Mathematics, Models, Biological, Models, Cardiovascular, O/sub 2/ dependent cerebral blood flow regulation, Oxygen Consumption, partial differential equations, Partial differential equations, perivascular adenosine concentration, Production, rat, Rats, vasoactive chemical factors, vasoactive metabolites},
	pages = {183--191},
	file = {IEEE Xplore Abstract Record:C\:\\Users\\centrifuge\\Zotero\\storage\\L66J7CYJ\\16465.html:text/html},
}

@article{zhang_lattice_2019,
	title = {Lattice {Boltzmann} simulation of advection-diffusion of chemicals and applications to blood flow},
	volume = {187},
	issn = {0045-7930},
	url = {http://www.sciencedirect.com/science/article/pii/S004579301930132X},
	doi = {10.1016/j.compfluid.2019.04.018},
	abstract = {Diffusion of solutes is often encountered in many biological processes. In the blood micro circulation system, solutes, such as oxygen and calcium molecules, as well as Adenosine Triphosphate (ATP) and biochemical messengers, are released by cells (like red blood and endothelial cells), and are dispersed via diffusion and advection. Moreover, several targeted drug delivery strategies rely on an encapsulation of chemicals and on their release in the blood stream at specific location. The released chemicals couple to blood flow, in which red blood cells (RBCs) constitute the major component. Thus, the development of numerical methods which take into account both dynamics of RBCs and their coupling with chemicals is of great importance for many biomedical applications. We develop here a lattice-Boltzmann based method that deals with generic moving boundary conditions in an advection-diffusion field representing the chemicals. The boundary condition of the solutes at the cell membrane is based on a modified bounce-back scheme. We prove analytically, and validate numerically, that it enjoys second order precision. The solver is validated with several benchmarks and is then coupled with a solver for a suspension of RBCs, we developed previously. We then exemplify the method on the problem of liposome drug delivery in arterioles. The results show that for a rigid drug carrier at a scale of about 1 μm, the presence of RBCs facilitates the drug absorption along the vessel wall. We also exemplify the solver for the release of chemicals induced by membrane shear stress, a feature which is omnipresent in mechano-involved signaling processes. As a way of example, we briefly study the problem of ATP release by RBCs. We point out several possible generalizations.},
	language = {en},
	urldate = {2021-01-06},
	journal = {Computers \& Fluids},
	author = {Zhang, Hengdi and Misbah, Chaouqi},
	month = jun,
	year = {2019},
	keywords = {Blood flow, Chemical signaling, Lattice boltzmann},
	pages = {46--59},
	file = {ScienceDirect Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\XU7NM67N\\Zhang and Misbah - 2019 - Lattice Boltzmann simulation of advection-diffusio.pdf:application/pdf;ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\DC4K8HY3\\S004579301930132X.html:text/html},
}

@article{nicholson_extracellular_1998,
	title = {Extracellular space structure revealed by diffusion analysis},
	volume = {21},
	issn = {0166-2236},
	url = {http://www.sciencedirect.com/science/article/pii/S0166223698012612},
	doi = {10.1016/S0166-2236(98)01261-2},
	abstract = {The structure of brain extracellular space resembles foam. Diffusing molecules execute random movements that cause their collision with membranes and affect their concentration distribution. By measuring this distribution, the volume fraction (α) and the tortuosity (λ) can be estimated. The volume fraction indicates the relative amount of extracellular space and tortuosity is a measure of hindrance of cellular obstructions. Diffusion measurements with molecules {\textless}500 Mr show that α ≈0.2 and λ ≈1.6, although some brain regions are anisotropic. Molecules ≥3000 Mr show more hindrance, but molecules of 70000 Mr can move through the extracellular space. During stimulation, and in pathophysiological states, α and λ change, for example in severe ischemia α = 0.04 and λ = 2.2. These data support the feasibility of extrasynaptic or volume transmission in the extracellular space.},
	language = {en},
	number = {5},
	urldate = {2021-01-05},
	journal = {Trends in Neurosciences},
	author = {Nicholson, Charles and Syková, Eva},
	month = may,
	year = {1998},
	pages = {207--215},
	file = {ScienceDirect Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\HH68ESCP\\Nicholson and Syková - 1998 - Extracellular space structure revealed by diffusio.pdf:application/pdf;ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\VWP88HCW\\S0166223698012612.html:text/html},
}

@article{low_diffusion-weighted_2007,
	title = {Diffusion-weighted {MRI} ({DWI}) in the oncology patient: value of breathhold {DWI} compared to unenhanced and gadolinium-enhanced {MRI}},
	volume = {25},
	issn = {1053-1807},
	shorttitle = {Diffusion-weighted {MRI} ({DWI}) in the oncology patient},
	doi = {10.1002/jmri.20864},
	abstract = {PURPOSE: To evaluate the feasibility and added value of single breathhold diffusion-weighted (DW) imaging (DWI) in oncology patients undergoing abdominal MRI.
MATERIALS AND METHODS: A total of 169 patients with malignancy underwent abdominal MRI at 1.5T, including T1-weighted (T1W), T2-weighted (T2W), and dynamic gadolinium-enhanced imaging. Axial DWI was performed with a single-shot spin-echo (SE) echo-planar imaging (EPI) sequence using a b-value of 500 seconds/mm2. A total of 24 slices were obtained during a 20-second breathhold. Two observers reviewed the conventional MR images for tumor. Next, the DW images were reviewed for additional tumor not depicted on conventional MR images
RESULTS: For the 169 patients, additional tumors were noted on the DW images in 77 (0.46) for observer 1 and 67 (0.40) for observer 2. For observer 1 the additional tumor included lymphadenopathy (47), peritoneal metastases (15), renal (1), liver (12), and osseous (2), while for observer 2 the corresponding values were lymphadenopathy (40), peritoneal (12), renal (1), liver (6), osseous (4), and gastrointestinal (1). The DW images resolved as benign findings noted on the conventional MR images in three patients for observer 1 and four patients for observer 2. The conventional MR exam was entirely normal while the DW images showed tumor in 12 (0.07) patients for observer 1 and 10 (0.06) patients for observer 2.
CONCLUSION: DWI is feasible in a single breathhold and provides additional clinically important information in oncology patients when added to routine abdominal MR sequences.},
	language = {eng},
	number = {4},
	journal = {Journal of magnetic resonance imaging: JMRI},
	author = {Low, Russell N. and Gurney, Jonathan},
	month = apr,
	year = {2007},
	pmid = {17335018},
	keywords = {Humans, Abdominal Neoplasms, Contrast Media, Diffusion Magnetic Resonance Imaging, Feasibility Studies, Female, Gadolinium, Lymphoma, Male, Middle Aged, Retrospective Studies},
	pages = {848--858},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\ZU9LW5NF\\Low and Gurney - 2007 - Diffusion-weighted MRI (DWI) in the oncology patie.pdf:application/pdf},
}

@article{le_bihan_mr_1986,
	title = {{MR} imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders.},
	volume = {161},
	issn = {0033-8419},
	shorttitle = {{MR} imaging of intravoxel incoherent motions},
	url = {https://pubs.rsna.org/doi/10.1148/radiology.161.2.3763909},
	doi = {10.1148/radiology.161.2.3763909},
	abstract = {Molecular diffusion and microcirculation in the capillary network result in a distribution of phases in a single voxel in the presence of magnetic field gradients. This distribution produces a spin-echo attenuation. The authors have developed a magnetic resonance (MR) method to image such intravoxel incoherent motions (IVIMs) by using appropriate gradient pulses. Images were generated at 0.5 T in a high-resolution, multisection mode. Diffusion coefficients measured on images of water and acetone phantoms were consistent with published values. Images obtained in the neurologic area from healthy subjects and patients were analyzed in terms of an apparent diffusion coefficient (ADC) incorporating the effect of all IVIMs. Differences were found between various normal and pathologic tissues. The ADC of in vivo water differed from the diffusion coefficient of pure water. Results were assessed in relation to water compartmentation in biologic tissues (restricted diffusion) and tissue perfusion. Nonuniform slow flow of cerebrospinal fluid appeared as a useful feature on IVIM images. Observation of these motions may significantly extend the diagnostic capabilities of MR imaging.},
	number = {2},
	urldate = {2021-01-05},
	journal = {Radiology},
	author = {Le Bihan, D and Breton, E and Lallemand, D and Grenier, P and Cabanis, E and Laval-Jeantet, M},
	month = nov,
	year = {1986},
	note = {Publisher: Radiological Society of North America},
	pages = {401--407},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\RVMJLIGC\\radiology.161.2.html:text/html;Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\VAMNTSBN\\Le Bihan et al. - 1986 - MR imaging of intravoxel incoherent motions appli.pdf:application/pdf},
}

@article{wijman_prognostic_2009,
	title = {Prognostic value of brain diffusion-weighted imaging after cardiac arrest},
	volume = {65},
	issn = {1531-8249},
	doi = {10.1002/ana.21632},
	abstract = {OBJECTIVE: Outcome prediction is challenging in comatose postcardiac arrest survivors. We assessed the feasibility and prognostic utility of brain diffusion-weighted magnetic resonance imaging (DWI) during the first week.
METHODS: Consecutive comatose postcardiac arrest patients were prospectively enrolled. AWI data of patients who met predefined specific prognostic criteria were used to determine distinguishing apparent diffusion coefficient (ADC) thresholds. Group 1 criteria were death at 6 months and absent motor response or absent pupillary reflexes or bilateral absent cortical responses at 72 hours or vegetative at 1 month. Group 2 criterion was survival at 6 months with a Glasgow Outcome Scale score of 4 or 5 (group 2A) or 3 (group 2B). The percentage of voxels below different ADC thresholds was calculated at 50 x 10(-6) mm(2)/sec intervals.
RESULTS: Overall, 86\% of patients underwent DWI. Fifty-one patients with 62 brain DWIs were included. Forty patients met the specific prognostic criteria. The percentage of brain volume with an ADC value less than 650 to 700 x 10(-6)mm(2)/sec best differentiated between Group 1 and Groups 2A and 2B combined (p {\textless} 0.001), whereas the 400 to 450 x 10(-6)mm(2)/sec threshold best differentiated between Groups 2A and 2B (p = 0.003). The ideal time window for prognostication using DWI was between 49 and 108 hours after the arrest. When comparing DWI in this time window with the 72-hour neurological examination, DWI improved the sensitivity for predicting poor outcome by 38\% while maintaining 100\% specificity (p = 0.021).
INTERPRETATION: Quantitative DWI in comatose postcardiac arrest survivors holds promise as a prognostic adjunct.},
	language = {eng},
	number = {4},
	journal = {Annals of Neurology},
	author = {Wijman, Christine A. C. and Mlynash, Michael and Caulfield, Anna Finley and Hsia, Amie W. and Eyngorn, Irina and Bammer, Roland and Fischbein, Nancy and Albers, Gregory W. and Moseley, Michael},
	month = apr,
	year = {2009},
	pmid = {19399889},
	pmcid = {PMC2677115},
	keywords = {Time Factors, Humans, Diffusion Magnetic Resonance Imaging, Feasibility Studies, Female, Male, Middle Aged, Adult, Aged, Brain, Brain Mapping, Disease Progression, Heart Arrest, Image Processing, Computer-Assisted, Neurologic Examination, Predictive Value of Tests, Prognosis, Prospective Studies, Statistics, Nonparametric, Young Adult},
	pages = {394--402},
	file = {Accepted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\JFTMB8B7\\Wijman et al. - 2009 - Prognostic value of brain diffusion-weighted imagi.pdf:application/pdf},
}

@article{han_assessment_2015,
	title = {Assessment of apparent diffusion coefficient of normal fetal brain development from gestational age week 24 up to term age: a preliminary study},
	volume = {37},
	issn = {1421-9964},
	shorttitle = {Assessment of apparent diffusion coefficient of normal fetal brain development from gestational age week 24 up to term age},
	doi = {10.1159/000363650},
	abstract = {OBJECTIVES: This study was designed to investigate the feasibility of apparent diffusion coefficient (ADC) values in evaluating normal fetal brain development from gestational week 24 up to term age.
METHODS: Diffusion-weighted imaging (DWI) was performed on 40 normal fetuses (with normal results on sonography and normal fetal MRI results), with two b-values of 0 and 600 s/mm² in the three (x, y, z) orthogonal axes. Ten regions of interest (ROIs) were manually placed symmetrically in the bilateral frontal white matter (FWM), occipital white matter (OWM), thalamus (THAL), basal ganglia (BG), and cerebellar hemispheres (CH). ADC values of the ten ROIs in all subjects were measured by two radiologists independently. One-way ANOVA was used to calculate the differences among the five regions in the fetal brain and linear regression analysis was used to evaluate the correlation between ADC values and gestational age (GA). p {\textless} 0.05 was considered significantly different.
RESULTS: Mean GA was 31.3 ± 3.9 (range 24-41) weeks. The overall mean ADC values (× 10⁻⁶ mm²/s) of the fetuses were 1,800 ± 214 (FWM), 1,400 ± 100 (BG), 1,300 ± 126 (THAL), 1,700 ± 133 (OWM) and 1,400 ± 155 (CH), respectively. The ADC value of BG was not significantly different from those of THAL and CH, while the other four ROIs had significant differences with each other. The ADC values of BG, THAL, OWM and CH had strong negative correlations with increasing GA (R were -0.568, -0.716, -0.830 and -0.700, respectively, all p {\textless} 0.01), OWM declined fastest with GA, followed by CH and THAL, the slowest being BG. The ADC value of FWM had no significant change with GA (p = 0.366).
CONCLUSIONS: The measurement of ADC values is feasible to evaluate fetal brain development with high reliability and reproducibility.},
	language = {eng},
	number = {2},
	journal = {Fetal Diagnosis and Therapy},
	author = {Han, Rui and Huang, Lu and Sun, Ziyan and Zhang, Dongyou and Chen, Xinlin and Yang, Xiaohong and Cao, Zhongqiang},
	year = {2015},
	pmid = {25095737},
	keywords = {Humans, Diffusion Magnetic Resonance Imaging, Female, Brain, Fetal Development, Fetal Organ Maturity, Gestational Age, Pregnancy},
	pages = {102--107},
}

@article{abdel_razek_apparent_2019,
	title = {Apparent {Diffusion} {Coefficient} of the {Placenta} and {Fetal} {Organs} in {Intrauterine} {Growth} {Restriction}},
	volume = {43},
	issn = {0363-8715},
	url = {https://journals.lww.com/jcat/Abstract/2019/05000/Apparent_Diffusion_Coefficient_of_the_Placenta_and.23.aspx},
	doi = {10.1097/RCT.0000000000000844},
	abstract = {Purpose 
        This study aimed to assess apparent diffusion coefficient (ADC) of the placenta and fetal organs in intrauterine growth restriction (IUGR).
        Materials and methods 
        A prospective study of 30 consecutive pregnant women (aged 21–38 years with mean age of 31.5 years and a mean gestational week of 35 ± 2.3) with IUGR and 15 age-matched pregnant women was conducted. All patients and controls underwent diffusion-weighted magnetic resonance imaging. The ADCs of the placenta and fetal brain, kidney, and lung were calculated and correlated with neonates needing intensive care unit (ICU) admission.
        Results 
        There was a significant difference in ADC of the placenta and fetal brain, lung, and kidney (P = 0.001, 0.001, 0.04, and 0.04, respectively) between the patients and the controls. The cutoff ADCs of the placenta and fetal brain, lung, and kidney used to detect IUGR were 1.45, 1.15, 1.80, and 1.40 × 10−3 mm2/s, respectively, with areas under the curve (AUCs) of 0.865, 0.858, 0.812, and 0.650, respectively, and accuracy values of 75\%, 72.5\%, 72.5\%, and 70\%, respectively. Combined ADC of the placenta and fetal organs used to detect IUGR revealed an AUC of 1.00 and an accuracy of 100\%. There was a significant difference in ADC of the placenta and fetal brain, lung, and kidney between neonates needing admission and those not needing ICU admission (P = 0.001, 0.001, 0.002, and 0.002, respectively). The cutoff ADCs of the placenta and fetal brain, lung, and kidney used to define neonates needing ICU were 1.35, 1.25, 1.95, and 1.15 × 10−3 mm2/s with AUCs of 0.955, 0.880, 0.884, and 0.793, respectively, and accuracy values of 86.7\%, 46.7\%, 76.7\%, and 70\%, respectively. Combined placental and fetal brain ADC used to define neonates needing ICU revealed an AUC of 0.968 and an accuracy of 93.3\%.
        Conclusion 
        Combined ADC of the placenta and fetal organs can detect IUGR, and combined ADC of the placenta and fetal brain can define fetuses needing ICU.},
	language = {en-US},
	number = {3},
	urldate = {2021-01-04},
	journal = {Journal of Computer Assisted Tomography},
	author = {Abdel Razek, Ahmed Abdel Khalek and Thabet, Mahmoud and Salam, Eman Abdel},
	month = jun,
	year = {2019},
	pages = {507--512},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\5LEH8ZIZ\\Apparent_Diffusion_Coefficient_of_the_Placenta_and.23.html:text/html},
}

@article{le_bihan_diffusion_2014,
	title = {Diffusion {MRI}: what water tells us about the brain},
	volume = {6},
	issn = {1757-4676},
	shorttitle = {Diffusion {MRI}},
	url = {https://www.embopress.org/doi/full/10.1002/emmm.201404055},
	doi = {10.1002/emmm.201404055},
	abstract = {Diffusion MRI has been used worldwide to produce images of brain tissue structure and connectivity, in the normal and diseased brain. Diffusion MRI has revolutionized the management of acute brain ischemia (stroke), saving life of many patients and sparing them significant disabilities. In addition to stroke, diffusion MRI is now widely used for the detection of cancers and metastases (breast, prostate, liver). Another major field of application of diffusion MRI regards the wiring of the brain. Diffusion MRI is now used to map the circuitry of the human brain with incredible accuracy, opening up new lines of inquiry for human neuroscience and for the understanding of brain illnesses or mental disorders. Here, as a pioneer of the field, I provide a personal account on the historical development of these concepts over the last 30 years.},
	number = {5},
	urldate = {2021-01-04},
	journal = {EMBO Molecular Medicine},
	author = {Le Bihan, Denis},
	month = may,
	year = {2014},
	note = {Publisher: John Wiley \& Sons, Ltd},
	pages = {569--573},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\69YQTMYT\\Le Bihan - 2014 - Diffusion MRI what water tells us about the brain.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\VNKAEZHQ\\emmm.html:text/html;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\BHVW2IAP\\emmm.html:text/html},
}

@article{perrin_mouvement_1909,
	title = {Le {Mouvement} {Brownien} et la {Réalité} {Moleculaire}},
	volume = {18},
	number = {8},
	journal = {Ann. Chimi. Phys.},
	author = {Perrin, Jean Baptiste},
	year = {1909},
	keywords = {Humanities and Social Sciences, multidisciplinary, Science},
	pages = {5--114},
	file = {R. - 1911 - Brownian Movement and Molecular Reality:C\:\\Users\\centrifuge\\Zotero\\storage\\G77FC7HG\\R. - 1911 - Brownian Movement and Molecular Reality.pdf:application/pdf},
}

@article{schrodinger_zur_1915,
	title = {Zur theorie der fall-und steigversuche an teilchen mit brownscher bewegung},
	volume = {16},
	journal = {Physikalische Zeitschrift},
	author = {Schrödinger, Erwin},
	year = {1915},
	pages = {289--295},
}

@article{fick_v_1855,
	title = {V. {On} liquid diffusion},
	volume = {10},
	doi = {10.1080/14786445508641925},
	abstract = {This is an english abstracted version of the article in Annalen der Physik},
	number = {63},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Fick, Adolph},
	month = jul,
	year = {1855},
	pages = {30--39},
}

@article{barraquand_random-walk_2017,
	title = {Random-walk in {Beta}-distributed random environment},
	volume = {167},
	issn = {0178-8051, 1432-2064},
	url = {https://link.springer.com/article/10.1007/s00440-016-0699-z},
	doi = {10.1007/s00440-016-0699-z},
	abstract = {We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in ℤZ{\textbackslash}mathbb \{Z\} which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker’s position, we are able to prove second order cube-root scale corrections to the large deviation principle satisfied by the walker’s position, with convergence to the Tracy–Widom distribution. We also show that this limit theorem can be interpreted in terms of the maximum of strongly correlated random variables: the positions of independent walkers in the same environment. The zero-temperature counterpart of the Beta RWRE can be studied in a parallel way. We also prove a Tracy–Widom limit theorem for this model.},
	language = {en},
	number = {3-4},
	urldate = {2017-10-19},
	journal = {Probability Theory and Related Fields},
	author = {Barraquand, Guillaume and Corwin, Ivan},
	month = apr,
	year = {2017},
	pages = {1057--1116},
}

@article{gordon_single-molecule_2004,
	title = {Single-molecule high-resolution imaging with photobleaching},
	volume = {101},
	issn = {0027-8424},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC404067/},
	doi = {10.1073/pnas.0401638101},
	abstract = {Conventional light microscopy is limited in its resolving power by the Rayleigh limit to length scales on the order of 200 nm. On the other hand, spectroscopic techniques such as fluorescence resonance energy transfer cannot be used to measure distances {\textgreater}10 nm, leaving a “gap” in the ability of optical techniques to measure distances on the 10- to 100-nm scale. We have previously demonstrated the ability to localize single dye molecules to a precision of 1.5 nm with subsecond time resolution. Here we locate the position of two dyes and determine their separation with 5-nm precision, using the quantal photobleaching behavior of single fluorescent dye molecules. By fitting images both before and after photobleaching of one of the dyes, we may localize both dyes simultaneously and compute their separation. Hence, we have circumvented the Rayleigh limit and achieved nanometer-scale resolution. Specifically, we demonstrate the technique by measuring the distance between single fluorophores separated by 10–20 nm via attachment to the ends of double-stranded DNA molecules immobilized on a surface. In addition to bridging the gap in optical resolution, this technique may be useful for biophysical or genomic applications, including the generation of super-high-density maps of single-nucleotide polymorphisms.},
	number = {17},
	urldate = {2018-10-29},
	journal = {Proceedings of the National Academy of Sciences of the United States of America},
	author = {Gordon, Matthew P. and Ha, Taekjip and Selvin, Paul R.},
	month = apr,
	year = {2004},
	pmid = {15096603},
	pmcid = {PMC404067},
	pages = {6462--6465},
}

@article{diekmann_characterization_2017,
	title = {Characterization of an industry-grade {CMOS} camera well suited for single molecule localization microscopy – high performance super-resolution at low cost},
	volume = {7},
	copyright = {2017 The Author(s)},
	issn = {2045-2322},
	url = {https://www.nature.com/articles/s41598-017-14762-6},
	doi = {10.1038/s41598-017-14762-6},
	abstract = {Many commercial as well as custom-built fluorescence microscopes use scientific-grade cameras that represent a substantial share of the instrument’s cost. This holds particularly true for super-resolution localization microscopy where high demands are placed especially on the detector with respect to sensitivity, noise, and also image acquisition speed. Here, we present and carefully characterize an industry-grade CMOS camera as a cost-efficient alternative to commonly used scientific cameras. Direct experimental comparison of these two detector types shows widely similar performance for imaging by single molecule localization microscopy (SMLM). Furthermore, high image acquisition speeds are demonstrated for the CMOS detector by ultra-fast SMLM imaging.},
	language = {En},
	number = {1},
	urldate = {2017-10-31},
	journal = {Scientific Reports},
	author = {Diekmann, Robin and Till, Katharina and Müller, Marcel and Simonis, Matthias and Schüttpelz, Mark and Huser, Thomas},
	month = oct,
	year = {2017},
	pages = {14425},
}

@article{holm_blueprint_2014,
	title = {A {Blueprint} for {Cost}-{Efficient} {Localization} {Microscopy}},
	volume = {15},
	issn = {1439-7641},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/cphc.201300739/abstract},
	doi = {10.1002/cphc.201300739},
	language = {en},
	number = {4},
	urldate = {2017-10-31},
	journal = {ChemPhysChem},
	author = {Holm, Thorge and Klein, Teresa and Löschberger, Anna and Klamp, Tobias and Wiebusch, Gerd and van de Linde, Sebastian and Sauer, Markus},
	month = mar,
	year = {2014},
	keywords = {cost-efficiency, fluorescence, laser spectroscopy, localization microscopy, super-resolution imaging},
	pages = {651--654},
}

@article{ma_simple_2017,
	title = {A simple and cost-effective setup for super-resolution localization microscopy},
	volume = {7},
	copyright = {2017 The Author(s)},
	issn = {2045-2322},
	url = {https://www.nature.com/articles/s41598-017-01606-6},
	doi = {10.1038/s41598-017-01606-6},
	abstract = {Single molecule localization microscopy (SMLM) has become a powerful imaging tool for biomedical research, but it is mostly available in imaging facilities and a small number of laboratories due to its high cost. Here, we evaluate the possibility of replacing high-cost components on standard SMLM with appropriate low-cost alternatives and build a simple but high-performance super-resolution SMLM setup. Through numerical simulation and biological experiments, we demonstrate that our low-cost SMLM setup can yield similar localization precision and spatial resolution compared to the standard SMLM equipped with state-of-the-art components, but at a small fraction of their cost. Our low-cost SMLM setup can potentially serve as a routine laboratory microscope with high-performance super-resolution imaging capability.},
	language = {En},
	number = {1},
	urldate = {2017-10-31},
	journal = {Scientific Reports},
	author = {Ma, Hongqiang and Fu, Rao and Xu, Jianquan and Liu, Yang},
	month = may,
	year = {2017},
	pages = {1542},
}

@article{zhen_live-cell_2016,
	title = {Live-cell single-molecule tracking reveals co-recognition of {H3K27me3} and {DNA} targets polycomb {Cbx7}-{PRC1} to chromatin},
	volume = {5},
	issn = {2050-084X},
	url = {https://doi.org/10.7554/eLife.17667},
	doi = {10.7554/eLife.17667},
	abstract = {The Polycomb PRC1 plays essential roles in development and disease pathogenesis. Targeting of PRC1 to chromatin is thought to be mediated by the Cbx family proteins (Cbx2/4/6/7/8) binding to histone H3 with a K27me3 modification (H3K27me3). Despite this prevailing view, the molecular mechanisms of targeting remain poorly understood. Here, by combining live-cell single-molecule tracking (SMT) and genetic engineering, we reveal that H3K27me3 contributes significantly to the targeting of Cbx7 and Cbx8 to chromatin, but less to Cbx2, Cbx4, and Cbx6. Genetic disruption of the complex formation of PRC1 facilitates the targeting of Cbx7 to chromatin. Biochemical analyses uncover that the CD and AT-hook-like (ATL) motif of Cbx7 constitute a functional DNA-binding unit. Live-cell SMT of Cbx7 mutants demonstrates that Cbx7 is targeted to chromatin by co-recognizing of H3K27me3 and DNA. Our data suggest a novel hierarchical cooperation mechanism by which histone modifications and DNA coordinate to target chromatin regulatory complexes.},
	urldate = {2018-10-29},
	journal = {eLife},
	author = {Zhen, Chao Yu and Tatavosian, Roubina and Huynh, Thao Ngoc and Duc, Huy Nguyen and Das, Raibatak and Kokotovic, Marko and Grimm, Jonathan B and Lavis, Luke D and Lee, Jun and Mejia, Frances J and Li, Yang and Yao, Tingting and Ren, Xiaojun},
	editor = {Workman, Jerry L},
	month = oct,
	year = {2016},
	keywords = {chromatin, combinatorial recognition, Epigenetics, live-cell imaging, Polycomb, single-molecule tracking},
	pages = {e17667},
}

@article{barraquand_moderate_2020,
	title = {Moderate deviations for diffusion in time dependent random media},
	volume = {53},
	issn = {1751-8121},
	url = {https://doi.org/10.1088%2F1751-8121%2Fab8b39},
	doi = {10.1088/1751-8121/ab8b39},
	abstract = {The position x(t) of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray x = v 0 t, where v 0 is the average drift. However, it has been found that it exhibits at large time sample to sample fluctuations characteristic of the Kardar–Parisi–Zhang (KPZ) universality class when observed in an atypical direction, i.e. along the ray x = v t with v ≠ v 0. Here we show, from exact solutions, that in the moderate deviation regime x − v 0 t ∝ t 3/4 these fluctuations are precisely described by the finite time KPZ equation, which thus describes the crossover between the Gaussian typical regime and the KPZ fixed point regime for the large deviations. This confirms heuristic arguments given in [2]. These exact results include the discrete model known as the Beta random walk in a time dependent random environment, and a continuum diffusion. They predict the behavior of the maximum of a large number of independent walkers, which should be easier to observe (e.g. in experiments) in this moderate deviations regime.},
	language = {en},
	number = {21},
	urldate = {2020-08-04},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Barraquand, Guillaume and Doussal, Pierre Le},
	month = may,
	year = {2020},
	note = {Publisher: IOP Publishing},
	pages = {215002},
}

@article{kardar_dynamic_1986,
	title = {Dynamic {Scaling} of {Growing} {Interfaces}},
	volume = {56},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.56.889},
	doi = {10.1103/PhysRevLett.56.889},
	abstract = {A model is proposed for the evolution of the profile of a growing interface. The deterministic growth is solved exactly, and exhibits nontrivial relaxation patterns. The stochastic version is studied by dynamic renormalization-group techniques and by mappings to Burgers's equation and to a random directed-polymer problem. The exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations. Predictions are made for more dimensions.},
	number = {9},
	urldate = {2020-08-08},
	journal = {Physical Review Letters},
	author = {Kardar, Mehran and Parisi, Giorgio and Zhang, Yi-Cheng},
	month = mar,
	year = {1986},
	note = {Publisher: American Physical Society},
	pages = {889--892},
}

@article{grebenkov_exact_2020,
	title = {Exact first-passage time distributions for three random diffusivity models},
	url = {http://arxiv.org/abs/2007.05765},
	abstract = {We study the extremal properties of a stochastic process \$x\_t\$ defined by a Langevin equation \${\textbackslash}dot\{x\}\_t={\textbackslash}sqrt\{2 D\_0 V(B\_t)\}{\textbackslash},{\textbackslash}xi\_t\$, where \${\textbackslash}xi\_t\$ is a Gaussian white noise with zero mean, \$D\_0\$ is a constant scale factor, and \$V(B\_t)\$ is a stochastic "diffusivity" (noise strength), which itself is a functional of independent Brownian motion \$B\_t\$. We derive exact, compact expressions for the probability density functions (PDFs) of the first passage time (FPT) \$t\$ from a fixed location \$x\_0\$ to the origin for three different realisations of the stochastic diffusivity: a cut-off case \$V(B\_t) ={\textbackslash}Theta(B\_t)\$ (Model I), where \${\textbackslash}Theta(x)\$ is the Heaviside theta function; a Geometric Brownian Motion \$V(B\_t)={\textbackslash}exp(B\_t)\$ (Model II); and a case with \$V(B\_t)=B\_t{\textasciicircum}2\$ (Model III). We realise that, rather surprisingly, the FPT PDF has exactly the L{\textbackslash}'evy-Smirnov form (specific for standard Brownian motion) for Model II, which concurrently exhibits a strongly anomalous diffusion. For Models I and III either the left or right tails (or both) have a different functional dependence on time as compared to the L{\textbackslash}'evy-Smirnov density. In all cases, the PDFs are broad such that already the first moment does not exist. Similar results are obtained in three dimensions for the FPT PDF to an absorbing spherical target.},
	urldate = {2020-08-04},
	journal = {arXiv:2007.05765 [cond-mat, physics:physics]},
	author = {Grebenkov, D. S. and Sposini, V. and Metzler, R. and Oshanin, G. and Seno, F.},
	month = jul,
	year = {2020},
	note = {arXiv: 2007.05765},
	keywords = {Condensed Matter - Statistical Mechanics, Physics - Biological Physics},
}

@article{ramaswamy_mechanics_2010,
	title = {The {Mechanics} and {Statistics} of {Active} {Matter}},
	volume = {1},
	url = {https://doi.org/10.1146/annurev-conmatphys-070909-104101},
	doi = {10.1146/annurev-conmatphys-070909-104101},
	abstract = {Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles–active matter–with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.},
	number = {1},
	urldate = {2020-08-07},
	journal = {Annual Review of Condensed Matter Physics},
	author = {Ramaswamy, Sriram},
	year = {2010},
	note = {\_eprint: https://doi.org/10.1146/annurev-conmatphys-070909-104101},
	pages = {323--345},
}

@article{kanazawa_loopy_2020,
	title = {Loopy {Lévy} flights enhance tracer diffusion in active suspensions},
	volume = {579},
	copyright = {2020 The Author(s), under exclusive licence to Springer Nature Limited},
	issn = {1476-4687},
	url = {https://www.nature.com/articles/s41586-020-2086-2},
	doi = {10.1038/s41586-020-2086-2},
	abstract = {Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3–10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15.},
	language = {en},
	number = {7799},
	urldate = {2020-08-04},
	journal = {Nature},
	author = {Kanazawa, Kiyoshi and Sano, Tomohiko G. and Cairoli, Andrea and Baule, Adrian},
	month = mar,
	year = {2020},
	note = {Number: 7799
Publisher: Nature Publishing Group},
	pages = {364--367},
}

@article{thiery_exact_2017,
	title = {Exact solution for a random walk in a time-dependent {1D} random environment: the point-to-point {Beta} polymer},
	volume = {50},
	issn = {1751-8121},
	shorttitle = {Exact solution for a random walk in a time-dependent {1D} random environment},
	url = {http://stacks.iop.org/1751-8121/50/i=4/a=045001},
	doi = {10.1088/1751-8121/50/4/045001},
	abstract = {We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin (BC) (2016 Probab. Theory Relat. Fields 1 [http://dx.doi.org/10.1007/s00440-016-0699-z] – 16 [http://dx.doi.org/10.1007/s00440-016-0699-z] ). We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a random walk in a time-dependent (and in general biased) 1D random environment. In this formulation, we study the sample to sample fluctuations of the transition probability distribution function (PDF) of the random walk. Using the Bethe ansatz we obtain exact formulas for the integer moments, and Fredholm determinant formulas for the Laplace transform of the directed polymer partition sum/random walk transition probability. The asymptotic analysis of these formulas at large time t is performed both (i) in a diffusive vicinity, \#\#IMG\#\# [http://ej.iop.org/images/1751-8121/50/4/045001/aaa50a0ieqn003.gif] \$x{\textbackslash}sim t{\textasciicircum}1/2\$ , of the optimal direction (in space-time) chosen by the random walk, where the fluctuations of the PDF are found to be Gamma distributed; (ii) in the large deviations regime, \#\#IMG\#\# [http://ej.iop.org/images/1751-8121/50/4/045001/aaa50a0ieqn004.gif] \$x{\textbackslash}sim t\$ , of the random walk, where the fluctuations of the logarithm of the PDF are found to grow with time as t 1/3 and to be distributed according to the Tracy–Widom GUE distribution. Our exact results complement those of BC for the cumulative distribution function of the random walk in regime (ii), and in regime (i) they unveil a novel fluctuation behavior. We also discuss the crossover regime between (i) and (ii), identified as \#\#IMG\#\# [http://ej.iop.org/images/1751-8121/50/4/045001/aaa50a0ieqn005.gif] \$x{\textbackslash}sim t{\textasciicircum}3/4\$ . Our results are confronted to extensive numerical simulations of the model.},
	language = {en},
	number = {4},
	urldate = {2017-10-19},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Thiery, Thimothée and Doussal, Pierre Le},
	year = {2017},
	pages = {045001},
}

@article{hufnagel_forecast_2004,
	title = {Forecast and control of epidemics in a globalized world},
	volume = {101},
	copyright = {Copyright © 2004, The National Academy of Sciences},
	issn = {0027-8424, 1091-6490},
	url = {https://www.pnas.org/content/101/42/15124},
	doi = {10.1073/pnas.0308344101},
	abstract = {The rapid worldwide spread of severe acute respiratory syndrome demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model that describes the worldwide spread of infectious diseases and demonstrate that a forecast of the geographical spread of epidemics is indeed possible. This model combines a stochastic local infection dynamics among individuals with stochastic transport in a worldwide network, taking into account national and international civil aviation traffic. Our simulations of the severe acute respiratory syndrome outbreak are in surprisingly good agreement with published case reports. We show that the high degree of predictability is caused by the strong heterogeneity of the network. Our model can be used to predict the worldwide spread of future infectious diseases and to identify endangered regions in advance. The performance of different control strategies is analyzed, and our simulations show that a quick and focused reaction is essential to inhibiting the global spread of epidemics.},
	language = {en},
	number = {42},
	urldate = {2020-08-06},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Hufnagel, L. and Brockmann, D. and Geisel, T.},
	month = oct,
	year = {2004},
	pmid = {15477600},
	note = {Publisher: National Academy of Sciences
Section: Biological Sciences},
	pages = {15124--15129},
}

@article{gonzalez_understanding_2008,
	title = {Understanding individual human mobility patterns},
	volume = {453},
	url = {https://www.nature.com/articles/nature06958},
	doi = {10.1038/nature06958},
	abstract = {Despite their importance for urban planning, traffic forecasting and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Lévy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time-independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modelling. ©2008 Nature Publishing Group.},
	number = {7196},
	journal = {Nature},
	author = {González, Marta C. and Hidalgo, César A. and Barabási, Albert László},
	month = jun,
	year = {2008},
	keywords = {Humanities and Social Sciences, multidisciplinary, Science},
	pages = {779--782},
}

@article{le_doussal_diffusion_2017,
	title = {Diffusion in time-dependent random media and the {Kardar}-{Parisi}-{Zhang} equation},
	volume = {96},
	url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.010102},
	doi = {10.1103/PhysRevE.96.010102},
	abstract = {Although time-dependent random media with short-range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in one-dimensional (1D) lattice random walks, where statistics related to the 1D Kardar-Parisi-Zhang (KPZ) universality class, i.e., the Gaussian unitary ensemble Tracy-Widom distribution, were shown to arise. Here, we provide a simple picture for this correspondence, directly in the continuum, which allows one to study arbitrary space dimensions and to predict a variety of universal distributions. In d=1, we predict and verify numerically the emergence of the Gaussian orthogonal ensemble Tracy-Widom distribution for fluctuations of the transition probability. In d=3, we predict a phase transition from Gaussian fluctuations to three-dimensional KPZ-type fluctuations as the bias is increased. We predict KPZ universal distributions for the arrival time of a first particle from a cloud diffusing in such media.},
	number = {1},
	journal = {Physical Review E},
	author = {Le Doussal, Pierre and Thiery, Thimothée},
	month = jul,
	year = {2017},
	pages = {010102--010102},
}

@article{berkowitz_modeling_2006,
	title = {Modeling {Non}-fickian transport in geological formations as a continuous time random walk},
	volume = {44},
	url = {https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005RG000178},
	doi = {10.1029/2005RG000178},
	abstract = {Non-Fickian (or anomalous) transport of contaminants has been observed at field and laboratory scales in a wide variety of porous and fractured geological formations. Over many years a basic challenge to the hydrology community has been to develop a theoretical framework that quantitatively accounts for this widespread phenomenon. Recently, continuous time random walk (CTRW) formulations have been demonstrated to provide general and effective means to quantify non-Fickian transport. We introduce and develop the CTRW framework from its conceptual picture of transport through its mathematical development to applications relevant to laboratory- and field-scale systems. The CTRW approach contrasts with ones used extensively on the basis of the advection-dispersion equation and use of upscaling, volume averaging, and homogenization. We examine the underlying assumptions, scope, and differences of these approaches, as well as stochastic formulations, relative to CTRW. We argue why these methods have not been successful in fitting actual measurements. The CTRW has now been developed within the framework of partial differential equations and has been generalized to apply to nonstationary domains and interactions with immobile states (matrix effects). We survey models based on multirate mass transfer (mobile-immobile) and fractional derivatives and show their connection as subsets within the CTRW framework. Copyright 2006 by the American Geophysical Union.},
	number = {2},
	journal = {Reviews of Geophysics},
	author = {Berkowitz, Brian and Cortis, Andrea and Dentz, Marco and Scher, Harvey},
	month = jun,
	year = {2006},
	keywords = {anomalous transport, continuous time random walk},
}

@article{metzler_brownian_2019,
	title = {Brownian motion and beyond: first-passage, power spectrum, non-{Gaussianity}, and anomalous diffusion},
	volume = {2019},
	url = {https://doi.org/10.1088/1742-5468/ab4988},
	doi = {10.1088/1742-5468/ab4988},
	abstract = {Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exists a very large range of applications of stochastic processes in various disciplines. Here we provide a summary of some of the recent developments in the field of stochastic processes, highlighting both the experimental findings and theoretical frameworks.},
	number = {11},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Metzler, Ralf},
	month = nov,
	year = {2019},
	keywords = {Brownian motion, diffusion},
	pages = {114003--114003},
}

@article{wang_when_2012,
	title = {When {Brownian} diffusion is not {Gaussian}},
	volume = {11},
	url = {www.nature.com/naturematerials},
	doi = {10.1038/nmat3308},
	abstract = {It is commonly presumed that the random displacements that particles undergo as a result of the thermal jiggling of the environment follow a normal, or Gaussian, distribution. However, non-Gaussian diffusion in soft materials is more prevalent than expected.},
	number = {6},
	journal = {Nature Materials},
	author = {Wang, Bo and Kuo, James and Bae, Sung Chul and Granick, Steve},
	month = may,
	year = {2012},
	keywords = {Soft materials},
	pages = {481--485},
}

@article{von_smoluchowski_zur_1906,
	title = {Zur kinetischen {Theorie} der {Brownschen} {Molekularbewegung} und der {Suspensionen}},
	volume = {326},
	doi = {10.1002/andp.19063261405},
	number = {14},
	journal = {Annalen der Physik},
	author = {von Smoluchowski, M.},
	year = {1906},
	pages = {756--780},
}

@article{einstein_uber_1905,
	title = {Über die von der molekularkinetischen {Theorie} der {Wärme} geforderte {Bewegung} von in ruhenden {Flüssigkeiten} suspendierten {Teilchen}},
	volume = {322},
	url = {https://onlinelibrary.wiley.com/doi/full/10.1002/andp.19053220806},
	doi = {10.1002/andp.19053220806},
	number = {8},
	journal = {Annalen der Physik},
	author = {Einstein, A.},
	month = jan,
	year = {1905},
	pages = {549--560},
}

@article{brown_xxiv_1829,
	title = {{XXIV}. {Additional} remarks on active molecules},
	volume = {6},
	url = {https://www.tandfonline.com/doi/abs/10.1080/14786442908675115},
	doi = {10.1080/14786442908675115},
	number = {33},
	journal = {The Philosophical Magazine},
	author = {Brown, Robert},
	month = sep,
	year = {1829},
	pages = {161--166},
}

@article{bouchaud_anomalous_1990,
	title = {Anomalous diffusion in disordered media: {Statistical} mechanisms, models and physical applications},
	volume = {195},
	doi = {10.1016/0370-1573(90)90099-N},
	abstract = {The subject of this paper is the evolution of Brownian particles in disordered environments. The "Ariadne's clew" we follow is understanding of the general statistical mechanisms which may generate "anomalous" (non-Brownian) diffusion laws; this allows us to develop simple arguments to obtain a qualitative (but often quite accurate) picture of most situations. Several analytical techniques-such as the Green function formalism and renormalization group methods-are also exposed. Care is devoted to the problem of sample to sample fluctuations, particularly acute here. We consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder. An effort is made to illustrate the theoretical models by describing many physical situations where anomalous diffusion laws have been-or could be-observed. © 1990.},
	number = {4-5},
	journal = {Physics Reports},
	author = {Bouchaud, Jean Philippe and Georges, Antoine},
	month = nov,
	year = {1990},
	pages = {127--293},
}

@book{metzler_first-passage_2014,
	title = {First-passage phenomena and their applications},
	isbn = {978-981-4590-29-7},
	abstract = {The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic.},
	publisher = {World Scientific Publishing Co.},
	author = {Metzler, Ralf and Oshanin, Gleb and Redner, Sidney},
	month = jan,
	year = {2014},
	doi = {10.1142/9104},
}

@article{brown_xxvii_1828,
	title = {{XXVII}. {A} brief account of microscopical observations made in the months of {June}, {July} and {August} 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies},
	volume = {4},
	doi = {10.1080/14786442808674769},
	abstract = {Download full textRelated var addthis\_config = \{ ui\_cobrand: "Taylor \& Francis Online", services\_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" \}; Share on facebook Share on twitter Share on email More Sharing Services var addthis\_config = \{"data\_track\_addressbar":true,"ui\_click":true\}; Add to shortlist Link Permalink http://dx.doi.org/10.1080/14786442808674769 Download Citation Recommend to: A friend},
	number = {21},
	journal = {The Philosophical Magazine},
	author = {Brown, Robert},
	month = sep,
	year = {1828},
	pages = {161--173},
}

@article{iyer-biswas_first_2015,
	title = {First {Passage} processes in cellular biology},
	volume = {160},
	url = {http://arxiv.org/abs/1503.00291},
	abstract = {Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy or stochastic dynamics, there is a corresponding variability in the times when the same change occurs in each cell of a population. This time is called the "first passage" time and the corresponding process is a "first passage" (FP) process, referring to the event when a random variable first passes the threshold value. In this review we first present and elucidate fundamentals of the FP formalism within a unified conceptual framework, which naturally integrates the existing techniques. We then discuss applications thereof, with emphasis on the practical use of FP techniques in biophysical systems. Our focus here is on covering a diverse set of analytical techniques; the number of reviewed biological applications is thus limited, out of necessity. We focus on three specific areas: channel transport; receptor binding and adhesion; and single-cell growth and division.},
	journal = {Advances in Chemical Physics},
	author = {Iyer-Biswas, Srividya and Zilman, Anton},
	month = mar,
	year = {2015},
	keywords = {First passage process, Cellular biology, Channel transport, Receptor binding, Single-cell growth},
	pages = {261--306},
}

@article{rossetto_isotropic_2022,
	title = {Isotropic radiative transfer as a phase space process: {Lorentz} covariant {Green}'s functions and first-passage times},
	volume = {139},
	issn = {0295-5075},
	shorttitle = {Isotropic radiative transfer as a phase space process},
	url = {https://dx.doi.org/10.1209/0295-5075/ac747c},
	doi = {10.1209/0295-5075/ac747c},
	abstract = {The solutions of the radiative transfer equation, known for the energy density, do not satisfy the fundamental transitivity property for Green's functions expressed by Chapman-Kolmogorov's relation. I show that this property is retrieved by considering the radiance distribution in phase space. Exact solutions are obtained in one and two dimensions as probability density functions of continous-time persistent random walks, the Fokker-Planck equation of which is the radiative transfer equation. The expected property of Lorentz covariance is verified. I also discuss the measured signal from a pulse source in one dimension, which is a first-passage time distribution, and unveil an effective random delay when the pulse is emitted away from the observer.},
	language = {en},
	number = {1},
	urldate = {2024-09-23},
	journal = {Europhysics Letters},
	author = {Rossetto, Vincent},
	month = jul,
	year = {2022},
	note = {Publisher: EDP Sciences, IOP Publishing and Società Italiana di Fisica},
	pages = {11001},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\CLXR2TAP\\Rossetto - 2022 - Isotropic radiative transfer as a phase space proc.pdf:application/pdf},
}

@article{marris_persistent_2024,
	title = {Persistent and anti-persistent motion in bounded and unbounded space: resolution of the first-passage problem},
	volume = {26},
	issn = {1367-2630},
	shorttitle = {Persistent and anti-persistent motion in bounded and unbounded space},
	url = {https://dx.doi.org/10.1088/1367-2630/ad5d85},
	doi = {10.1088/1367-2630/ad5d85},
	abstract = {The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems has led to a large literature on the modelling of temporally correlated movement paths. Despite the substantial body of work, little progress has been made to determine the dynamical properties of various transport related quantities, including the first-passage or first-hitting probability to one or multiple absorbing targets when space is bounded. To bridge this knowledge gap we generalise the renewal theory of first-passage and splitting probabilities to correlated discrete variables. We do so in arbitrary dimensions on a lattice for the so-called correlated or persistent random walk, the one step non-Markovian extension of the simple lattice random walk in bounded and unbounded space. We focus on bounded domains and consider both persistent and anti-persistent motion in hypercubic lattices as well as the hexagonal lattice. The discrete formalism allows us to extend the notion of the first-passage to that of the directional first-passage, whereby the walker must reach the target from a prescribed direction for a hitting event to occur. As an application to spatio-temporal observations of correlated moving cells that may be either repelled or attracted to hard surfaces, we compare the first-passage statistics to a target within a reflecting domain depending on whether an interaction with the reflective interface invokes a reversal of the movement direction or not. With strong persistence we observe multi-modality in the first-passage distribution in the former case, which instead is greatly suppressed in the latter.},
	language = {en},
	number = {7},
	urldate = {2024-09-23},
	journal = {New Journal of Physics},
	author = {Marris, Daniel and Giuggioli, Luca},
	month = jul,
	year = {2024},
	note = {Publisher: IOP Publishing},
	pages = {073020},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\ZGINWY3J\\Marris and Giuggioli - 2024 - Persistent and anti-persistent motion in bounded a.pdf:application/pdf},
}

@article{dudko_photon_2005,
	title = {Photon diffusion in biological tissues},
	volume = {2},
	copyright = {Copyright (c) 2005 The author(s)},
	issn = {1862-4138},
	url = {https://diffusion.journals.qucosa.de/diffusion/article/view/300},
	doi = {10.62721/diffusion-fundamentals.2.300},
	abstract = {The use of laser-based optical techniques for medical imaging is an attractive alternative to other methods that utilize ionizing radiation. Beside being non-carcinogenic, it is non-invasive, the equipment is transportable, and the methodology can be used to examine properties of soft tissue. However, unlike x-ray photons, optical photons generated in the near-infrared suffer significant amounts of scattering by heterogeneous bodies (e.g., organelles) found in biological tissue. Thus, theory is required to interpret experimental data which appear in the form o spatially or temporally varying light patterns on the skin surface. There is a wide range of parameters over which either diffusion theory or the theory of lattice random walks can be called on to translate optical data into medically significant information embodied in optical parameters of the tissue. We discuss several problems in diffusion theory arising in the analysis of optical measurements, for tissues modeled by a semi-infinite or slab geometry, having either isotropic or anisotropic optical parameters. The measured quantities are related to the intensity of light re-emitted on the tissue surface. A brief discussion is given related to the telegrapher’s equation, which has been suggested as a simple way of incorporating the effects of forward scattering. Mention is made of calculations related to layered media which frequently occur in tissues such as skull and esophagus. Finally, we briefly discuss discrete random walk models for photon migration. These have recently been used to provide parameters conveying information related to the region interrogated by photons constrained to reappear on skin surface.},
	language = {en},
	urldate = {2024-09-23},
	journal = {Diffusion Fundamentals},
	author = {Dudko, Olga K. and Weiss, George H.},
	month = sep,
	year = {2005},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\66GRQP6Q\\Dudko and Weiss - 2005 - Photon diffusion in biological tissues.pdf:application/pdf},
}

@article{das_non-fickian_1998,
	title = {Some {Non}-{Fickian} {Diffusion} {Equations}: {Theory} and {Applications}},
	volume = {162-163},
	issn = {1662-9507},
	shorttitle = {Some {Non}-{Fickian} {Diffusion} {Equations}},
	url = {https://www.scientific.net/DDF.162-163.97},
	doi = {10.4028/www.scientific.net/DDF.162-163.97},
	language = {en},
	urldate = {2024-09-23},
	journal = {Defect and Diffusion Forum},
	author = {Das, Amal K.},
	year = {1998},
	note = {Publisher: Trans Tech Publications Ltd},
	pages = {97--118},
}

@book{case_linear_1967,
	title = {Linear transport theory},
	url = {http://archive.org/details/lineartransportt0000case},
	abstract = {ix, 342 p. ; 24 cm; DON201/1999; Includes bibliographical references and index; 2000 03 10},
	language = {eng},
	urldate = {2024-08-20},
	publisher = {Reading, MA. : Addison-Wesley Pub. Co.},
	author = {Case, Kenneth M.},
	collaborator = {{Internet Archive}},
	year = {1967},
	keywords = {Transport theory},
}

@article{weiss_first_1984,
	title = {First passage times for correlated random walks and some generalizations},
	volume = {37},
	issn = {1572-9613},
	url = {https://doi.org/10.1007/BF01011837},
	doi = {10.1007/BF01011837},
	abstract = {It is generally difficult to solve Fokker-Planck equations in the presence of absorbing boundaries when both spatial and momentum coordinates appear in the boundary conditions. In this note we analyze a simple, exactly solvable model of the correlated random walk and its continuum analogue. It is shown that one can solve for the moments recursively in one dimension in exact analogy with first passage problems for the Fokker-Planck equation, although the boundary conditions are somewhat more complicated. Further generalizations are suggested to multistate random walks.},
	language = {en},
	number = {3},
	urldate = {2024-08-16},
	journal = {Journal of Statistical Physics},
	author = {Weiss, George H.},
	month = nov,
	year = {1984},
	keywords = {correlated random walks, first passage times, multistate random walks, Random walks, telegraphers equation},
	pages = {325--330},
}

@article{loumaigne_intrinsic_2015,
	title = {The intrinsic luminescence of individual plasmonic nanostructures in aqueous suspension by photon time-of-flight spectroscopy},
	volume = {7},
	issn = {2040-3372},
	url = {https://pubs.rsc.org/en/content/articlelanding/2015/nr/c5nr00363f},
	doi = {10.1039/C5NR00363F},
	abstract = {We have studied the intrinsic one-photon excited luminescence of freely diffusing gold nanoparticles of different shapes in aqueous suspension. Gold nanospheres were used as a reference, since their luminescence has been investigated previously and their light absorption and scattering properties are described analytically by Mie theory. We then studied gold nanobipyramids and nanostars that have recently gained interest as building blocks for new plasmonic nanosensors. The aim of our study is to determine whether the luminescence of gold nanoparticles of complex shape (bipyramids and nanostars) is a plasmon-assisted process, in line with the conclusions of recent spectroscopic studies on spheres and nanorods. Our study has been performed on particles in suspension in order to avoid any artefact from the heterogeneous environment created when particles are deposited on a substrate. We employ a recently developed photon time-of-flight method in combination with correlation spectroscopy of the light scattered by the particles to probe the luminescent properties of individual particles based on a particle-by-particle spectral analysis. Furthermore, we have performed resonant light scattering spectroscopic measurements on the same samples. Our work demonstrates the power of our time-of flight method for uncovering the plasmonic signatures of individual bipyramids and nanostars during their brief passage in the focal volume of a confocal set-up. These spectral features of individual particles remain hidden in macroscopic measurements. We find that the intrinsic photoluminescence emission of gold bipyramids and gold nanostars is mediated by their localized surface plasmons.},
	language = {en},
	number = {19},
	urldate = {2024-08-14},
	journal = {Nanoscale},
	author = {Loumaigne, Matthieu and Navarro, Julien R. G. and Parola, Stéphane and Werts, Martinus H. V. and Débarre, Anne},
	month = may,
	year = {2015},
	note = {Publisher: The Royal Society of Chemistry},
	pages = {9013--9024},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\5E2ICDXZ\\Loumaigne et al. - 2015 - The intrinsic luminescence of individual plasmonic.pdf:application/pdf;Supplementary Information PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\PEST2EHU\\Loumaigne et al. - 2015 - The intrinsic luminescence of individual plasmonic.pdf:application/pdf},
}

@article{aleandri_dynamic_2018,
	title = {Dynamic {Light} {Scattering} of {Biopharmaceutics}—{Can} {Analytical} {Performance} {Be} {Enhanced} by {Laser} {Power}?},
	volume = {10},
	copyright = {http://creativecommons.org/licenses/by/3.0/},
	issn = {1999-4923},
	url = {https://www.mdpi.com/1999-4923/10/3/94},
	doi = {10.3390/pharmaceutics10030094},
	abstract = {Background: Dynamic light scattering (DLS) is an important tool to characterize colloidal systems and adequate sizing is particularly critical in the field of protein formulations. Among the different factors that can influence the measurement result, the effect of laser power has so far not been studied thoroughly. Methods: The sensitivity of a DLS instrument was first considered on a theoretical level, followed by experiments using DLS instruments, equipped with two different lasers of (nominal) 45 mW, and 100 mW, respectively. This work analyzes dilute colloidal dispersions of lysozyme as model protein. Results: Theoretical findings agreed with experiments in that only enhanced laser power of 100 mW laser allowed measuring a 0.1 mg/mL protein dispersion in a reliable manner. Results confirmed the usefulness of the presented theoretical considerations in improving a general understanding of the limiting factors in DLS. Conclusions: Laser power is a critical aspect regarding adequate colloidal analysis by DLS. Practical guidance is provided to help scientists specifically with measuring dilute samples to choose both an optimal instrument configuration as well as a robust experimental procedure.},
	language = {en},
	number = {3},
	urldate = {2024-08-14},
	journal = {Pharmaceutics},
	author = {Aleandri, Simone and Vaccaro, Andrea and Armenta, Ricardo and Völker, Andreas Charles and Kuentz, Martin},
	month = sep,
	year = {2018},
	note = {Number: 3
Publisher: Multidisciplinary Digital Publishing Institute},
	keywords = {dynamic light scattering (DSL), laser power, lysozyme, protein aggregation, protein formulation},
	pages = {94},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\CGZNNELQ\\Aleandri et al. - 2018 - Dynamic Light Scattering of Biopharmaceutics—Can A.pdf:application/pdf},
}

@article{zeller_light_2020,
	title = {Light scattering as a {Poisson} process and first-passage probability},
	volume = {2020},
	issn = {1742-5468},
	url = {https://dx.doi.org/10.1088/1742-5468/ab811f},
	doi = {10.1088/1742-5468/ab811f},
	abstract = {A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately either achieves first-passage, leaving the medium, or it is absorbed. The Kubelka–Munk model describes a flux of such particles moving perpendicular to the surface of a plane-parallel medium with a scattering rate and an absorption rate. The particle path alternates between the positive direction into the medium and the negative direction back towards the surface. Backscattering events from the positive to the negative direction occur at local maxima or peaks, while backscattering from the negative to the positive direction occur at local minima or valleys. The probability of a particle avoiding absorption as it follows its path decreases exponentially with the path-length λ. The reflectance of a semi-infinite slab is therefore the Laplace transform of the distribution of path-length that ends with a first-passage out of the medium. In the case of a constant scattering rate the random walk is a Poisson process. We verify our results with two iterative calculations, one using the properties of iterated convolution with a symmetric kernel and the other via direct calculation with an exponential step-length distribution. We present a novel demonstration, based on fluctuation theory of sums of random variables, that the first-passage probability as a function of the number of peaks n in the alternating path is a step-length distribution-free combinatoric expression involving Catalan numbers. Counting paths with backscattering on the real half-line results in the same Catalan number coefficients as Dyck paths on the whole numbers. Including a separate forward-scattering Poisson process results in a combinatoric expression related to counting Motzkin paths. We therefore connect walks on the real line to discrete path combinatorics.},
	language = {en},
	number = {6},
	urldate = {2024-08-14},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Zeller, Claude and Cordery, Robert},
	month = jun,
	year = {2020},
	note = {Publisher: IOP Publishing and SISSA},
	pages = {063404},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\XST6Y6M2\\Zeller and Cordery - 2020 - Light scattering as a Poisson process and first-pa.pdf:application/pdf},
}

@book{harris_introduction_1971,
	address = {New York},
	title = {An introduction to the theory of the {Boltzmann} equation.},
	isbn = {978-0-03-082789-1},
	abstract = {Includes bibliographical references (pages 209-210).},
	language = {eng},
	publisher = {Holt, Rinehart and Winston},
	author = {Harris, Stewart},
	year = {1971},
	keywords = {Transport theory},
}

@book{chandrasekhar_radiative_1950,
	address = {London},
	series = {The {International} {Series} of {Monographs} on {Physics}},
	title = {Radiative {Transfer}},
	url = {https://ui.adsabs.harvard.edu/abs/1950QJRMS..76Q.498./abstract},
	abstract = {"Radiative Transfer is the definitive work in the field. It provides workers and students in physics, nuclear physics, astrophysics, and atmospheric studies with the foundation for the analysis of stellar atmospheres, planetary illumination, and sky radiation. Though radiative transfer has been investigated chiefly as},
	language = {en},
	publisher = {Oxford, Clarendon Press},
	author = {Chandrasekhar, Subrahmanyan},
	year = {1950},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\TMQSI79Z\\9780486605906.html:text/html},
}

@article{masoliver_solutions_1992,
	title = {Solutions of the telegrapher's equation in the presence of traps},
	volume = {45},
	url = {https://link.aps.org/doi/10.1103/PhysRevA.45.2222},
	doi = {10.1103/PhysRevA.45.2222},
	abstract = {Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher’s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher’s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.},
	number = {4},
	urldate = {2024-08-12},
	journal = {Physical Review A},
	author = {Masoliver, Jaume and Porrà, Josep M. and Weiss, George H.},
	month = feb,
	year = {1992},
	note = {Publisher: American Physical Society},
	pages = {2222--2227},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\DX4T66Z2\\Masoliver et al. - 1992 - Solutions of the telegrapher's equation in the pre.pdf:application/pdf},
}

@article{masoliver_solution_1993,
	title = {Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries},
	volume = {48},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.48.939},
	doi = {10.1103/PhysRevE.48.939},
	abstract = {We show that the reflecting boundary condition for a one-dimensional telegrapher’s equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegrapher’s equation in the presence of these boundaries.},
	number = {2},
	urldate = {2024-08-09},
	journal = {Physical Review E},
	author = {Masoliver, Jaume and Porrà, Josep M. and Weiss, George H.},
	month = aug,
	year = {1993},
	note = {Publisher: American Physical Society},
	pages = {939--944},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\FWFA7EZH\\PhysRevE.48.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\TPYCGF6V\\Masoliver et al. - 1993 - Solution to the telegrapher's equation in the pres.pdf:application/pdf},
}

@article{bohren_multiple_1987,
	title = {Multiple scattering of light and some of its observable consequences},
	volume = {55},
	issn = {0002-9505},
	url = {https://doi.org/10.1119/1.15109},
	doi = {10.1119/1.15109},
	abstract = {Many common observations are inexplicable by single‐scattering arguments: the variation of brightness and color of the clear sky; the brightness of clouds; the whiteness of a glass of milk; the appearance of distant objects; the blueness of light transmitted in snow and other natural ice bodies; the darkening of sand upon wetting. Yet multiple scattering is seldom mentioned in optics textbooks. It is possible to understand many observable phenomena without invoking the complete theory of multiple (incoherent) scattering. A simple two‐stream theory, in which photons are constrained to be scattered in only two directions, forward and backward, is adequate for interpreting many observations, even quantitatively, and it paves the way for advanced study.},
	number = {6},
	urldate = {2024-08-09},
	journal = {American Journal of Physics},
	author = {Bohren, Craig F.},
	month = jun,
	year = {1987},
	pages = {524--533},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\JL2AQ2L4\\Bohren - 1987 - Multiple scattering of light and some of its obser.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\XPNTBZZR\\Multiple-scattering-of-light-and-some-of-its.html:text/html},
}

@article{klett_stable_1981,
	title = {Stable analytical inversion solution for processing lidar returns},
	volume = {20},
	copyright = {© 1981 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-20-2-211},
	doi = {10.1364/AO.20.000211},
	abstract = {A simple analytical method is presented that shows some potential for application to the problem of extracting attenuation and backscatter coefficients in an inhomogeneous atmosphere from the return signal of a monostatic single-wavelength lidar system. The method assumes the validity of the single-scattering lidar equation and a power law relationship between backscatter and attenuation. For optical depths greater than unity the inversion method can be applied in principle using only information contained in the signal itself. In contrast to a well-known related analytical inversion solution, the new solution form is shown to be stable with respect to perturbations in the signal, the postulated relationship between backscatter and attenuation, and the assumed or estimated boundary value of attenuation.},
	language = {EN},
	number = {2},
	urldate = {2024-08-08},
	journal = {Applied Optics},
	author = {Klett, James D.},
	month = jan,
	year = {1981},
	note = {Publisher: Optica Publishing Group},
	keywords = {Attenuation, Attenuation coefficient, Backscattering, Lidar, Multiple scattering, Remote sensing},
	pages = {211--220},
}

@article{viezee_lidar_1969,
	title = {Lidar {Observations} of {Airfield} {Approach} {Conditions}:{An} {Exploratory} {Study}},
	volume = {8},
	issn = {1520-0450},
	shorttitle = {Lidar {Observations} of {Airfield} {Approach} {Conditions}},
	url = {https://journals.ametsoc.org/view/journals/apme/8/2/1520-0450_1969_008_0274_looaac_2_0_co_2.xml},
	doi = {10.1175/1520-0450(1969)008<0274:LOOAAC>2.0.CO;2},
	abstract = {Lidar (laser radar) data obtained at Hamilton AFB, Calif., under conditions of low ceiling and visibility, are analyzed by hand and by electronic computer to explore the operational utility of lidar in determining cloud ceiling and visibility for aircraft landing operations. Hand analyses of the data show the ability of the lidar to describe the spatial configuration of the low-cloud structure in the direction of the landing-approach path. The problems inherent in evaluating lidar observations are discussed, and initial approaches to quantitative solutions by computer are presented. It is demonstrated that operationally useful information on the ceiling conditions contained in the hand analyses can be represented by digitizing the lidar data and subjecting these data to computer analysis.},
	language = {EN},
	number = {2},
	urldate = {2024-08-08},
	journal = {Journal of Applied Meteorology and Climatology},
	author = {Viezee, W. and Uthe, E. E. and Collis, R. T. H.},
	month = apr,
	year = {1969},
	note = {Publisher: American Meteorological Society
Section: Journal of Applied Meteorology and Climatology},
	pages = {274--283},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\VDNAP5E3\\Viezee et al. - 1969 - Lidar Observations of Airfield Approach Conditions.pdf:application/pdf},
}

@article{jagodnicka_particle_2009,
	title = {Particle size distribution retrieval from multiwavelength lidar signals for droplet aerosol},
	volume = {48},
	copyright = {© 2008 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-48-4-B8},
	doi = {10.1364/AO.48.0000B8},
	abstract = {A method of retrieval of the aerosol particle size distribution (APSD) from multiwavelength lidar signals is presented. Assumed distribution (usually a bimodal combination of lognormal functions) with a few free parameters is directly substituted into the lidar equations. The minimization technique allows one to find the parameters that provide the best fit of the assumed APSD by comparison of theoretically generated and experimental signals. Prior knowledge of the lidar ratio is not required. The approach was tested on a typical synthetic APSD consisting of spherical droplets. Comparison of lidar measurements with results from a condensation particle counter was also performed. For signals registered at 3-5 wavelengths from the UV to the near IR a satisfactory retrieval of synthetic APSD is possible for the particles within the 100-3000 nm range.},
	language = {EN},
	number = {4},
	urldate = {2024-08-08},
	journal = {Applied Optics},
	author = {Jagodnicka, Anna K. and Stacewicz, Tadeusz and Karasiński, Grzegorz and Posyniak, Michał and Malinowski, Szymon P.},
	month = feb,
	year = {2009},
	note = {Publisher: Optica Publishing Group},
	keywords = {Lidar, Remote sensing, Extinction coefficients, Mie scattering, Refractive index, Spatial resolution},
	pages = {B8--B16},
}

@article{brown_light_1975,
	title = {Light scattering study of dynamic and time-averaged correlations in dispersions of charged particles},
	volume = {8},
	issn = {0305-4470, 1361-6447},
	url = {https://iopscience.iop.org/article/10.1088/0305-4470/8/5/004},
	doi = {10.1088/0305-4470/8/5/004},
	language = {en},
	number = {5},
	urldate = {2024-08-08},
	journal = {Journal of Physics A: Mathematical and General},
	author = {Brown, J C and Pusey, P N and Goodwin, J W and Ottewill, R H},
	month = may,
	year = {1975},
	pages = {664--682},
	file = {Brown et al. - 1975 - Light scattering study of dynamic and time-average.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\4BSGAPKX\\Brown et al. - 1975 - Light scattering study of dynamic and time-average.pdf:application/pdf},
}

@article{dehghan_use_2009,
	title = {The use of {Chebyshev} cardinal functions for solution of the second-order one-dimensional telegraph equation},
	volume = {25},
	issn = {1098-2426},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.20382},
	doi = {10.1002/num.20382},
	abstract = {A numerical technique is presented for the solution of the second order one-dimensional linear hyperbolic equation. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem is reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009},
	language = {en},
	number = {4},
	urldate = {2024-06-07},
	journal = {Numerical Methods for Partial Differential Equations},
	author = {Dehghan, Mehdi and Lakestani, Mehrdad},
	year = {2009},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.20382},
	keywords = {Chebyshev cardinal functions, operational matrix of derivative, telegraph equation, the second order hyperbolic equation},
	pages = {931--938},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\M3URPJSV\\Dehghan and Lakestani - 2009 - The use of Chebyshev cardinal functions for soluti.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\TXBTTVQL\\num.html:text/html},
}

@article{dehghan_numerical_2008,
	title = {A numerical method for solving the hyperbolic telegraph equation},
	volume = {24},
	issn = {1098-2426},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.20306},
	doi = {10.1002/num.20306},
	abstract = {Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008},
	language = {en},
	number = {4},
	urldate = {2024-06-05},
	journal = {Numerical Methods for Partial Differential Equations},
	author = {Dehghan, Mehdi and Shokri, Ali},
	year = {2008},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.20306},
	keywords = {collocation, radial basis function (RBF), second-order hyperbolic telegraph equation, thin plate splines (TPS)},
	pages = {1080--1093},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\LVK6EUYH\\Dehghan and Shokri - 2008 - A numerical method for solving the hyperbolic tele.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\W5UBJGA2\\num.html:text/html},
}

@article{mohebbi_high_2008,
	title = {High order compact solution of the one-space-dimensional linear hyperbolic equation},
	volume = {24},
	issn = {1098-2426},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.20313},
	doi = {10.1002/num.20313},
	abstract = {In this article, we introduce a high-order accurate method for solving one-space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high-order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one-space-dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, Appl Math Lett 17 (2004), 101–105).© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008},
	language = {en},
	number = {5},
	urldate = {2024-06-05},
	journal = {Numerical Methods for Partial Differential Equations},
	author = {Mohebbi, Akbar and Dehghan, Mehdi},
	year = {2008},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.20313},
	keywords = {telegraph equation, collocation technique, compact finite difference scheme, high accuracy, linear hyperbolic equation},
	pages = {1222--1235},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\GVFSGH8K\\Mohebbi and Dehghan - 2008 - High order compact solution of the one-space-dimen.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\7GBGPE95\\num.html:text/html},
}

@article{mohanty_unconditionally_2005,
	title = {An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients},
	volume = {165},
	issn = {0096-3003},
	url = {https://www.sciencedirect.com/science/article/pii/S0096300304003777},
	doi = {10.1016/j.amc.2004.07.002},
	abstract = {We propose a three level implicit unconditionally stable difference scheme of O(k2+h2) for the difference solution of second order linear hyperbolic equation utt+2α(x,t)ut+β2(x,t)u=A(x,t)uxx+f(x,t), 0{\textless}x{\textless}1, t{\textgreater}0 subject to appropriate initial and Dirichlet boundary conditions, where A(x,t){\textgreater}0, α(x,t){\textgreater}β(x,t)⩾0. The proposed formula is applicable to the problems having singularity at x=0. The resulting tri-diagonal linear system of equations is solved by using Gauss-elimination method. Numerical examples are provided to illustrate the unconditionally stable character of the proposed method.},
	number = {1},
	urldate = {2024-06-05},
	journal = {Applied Mathematics and Computation},
	author = {Mohanty, R. K.},
	month = jun,
	year = {2005},
	keywords = {Telegraph equation, Implicit scheme, Linear hyperbolic equation, RMS errors, Singular equation, Unconditionally stable, Variable coefficients},
	pages = {229--236},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\VJE6PBB5\\S0096300304003777.html:text/html},
}

@article{chandrasekhar_stochastic_1943,
	title = {Stochastic {Problems} in {Physics} and {Astronomy}},
	volume = {15},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.15.1},
	doi = {10.1103/RevModPhys.15.1},
	abstract = {DOI:https://doi.org/10.1103/RevModPhys.15.1},
	number = {1},
	urldate = {2024-05-10},
	journal = {Reviews of Modern Physics},
	author = {Chandrasekhar, S.},
	month = jan,
	year = {1943},
	note = {Publisher: American Physical Society},
	pages = {1--89},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\VL8FRF5D\\RevModPhys.15.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\BPW4AHFJ\\Chandrasekhar - 1943 - Stochastic Problems in Physics and Astronomy.pdf:application/pdf},
}

@article{henyey_diffuse_1941,
	title = {Diffuse radiation in the {Galaxy}.},
	volume = {93},
	issn = {0004-637X},
	url = {https://ui.adsabs.harvard.edu/abs/1941ApJ....93...70H},
	doi = {10.1086/144246},
	abstract = {Observations have been obtained to verify the existence of diffuse interstellar radiation. A Fabry photometer, attached to the 40-inch refractor at the Yerkes Observatory, was used to measure the brightness of regions over a wide range of galactic latitude. The intensities in the photographic region of the spectrum were calibrated by means of the Polar Sequence stars. The mean of four such runs across the Milky Way, on circles of nearly constant longitude, l = 40°, shows a maximum of brightness of 80 stars of the tenth magnitude per square degree for the diffuse extra-terrestrial radiation. The mean of three runs near l = 140° shows a maximum of 35 in the same units. It is shown that the observed intensity of diffuse light may be explained as scattered stellar radiation if the phase function governing the scattering of starlight by the interstellar matter is strongly forward-throwing. The concentration of the diffuse light toward the galactic circle is also in agreement with this property of the phase function. The observations also indicate that the scattering efficiency, or albedo, of the particles is greater than 0.3},
	urldate = {2024-05-08},
	journal = {The Astrophysical Journal},
	author = {Henyey, L. G. and Greenstein, J. L.},
	month = jan,
	year = {1941},
	note = {Publisher: IOP
ADS Bibcode: 1941ApJ....93...70H},
	pages = {70--83},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\QFUZ2SXT\\Henyey and Greenstein - 1941 - Diffuse radiation in the Galaxy..pdf:application/pdf},
}

@article{yoo_when_1990,
	title = {When does the diffusion approximation fail to describe photon transport in random media?},
	volume = {64},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.64.2647},
	doi = {10.1103/PhysRevLett.64.2647},
	abstract = {The transport of photons through a slab of random medium is shown to deviate from the diffusion approximation when z/lt is small, where z is the thickness of the slab and lt is the transport mean free path. When z/lt=10 and z=10 mm, the average time of arrival is about 0.9 times that predicted by diffusion theory. Photons are found to arrive earlier than that predicted by the diffusion theory as z/lt becomes smaller or the anisotropic scattering increases.},
	number = {22},
	urldate = {2024-05-08},
	journal = {Physical Review Letters},
	author = {Yoo, K. M. and Liu, Feng and Alfano, R. R.},
	month = may,
	year = {1990},
	note = {Publisher: American Physical Society},
	pages = {2647--2650},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\8F4EZ2EZ\\PhysRevLett.64.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\XMHKWKDD\\Yoo et al. - 1990 - When does the diffusion approximation fail to desc.pdf:application/pdf},
}

@article{durian_two-stream_1996,
	title = {Two-stream theory of diffusing light spectroscopies},
	volume = {229},
	issn = {0378-4371},
	url = {https://www.sciencedirect.com/science/article/pii/0378437196000209},
	doi = {10.1016/0378-4371(96)00020-9},
	abstract = {A theory for the propagation of light through a randomly scattering slab is developed that does not take advantage of a diffusion approximation but can be solved analytically. The treatment allows for scattering anisotropy and boundary reflectivity to be incorporated in a straightforward fashion for slabs of arbitrary thickness. Predictions are found for both the transmission probability and the electric field autocorrelation function which, respectively, can be used to analyze diffuse-transmission spectroscopy and diffusing-wave spectroscopy data more accurately.},
	number = {2},
	urldate = {2024-04-22},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Durian, D. J.},
	month = jul,
	year = {1996},
	keywords = {Complex fluids, Multiple light scattering, Transport},
	pages = {218--235},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\PHWXJH94\\0378437196000209.html:text/html},
}

@article{durian_photon_1997,
	title = {Photon migration at short times and distances and in cases of strong absorption},
	volume = {14},
	copyright = {© 1997 Optical Society of America},
	issn = {1520-8532},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-14-1-235},
	doi = {10.1364/JOSAA.14.000235},
	abstract = {Diffusion theory is widely used to describe photon migration in turbid media because it is simple and, in certain cases, can be accurate to within a few percent. However, it neglects the ballistic nature of photon propagation between successive scattering events and hence entirely breaks down for short times and distances, as well as for strong absorption. Here we generalize on the exact two-stream theory of one-dimensional photon migration to obtain a telegrapher equation that accounts for both diffusive and ballistic aspects of propagation in three-dimensional media. At long times and distances the standard diffusion theory is recovered, whereas at short times and distances we find improved predictions for such phenomena as pulse spreading, diffuse photon-density wave dispersion, transmission through a slab, and pulse reflection from a semi-infinite medium. Our theory should be useful for accurately characterizing turbid media, such as biological tissues, and may also aid in improving the spatial resolution of images made with diffuse light.},
	language = {EN},
	number = {1},
	urldate = {2024-04-22},
	journal = {JOSA A},
	author = {Durian, D. J. and Rudnick, J.},
	month = jan,
	year = {1997},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Spatial resolution, Fourier transforms, Image resolution, Numerical simulation, Turbid media},
	pages = {235--245},
}

@article{lemieux_diffusing-light_1998,
	title = {Diffusing-light spectroscopies beyond the diffusion limit: {The} role of ballistic transport and anisotropic scattering},
	volume = {57},
	shorttitle = {Diffusing-light spectroscopies beyond the diffusion limit},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.57.4498},
	doi = {10.1103/PhysRevE.57.4498},
	abstract = {Diffuse transmission and diffusing-wave spectroscopy (DWS) can be used to probe the structure and dynamics of opaque materials such as colloids, foams, and sand. A crucial step is to model photon transport as a diffusion process. This approach is acceptable for optically thick samples, far into the limit of strong multiple scattering; however, it becomes increasingly inaccurate for thinner samples for several reasons. Here, we correct for two of these defects. By modeling photon propagation by a telegrapher equation with suitable boundary conditions, we can account for the ballistic transport of photons at finite speed between successive scattering events. By introducing a discontinuity in the photon concentration at the source point, and then averaging over a range of penetration depths, we can account for the fact that photons usually scatter anisotropically into the forward direction, rather than being completely randomized at each event. The accuracy of our approach is tested by comparison both with random walk computer simulations and with experiments on specially designed suspensions of polystyrene spheres. We find that our predictions extend the utility of diffuse transmission to slabs of all thicknesses and of DWS to slabs down to about two transport mean free paths.},
	number = {4},
	urldate = {2024-04-22},
	journal = {Physical Review E},
	author = {Lemieux, P.-A. and Vera, M. U. and Durian, D. J.},
	month = apr,
	year = {1998},
	note = {Publisher: American Physical Society},
	pages = {4498--4515},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\VQP9K6E8\\PhysRevE.57.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\7VGTTWZN\\Lemieux et al. - 1998 - Diffusing-light spectroscopies beyond the diffusio.pdf:application/pdf},
}

@article{allgaier_diffuse_2021,
	title = {Diffuse optics for glaciology},
	volume = {29},
	copyright = {© 2021 Optical Society of America},
	issn = {1094-4087},
	url = {https://opg.optica.org/oe/abstract.cfm?uri=oe-29-12-18845},
	doi = {10.1364/OE.425630},
	abstract = {Optical probing of glaciers has the potential for tremendous impact on environmental science. However, glacier ice is turbid, which prohibits the use of most established optical measurements for determining a glacier\&\#x2019;s interior structure. Here, we propose a method for determining the depth, scattering and absorption length based upon diffuse propagation of short optical pulses. Our model allows us to extract several characteristics of the glacier. Performing Monte Carlo simulations implementing Mie scattering and mixed boundary conditions, we show that the proposed approach should be feasible with current technology. The results suggest that the optical properties and geometry of the glacier can be extracted from realistic measurements, which could be implemented with a low cost and small footprint.},
	language = {EN},
	number = {12},
	urldate = {2024-01-19},
	journal = {Optics Express},
	author = {Allgaier, Markus and Smith, Brian J.},
	month = jun,
	year = {2021},
	note = {Publisher: Optica Publishing Group},
	keywords = {Mie scattering, Crystal orientation, Diffuse optical imaging, Optical components, Optical properties, Total internal reflection},
	pages = {18845--18864},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\4L42FX2H\\Allgaier and Smith - 2021 - Diffuse optics for glaciology.pdf:application/pdf},
}

@article{noauthor_first_nodate,
	title = {First {Messengers} - {Kodis} - - {Major} {Reference} {Works} - {Wiley} {Online} {Library}},
	url = {https://onlinelibrary.wiley.com/doi/10.1002/9780470015902.a0024167},
	urldate = {2022-05-13},
	file = {First Messengers - Kodis - - Major Reference Works - Wiley Online Library:C\:\\Users\\centrifuge\\Zotero\\storage\\37LR2E7M\\9780470015902.html:text/html},
}

@article{weiss_order_1983,
	title = {Order statistics for first passage times in diffusion processes},
	volume = {31},
	issn = {1572-9613},
	url = {https://doi.org/10.1007/BF01011582},
	doi = {10.1007/BF01011582},
	abstract = {We consider the problem of the first passage times for absorption (trapping) of the firstj (j = 1,2, ....) ofk, j {\textless}k, identical and independent diffusing particles for the asymptotic case k≫{\textgreater}1. Our results are a special case of the theory of order statistics. We show that in one dimension the mean time to absorption at a boundary for the first ofk diffusing particles, μ1,k, goes as (lnk)−1 for the set of initial conditions in which none of thek particles is located at a boundary and goes ask−2 for the set of initial conditions in which some of thek particles may be located at the boundary. We demonstrate that in one dimension our asymptotic results (k21) are independent of the potential field in which the diffusion takes place for a wide class of potentials. We conjecture that our results are independent of dimension and produce some evidence supporting this conjecture. We conclude with a discussion of the possible import of these results on diffusion-controlled rate processes.},
	language = {en},
	number = {2},
	urldate = {2024-01-04},
	journal = {Journal of Statistical Physics},
	author = {Weiss, George H. and Shuler, Kurt E. and Lindenberg, Katja},
	month = may,
	year = {1983},
	keywords = {Diffusion, mean first passage times, mean trapping times, order statistics},
	pages = {255--278},
}

@article{linn_extreme_2022,
	title = {Extreme hitting probabilities for diffusion},
	volume = {55},
	issn = {1751-8121},
	url = {https://dx.doi.org/10.1088/1751-8121/ac8191},
	doi = {10.1088/1751-8121/ac8191},
	abstract = {A variety of systems in physics, chemistry, biology, and psychology are modeled in terms of diffusing ‘searchers’ looking for ‘targets’. Examples range from gene regulation, to cell sensing, to human decision-making. A commonly studied statistic in these models is the so-called hitting probability for each target, which is the probability that a given single searcher finds that particular target. However, the decisive event in many systems is not the arrival of a given single searcher to a target, but rather the arrival of the fastest searcher to a target out of many searchers. In this paper, we study the probability that the fastest diffusive searcher hits a given target in the many searcher limit, which we call the extreme hitting probability. We first prove an upper bound for the decay of the probability that the searcher finds a target other than the closest target. This upper bound applies in very general settings and depends only on the relative distances to the targets. Furthermore, we find the exact asymptotics of the extreme hitting probabilities in terms of the short-time distribution of when a single searcher hits a target. These results show that the fastest searcher always hits the closest target in the many searcher limit. While this fact is intuitive in light of recent results on the time it takes the fastest searcher to find a target, our results give rigorous, quantitative estimates for the extreme hitting probabilities. We illustrate our results in several examples and numerical solutions.},
	language = {en},
	number = {34},
	urldate = {2024-01-04},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Linn, Samantha and Lawley, Sean D.},
	month = aug,
	year = {2022},
	note = {Publisher: IOP Publishing},
	pages = {345002},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\FEBCRJPZ\\Linn and Lawley - 2022 - Extreme hitting probabilities for diffusion.pdf:application/pdf},
}

@article{lawley_slowest_2023,
	title = {Slowest first passage times, redundancy, and menopause timing},
	volume = {86},
	issn = {1432-1416},
	url = {https://doi.org/10.1007/s00285-023-01921-9},
	doi = {10.1007/s00285-023-01921-9},
	abstract = {Biological events are often initiated when a random “searcher” finds a “target,” which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest searcher(s) to find a target. For example, of the hundreds of thousands of primordial follicles in a woman’s ovarian reserve, it is the slowest to leave that trigger the onset of menopause. Such slowest FPTs may also contribute to the reliability of cell signaling pathways and influence the ability of a cell to locate an external stimulus. In this paper, we use extreme value theory and asymptotic analysis to obtain rigorous approximations to the full probability distribution and moments of slowest FPTs. Though the results are proven in the limit of many searchers, numerical simulations reveal that the approximations are accurate for any number of searchers in typical scenarios of interest. We apply these general mathematical results to models of ovarian aging and menopause timing, which reveals the role of slowest FPTs for understanding redundancy in biological systems. We also apply the theory to several popular models of stochastic search, including search by diffusive, subdiffusive, and mortal searchers.},
	language = {en},
	number = {6},
	urldate = {2024-01-04},
	journal = {Journal of Mathematical Biology},
	author = {Lawley, Sean D. and Johnson, Joshua},
	month = may,
	year = {2023},
	keywords = {Diffusion, 60G70, 92C05, 92C30, Aging, First passage time, Ovarian biology},
	pages = {90},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\M3KVZ7XA\\Lawley and Johnson - 2023 - Slowest first passage times, redundancy, and menop.pdf:application/pdf},
}

@article{madrid_competition_2020,
	title = {Competition between slow and fast regimes for extreme first passage times of diffusion*},
	volume = {53},
	issn = {1751-8121},
	url = {https://dx.doi.org/10.1088/1751-8121/ab96ed},
	doi = {10.1088/1751-8121/ab96ed},
	abstract = {Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the target is small (the narrow escape problem) or if the searcher must escape a potential well. However, many systems depend on the first time a searcher finds the target out of a large group of searchers, which is the so-called extreme FPT. Since this extreme FPT vanishes in the limit of many searchers, the prohibitively slow FPTs of diffusive search can be negated by deploying enough searchers. However, the notion of ‘enough searchers’ is poorly understood. How can one determine if a system is in the slow regime (dominated by small targets or a deep potential, for example) or the fast regime (dominated by many searchers)? How can one estimate the extreme FPT in these different regimes? In this paper, we answer these questions by deriving conditions which ensure that a system is in either regime and finding approximations of the full distribution and all the moments of the extreme FPT in these regimes. Our analysis reveals the critical effect that initial searcher distribution and target reactivity can have on extreme FPTs.},
	language = {en},
	number = {33},
	urldate = {2024-01-04},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Madrid, Jacob B. and Lawley, Sean D.},
	month = jul,
	year = {2020},
	note = {Publisher: IOP Publishing},
	pages = {335002},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\ZEEQHYBG\\Madrid and Lawley - 2020 - Competition between slow and fast regimes for extr.pdf:application/pdf},
}

@article{lawley_universal_2020,
	title = {Universal formula for extreme first passage statistics of diffusion},
	volume = {101},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.101.012413},
	doi = {10.1103/PhysRevE.101.012413},
	abstract = {The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target. However, the more relevant quantity in many systems is the time it takes the fastest searcher to find a target from a large group of searchers. This fastest FPT depends on extremely rare events and has a drastically faster timescale than the FPT of a given single searcher. In this work, we prove a simple explicit formula for every moment of the fastest FPT. The formula is remarkably universal, as it holds for d-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on Riemannian manifolds, (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets. Our results rigorously confirm, generalize, correct, and unify various conjectures and heuristics about the fastest FPT.},
	number = {1},
	urldate = {2024-01-04},
	journal = {Physical Review E},
	author = {Lawley, Sean D.},
	month = jan,
	year = {2020},
	note = {Publisher: American Physical Society},
	pages = {012413},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\CRRHERUS\\Lawley - 2020 - Universal formula for extreme first passage statis.pdf:application/pdf},
}

@article{godec_first_2016,
	title = {First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time},
	volume = {6},
	copyright = {2016 The Author(s)},
	issn = {2045-2322},
	shorttitle = {First passage time distribution in heterogeneity controlled kinetics},
	url = {https://www.nature.com/articles/srep20349},
	doi = {10.1038/srep20349},
	abstract = {The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target.},
	language = {en},
	number = {1},
	urldate = {2024-01-04},
	journal = {Scientific Reports},
	author = {Godec, Aljaž and Metzler, Ralf},
	month = feb,
	year = {2016},
	note = {Number: 1
Publisher: Nature Publishing Group},
	keywords = {Computational biophysics, Statistical physics},
	pages = {20349},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\KNFJK7KL\\Godec and Metzler - 2016 - First passage time distribution in heterogeneity c.pdf:application/pdf},
}

@article{grebenkov_escape_2017,
	title = {The escape problem for mortal walkers},
	volume = {146},
	issn = {0021-9606},
	url = {https://doi.org/10.1063/1.4976522},
	doi = {10.1063/1.4976522},
	abstract = {We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a first-order kinetics (i.e., exponentially distributed lifetimes), we study the effect of the associated death rate onto the survival probability, the exit probability, and the mean first passage time. We derive the upper and lower bounds and some approximations for these quantities. We reveal three asymptotic regimes of small, intermediate, and large death rates. General estimates and asymptotics are compared to several explicit solutions for simple domains and to numerical simulations. These results allow one to account for stochastic photobleaching of fluorescent tracers in bio-imaging, degradation of mRNA molecules in genetic translation mechanisms, or high mortality rates of spermatozoa in the fertilization process. Our findings provide a mathematical ground for optimizing storage containers and materials to reduce the risk of leakage of dangerous chemicals or nuclear wastes.},
	number = {8},
	urldate = {2024-01-04},
	journal = {The Journal of Chemical Physics},
	author = {Grebenkov, D. S. and Rupprecht, J.-F.},
	month = feb,
	year = {2017},
	pages = {084106},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\2EFU5NNB\\Grebenkov and Rupprecht - 2017 - The escape problem for mortal walkers.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\V7X5KREM\\The-escape-problem-for-mortal-walkers.html:text/html},
}

@article{lawley_probabilistic_2020,
	title = {A {Probabilistic} {Approach} to {Extreme} {Statistics} of {Brownian} {Escape} {Times} in {Dimensions} 1, 2, and 3},
	volume = {30},
	issn = {1432-1467},
	url = {https://doi.org/10.1007/s00332-019-09605-9},
	doi = {10.1007/s00332-019-09605-9},
	abstract = {First passage time (FPT) theory is often used to estimate timescales in cellular and molecular biology. While the overwhelming majority of studies have focused on the time it takes a given single Brownian searcher to reach a target, cellular processes are instead often triggered by the arrival of the first molecule out of many molecules. In these scenarios, the more relevant timescale is the FPT of the first Brownian searcher to reach a target from a large group of independent and identical Brownian searchers. Though the searchers are identically distributed, one searcher will reach the target before the others and will thus have the fastest FPT. This fastest FPT depends on extremely rare events and its mean can be orders of magnitude faster than the mean FPT of a given single searcher. In this paper, we use rigorous probabilistic methods to study this fastest FPT. We determine the asymptotic behavior of all the moments of this fastest FPT in the limit of many searchers in a general class of two- and three-dimensional domains. We establish these results by proving that the fastest searcher takes an almost direct path to the target.},
	language = {en},
	number = {3},
	urldate = {2024-01-04},
	journal = {Journal of Nonlinear Science},
	author = {Lawley, Sean D. and Madrid, Jacob B.},
	month = jun,
	year = {2020},
	keywords = {Diffusion, 60G70, 92C05, First passage time, 60J60, 60J65, Asymptotic analysis, Extreme value theory},
	pages = {1207--1227},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\W9MV4Z7T\\Lawley and Madrid - 2020 - A Probabilistic Approach to Extreme Statistics of .pdf:application/pdf},
}

@article{lathrop_absorption_1966,
	title = {Absorption of {Radiation} in a {Diffusely} {Scattering} {Medium}},
	volume = {56},
	copyright = {© 1966 Optical Society of America},
	url = {https://opg.optica.org/josa/abstract.cfm?uri=josa-56-7-926},
	doi = {10.1364/JOSA.56.000926},
	abstract = {A theory is presented with which the absorption of radiation in a diffusely light-scattering plane layer of infinite extent can be predicted when the Bouguer-law absorption and particle size of the material in the layer are known. The absorption of the scattering layer depends on the mass of absorbing material in a thin “monolayer” that is characteristic of the particular scattering layer. This monolayer thickness is closely related to the size of the particles in the layer. The absorption coefficient of the scattering layer is shown to be a large multiple of the Bouguer-law absorption coefficient when the absorption and particle size are small, and is a small multiple in the opposite case. An experimental test is in good agreement with the predictions of the theory.},
	language = {EN},
	number = {7},
	urldate = {2023-05-10},
	journal = {JOSA},
	author = {Lathrop, Arthur L.},
	month = jul,
	year = {1966},
	note = {Publisher: Optica Publishing Group},
	keywords = {Absorption coefficient, Light wavelength, Particle scattering, Scattering, Scattering media, Scattering theory},
	pages = {926--929},
}

@article{goring_light-scattering_1957,
	title = {Light-scattering calibration with {Ludox}},
	volume = {12},
	issn = {0095-8522},
	url = {https://www.sciencedirect.com/science/article/pii/0095852257900405},
	doi = {10.1016/0095-8522(57)90040-5},
	language = {en},
	number = {4},
	urldate = {2023-02-25},
	journal = {Journal of Colloid Science},
	author = {Goring, D. A. I and Senez, M and Melanson, B and Huque, M. M},
	month = aug,
	year = {1957},
	pages = {412--416},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\EWVZF2PS\\0095852257900405.html:text/html},
}

@article{bonnelycke_light_1959,
	title = {Light scattering of colloidal silica},
	volume = {14},
	issn = {0095-8522},
	url = {https://www.sciencedirect.com/science/article/pii/0095852259900236},
	doi = {10.1016/0095-8522(59)90023-6},
	abstract = {The absence of absorption in colloidal silica was demonstrated by varying the solvent refractive index of a set of solutions of the same silica concentration and by showing that the excess turbidity and scattering go to zero concomitantly. A spectrophotometer with a 50-cm. cell was used.},
	language = {en},
	number = {6},
	urldate = {2023-02-25},
	journal = {Journal of Colloid Science},
	author = {Bonnelycke, Byrg E and Dandliker, W. B},
	month = dec,
	year = {1959},
	pages = {567--571},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\IAEY7D5P\\0095852259900236.html:text/html},
}

@article{zhang_wave_2002,
	title = {Wave transport through thin slabs of random media with internal reflection: {Ballistic} to diffusive transition},
	volume = {66},
	shorttitle = {Wave transport through thin slabs of random media with internal reflection},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.66.016612},
	doi = {10.1103/PhysRevE.66.016612},
	abstract = {The static and dynamic properties of wave transport through thin slabs of random media in the presence of internal reflection are investigated by performing first-principles calculations. These results are compared with results from time-independent and time-dependent diffusion equations, respectively, where the effects due to internal reflection are incorporated into an average extrapolation length in the boundary conditions. For the static properties, we find an abrupt transition from ballistic to diffusive behavior when sample thickness is about three mean free paths, i.e., L≈3l. The diffusion approximation is valid when L{\textgreater}3l, independent of the amount of internal reflection. For the dynamic properties, both the peak arrival time at short times and the diffusion constant at long times of the transmitted pulse indicate that there is a region of anomalous diffusion when 3l{\textless}L{\textless}Lc. The diffusion constant in this region increases with decreasing L. It also increases with the amount of internal reflection. The physical origin of the existence of such an anomalous region is the resonance-induced wave focusing effect. Due to the presence of internal reflection, the wave energy tends to concentrate in the forward direction at output boundary. It makes direction randomization difficult in the scattered waves. A similar wave focusing effect has been found in resonant tunneling systems of electrons in the presence of elastic scattering. The diffusion approximation is valid when L{\textgreater}Lc. The value of Lc is about ten times the average extrapolation length, i.e., L≈10ze, where ze is a fast increasing function of the amount of internal reflection.},
	number = {1},
	urldate = {2023-02-25},
	journal = {Physical Review E},
	author = {Zhang, Xiangdong and Zhang, Zhao-Qing},
	month = jul,
	year = {2002},
	note = {Publisher: American Physical Society},
	pages = {016612},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\ESSCFZBW\\PhysRevE.66.html:text/html;Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\T4ACVHW5\\Zhang and Zhang - 2002 - Wave transport through thin slabs of random media .pdf:application/pdf},
}

@article{elaloufi_time-dependent_2002,
	title = {Time-dependent transport through scattering media: from radiative transfer to diffusion},
	volume = {4},
	issn = {1464-4258},
	shorttitle = {Time-dependent transport through scattering media},
	url = {https://dx.doi.org/10.1088/1464-4258/4/5/355},
	doi = {10.1088/1464-4258/4/5/355},
	abstract = {We study the propagation of light pulses through scattering media using the time-dependent radiative transfer equation. A standard discrete-ordinate method is used to solve this equation in the space-frequency domain. We present calculations of diffuse transmission through scattering slabs, in the presence of absorption and anisotropic scattering. We show that the diffusive regime is attained at long times only for thick slabs. Comparisons with diffusion theory show that the proper choice of the diffusion constant is an important issue for time-dependent transport.},
	language = {en},
	number = {5},
	urldate = {2023-02-25},
	journal = {Journal of Optics A: Pure and Applied Optics},
	author = {Elaloufi, Rachid and Carminati, Rémi and Greffet, Jean-Jacques},
	month = aug,
	year = {2002},
	pages = {S103},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\YRR3F7ET\\Elaloufi et al. - 2002 - Time-dependent transport through scattering media.pdf:application/pdf},
}

@article{kim_optical_1998,
	title = {Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer},
	volume = {37},
	copyright = {© 1998 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-37-22-5313},
	doi = {10.1364/AO.37.005313},
	abstract = {We discuss several outstanding theoretical problems in optical diffusion in random media. Specifically, we discuss which of several diffusion theories most closely approximates exact solutions of the equation of transfer. We consider a plane wave impinging upon a plane-parallel slab of a random medium as a model problem to compare the diffusion theories with a numerical solution of the equation of transfer for continuous-wave, pulsed, and photon density waves. In addition, we discuss the validity of the diffusion approximation for a variety of parameter settings to ascertain the diffusion approximation’s applicability to imaging biological media.},
	language = {EN},
	number = {22},
	urldate = {2023-02-25},
	journal = {Applied Optics},
	author = {Kim, Arnold D. and Ishimaru, Akira},
	month = aug,
	year = {1998},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Multiple scattering, Scattering media, Fast Fourier transforms, Photon density waves, Radiative transfer},
	pages = {5313--5319},
	file = {Kim and Ishimaru - 1998 - Optical diffusion of continuous-wave, pulsed, and .pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\NCGHRVGL\\Kim and Ishimaru - 1998 - Optical diffusion of continuous-wave, pulsed, and .pdf:application/pdf},
}

@article{yaroshevsky_transition_2011,
	title = {Transition from the ballistic to the diffusive regime in a turbid medium},
	volume = {36},
	issn = {1539-4794},
	doi = {10.1364/OL.36.001395},
	abstract = {By varying the absorption coefficient and width of an intralipid-India ink solution in a quasi-one-dimensional experiment, we investigate the transition between the ballistic and the diffusive regimes. The medium's attenuation coefficient changes abruptly between two different values within a single mean free path. This problem is analyzed both experimentally and theoretically, and it is demonstrated that the transition location depends on the scattering coefficient as well as on the measuring solid angle.},
	language = {eng},
	number = {8},
	journal = {Optics Letters},
	author = {Yaroshevsky, Andre and Glasser, Ziv and Granot, Er'el and Sternklar, Shmuel},
	month = apr,
	year = {2011},
	pmid = {21499368},
	pages = {1395--1397},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\8H6FITC7\\Yaroshevsky et al. - 2011 - Transition from the ballistic to the diffusive reg.pdf:application/pdf},
}

@article{dezelic_determination_1960,
	title = {Determination of size of small particles by light scattering. experiments on ludox colloidal silica},
	volume = {173},
	issn = {1435-1536},
	url = {https://doi.org/10.1007/BF01513625},
	doi = {10.1007/BF01513625},
	abstract = {Four samples of Ludox colloidal silica were studied by the light transmission and angular scattering method and the size of particles determined. It was found essential for light scattering work to centrifuge the original Ludox solution in order to remove the aggregated material. After this treatment each Ludox sample regardless of age could be used successfully for calibration purposes. The apparent particle sizes in aqueous solutions of Ludox were smaller than those in 0.05 M NaCl solutions, the latter being in very good agreement with electron microscopic values. The refractive index increments of Ludox in water and 0.05 M NaCl were determined at three wavelengths. The influence of cell length and blackening of the cells in transmission measurements were also studied. Dissymmetries and depolarizations were small. All results indicated that particles of Ludox behave practically asRayleigh scatterers. The usefulness of these results for the calibration of light scattering photometers is discussed.},
	language = {en},
	number = {1},
	urldate = {2023-02-24},
	journal = {Kolloid-Zeitschrift},
	author = {Deželić, Gj. and Kratohvil, J. P.},
	month = nov,
	year = {1960},
	pages = {38--48},
	file = {Deželić and Kratohvil - 1960 - Determination of size of small particles by light .pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\66NBTBKG\\Deželić and Kratohvil - 1960 - Determination of size of small particles by light .pdf:application/pdf},
}

@article{lawley_distribution_2020,
	title = {Distribution of extreme first passage times of diffusion},
	volume = {80},
	issn = {1432-1416},
	url = {https://doi.org/10.1007/s00285-020-01496-9},
	doi = {10.1007/s00285-020-01496-9},
	abstract = {Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.},
	language = {en},
	number = {7},
	urldate = {2023-02-15},
	journal = {Journal of Mathematical Biology},
	author = {Lawley, Sean D.},
	month = jun,
	year = {2020},
	pages = {2301--2325},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\AFJ5PIUP\\Lawley - 2020 - Distribution of extreme first passage times of dif.pdf:application/pdf},
}

@article{durduran_does_1997,
	title = {Does the photon-diffusion coefficient depend on absorption?},
	volume = {14},
	copyright = {© 1997 Optical Society of America},
	issn = {1520-8532},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-14-12-3358},
	doi = {10.1364/JOSAA.14.003358},
	abstract = {We investigate the controversy over the precise form of the photon diffusion coefficient and suggest that it is largely independent of absorption, i.e., D0=v/3µs′. After presentation of the general theoretical arguments underlying this assertion, Monte Carlo simulations are performed and explicitly reveal that the absorption-independent diffusion coefficient gives better agreement with theory than the traditionally accepted photon diffusion coefficient, Dμa=v/3(μs′+μa). The importance of resolving this controversy for the proper characterization of the material optical properties is discussed.},
	language = {EN},
	number = {12},
	urldate = {2023-01-31},
	journal = {JOSA A},
	author = {Durduran, T. and Yodh, A. G. and Chance, B. and Boas, D. A.},
	month = dec,
	year = {1997},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Turbid media, Absorption coefficient, Photon diffusion, Photons, Tissue optical properties},
	pages = {3358--3365},
}

@article{dogbe_radiative_2001,
	title = {The radiative transfer equations: diffusion approximation under accretiveness and compactness assumptions},
	volume = {42},
	issn = {0898-1221},
	shorttitle = {The radiative transfer equations},
	url = {https://www.sciencedirect.com/science/article/pii/S0898122101001985},
	doi = {10.1016/S0898-1221(01)00198-5},
	abstract = {When the mean free path of photons is small the radiative transfer equations may be approximated by a nonlinear angular diffusion equation. In order to find the diffusion equation, one uses accretiveness assumptions. But theses assumptions impose some conditions on the opacity. To overcome this inconvenient, we propose to study the solution of the radiative transfer equations by compactness techniques.},
	language = {en},
	number = {6},
	urldate = {2023-01-31},
	journal = {Computers \& Mathematics with Applications},
	author = {Dogbe, C.},
	month = sep,
	year = {2001},
	keywords = {Diffusion approximation, Monotonicity and compactness methods, Radiative transfer equation},
	pages = {783--791},
	file = {ScienceDirect Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\K5GFU2HN\\Dogbe - 2001 - The radiative transfer equations diffusion approx.pdf:application/pdf},
}

@article{saulnier_scatterer_1990,
	title = {Scatterer correlation effects on photon transport in dense random media},
	volume = {42},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.42.2621},
	doi = {10.1103/PhysRevB.42.2621},
	abstract = {Optically disordered systems where the number of scatterers per cubic wave length exceeds unity typically exhibit mean-free-path lengths for photon transport longer than those predicted by the cross section given by Mie theory in the independent-scatterer approximation. The effects of spatial correlation among scatterers on photon transport are investigated in dense colloidal latex suspensions. Transport mean-free-path lengths obtained from time-resolved transmission of picosecond laser pulses, from suspensions successively diluted over two decades of scatterer density, are compared to conventional extinction lengths. Correlations introduced into the Mie formalism via a static structure factor based on a hard-core radial distribution function show good agreement with the experimental results.},
	number = {4},
	urldate = {2023-01-30},
	journal = {Physical Review B},
	author = {Saulnier, P. M. and Zinkin, M. P. and Watson, G. H.},
	month = aug,
	year = {1990},
	note = {Publisher: American Physical Society},
	pages = {2621--2623},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\TUYJQ5PD\\PhysRevB.42.html:text/html},
}

@article{haskell_boundary_1994,
	title = {Boundary conditions for the diffusion equation in radiative transfer},
	volume = {11},
	issn = {1084-7529},
	doi = {10.1364/josaa.11.002727},
	abstract = {Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3\%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50\% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100\%, and a minimum value of 98\% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach.},
	language = {eng},
	number = {10},
	journal = {Journal of the Optical Society of America. A, Optics, Image Science, and Vision},
	author = {Haskell, R. C. and Svaasand, L. O. and Tsay, T. T. and Feng, T. C. and McAdams, M. S. and Tromberg, B. J.},
	month = oct,
	year = {1994},
	pmid = {7931757},
	keywords = {Mathematics, Light, Scattering, Radiation},
	pages = {2727--2741},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\SH47VZKM\\Haskell et al. - 1994 - Boundary conditions for the diffusion equation in .pdf:application/pdf},
}

@article{elaloufi_definition_2003,
	title = {Definition of the diffusion coefficient in scattering and absorbing media},
	volume = {20},
	copyright = {© 2003 Optical Society of America},
	issn = {1520-8532},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-20-4-678},
	doi = {10.1364/JOSAA.20.000678},
	abstract = {We revisit the definition of the diffusion coefficient for light transport in scattering and absorbing media. From an asymptotic analysis of the transport equation, we present a novel derivation of the diffusion coefficient, which is restricted neither to low absorption nor to a situation in which the specific intensity is quasi-isotropic. Our result agrees with previous expressions of the diffusion coefficient in the appropriate limit. Using numerical simulations, we discuss the implications of the proper choice of the diffusion coefficient for time-dependent transport.},
	language = {EN},
	number = {4},
	urldate = {2023-01-26},
	journal = {JOSA A},
	author = {Elaloufi, Rachid and Carminati, Rémi and Greffet, Jean-Jacques},
	month = apr,
	year = {2003},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Numerical simulation, Scattering media, Radiative transfer, Forward scattering, Light scattering},
	pages = {678--685},
}

@article{grebenkov_molecular_2021,
	title = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes},
	volume = {23},
	issn = {1367-2630},
	shorttitle = {A molecular relay race},
	url = {https://dx.doi.org/10.1088/1367-2630/ac1e42},
	doi = {10.1088/1367-2630/ac1e42},
	abstract = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive ‘messengers’: the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.},
	language = {en},
	number = {9},
	urldate = {2023-01-25},
	journal = {New Journal of Physics},
	author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
	month = sep,
	year = {2021},
	note = {Publisher: IOP Publishing},
	pages = {093004},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\TGVL6WAV\\Grebenkov et al. - 2021 - A molecular relay race sequential first-passage e.pdf:application/pdf},
}

@article{osborn_photon_1961,
	title = {Photon transport theory},
	volume = {15},
	issn = {0003-4916},
	url = {https://www.sciencedirect.com/science/article/pii/0003491661900094},
	doi = {10.1016/0003-4916(61)90009-4},
	abstract = {A first order, momentum-configuration space transport equation for photons is derived for low energy (nonrelativistic) systems. The derivation is first order in the sense that the transition probabilities characterizing photon scattering emission and absorption are computed only to the first nonvanishing order by conventional perturbation methods. The present approach provides an essentially axiom-deduction development of the theory of radiative transfer (albeit via several ill-evaluated approximations) within the context of which various processes and their interrelationships may be investigated. Most of these processes have hitherto been studied only phenomenologically and usually piecemeal. Specific application to photon scattering, cyclotron radiation, recombination radiation, de-excitation radiation, and bremsstrahlung is made in the test. The derivation of an H-theorem for photon-particle systems is sketched; and contact is made with the usual statistical mechanical treatment of the equilibrium states of such systems. It is also shown that some aspects of collective particle behavior can be introduced quite naturally into the description of photon transport in the fully ionized plasma.},
	language = {en},
	number = {2},
	urldate = {2023-01-24},
	journal = {Annals of Physics},
	author = {Osborn, R. K and Klevans, E. H},
	month = aug,
	year = {1961},
	pages = {105--140},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\3LBWB3FH\\Osborn and Klevans - 1961 - Photon transport theory.pdf:application/pdf},
}

@article{pierrat_photon_2006,
	title = {Photon diffusion coefficient in scattering and absorbing media},
	volume = {23},
	copyright = {© 2006 Optical Society of America},
	issn = {1520-8532},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-23-5-1106},
	doi = {10.1364/JOSAA.23.001106},
	abstract = {We present a unified derivation of the photon diffusion coefficient for both steady-state and time-dependent transport in disordered absorbing media. The derivation is based on a modal analysis of the time-dependent radiative transfer equation. This approach confirms that the dynamic diffusion coefficient is given by the random-walk result D=cl*/3, where l* is the transport mean free path and c is the energy velocity, independent of the level of absorption. It also shows that the diffusion coefficient for steady-state transport, often used in biomedical optics, depends on absorption, in agreement with recent theoretical and experimental works. These two results resolve a recurrent controversy in light propagation and imaging in scattering media.},
	language = {EN},
	number = {5},
	urldate = {2023-01-24},
	journal = {JOSA A},
	author = {Pierrat, Romain and Greffet, Jean-Jacques and Carminati, Rémi},
	month = may,
	year = {2006},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Scattering media, Radiative transfer, Wave propagation, Photon diffusion, Light propagation},
	pages = {1106--1110},
}

@article{graaff_diffusion_2000,
	title = {Diffusion coefficient in photon diffusion theory},
	volume = {25},
	copyright = {© 2000 Optical Society of America},
	issn = {1539-4794},
	url = {https://opg.optica.org/ol/abstract.cfm?uri=ol-25-1-43},
	doi = {10.1364/OL.25.000043},
	abstract = {The choice of the diffusion coefficient to be used in photon diffusion theory has been a subject of discussion in recent publications on tissue optics. We compared several diffusion coefficients with the apparent diffusion coefficient from the more fundamental transport theory, Dapp. Application to point sources in turbid media, for which exact solutions are available, showed that Dapp has to be preferred. We give a simple equation to approximate Dapp for several phase functions that apply to tissue optics. Reasons for the remaining discrepancies in diffusion coefficients applied to time-resolved and time-averaged descriptions of photon propagation in homogeneous turbid media are discussed.},
	language = {EN},
	number = {1},
	urldate = {2023-01-24},
	journal = {Optics Letters},
	author = {Graaff, R. and Bosch, J. J. Ten},
	month = jan,
	year = {2000},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Attenuation coefficient, Turbid media, Absorption coefficient, Photon diffusion, Photons},
	pages = {43--45},
	file = {Graaff and Bosch - 2000 - Diffusion coefficient in photon diffusion theory.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\TT5WIG7T\\Graaff and Bosch - 2000 - Diffusion coefficient in photon diffusion theory.pdf:application/pdf},
}

@misc{noauthor_hydraharp_nodate,
	title = {{HydraHarp} 400 {\textbar} {PicoQuant}},
	url = {https://www.picoquant.com/products/category/tcspc-and-time-tagging-modules/hydraharp-400-multichannel-picosecond-event-timer-tcspc-module#documents},
	urldate = {2022-07-08},
	file = {HydraHarp 400 | PicoQuant:C\:\\Users\\centrifuge\\Zotero\\storage\\LSAP8LYR\\hydraharp-400-multichannel-picosecond-event-timer-tcspc-module.html:text/html},
}

@article{scott_diffusion_1962,
	title = {Diffusion of ideal gases in capillaries and porous solids},
	volume = {8},
	issn = {1547-5905},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/aic.690080126},
	doi = {10.1002/aic.690080126},
	abstract = {The steady state diffusion of gases through capillaries or through the pores of a solid when the total pressure in the system is constant is considered. It is shown that the ratio of the molar diffusion rate of the lighter gas to that of the heavier gas must be equal to the square root of the ratio of the molecular weight of the heavier to the lighter. From simple momentum transfer considerations a diffusion equation is derived to describe the diffusion rate as the nature of the process changes from ordinary mutual diffusion to Knudsen diffusion. This equation is shown to give good agreement with experimental measurements of diffusion rates in porous solids. A structural parameter of the porous solid, the diffusion ratio, is calculated from the experimental results and compared with the experimental value of the same ratio found from electrical resistance ratios and from flow measurements.},
	language = {en},
	number = {1},
	urldate = {2022-05-09},
	journal = {AIChE Journal},
	author = {Scott, D. S. and Dullien, F. a. L.},
	year = {1962},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/aic.690080126},
	pages = {113--117},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\PZRSKF3F\\aic.html:text/html},
}

@article{pollard_gaseous_1948,
	title = {On {Gaseous} {Self}-{Diffusion} in {Long} {Capillary} {Tubes}},
	volume = {73},
	url = {https://link.aps.org/doi/10.1103/PhysRev.73.762},
	doi = {10.1103/PhysRev.73.762},
	abstract = {A calculation is made of the rate of diffusion of "tagged" molecules in a pure gas at uniform pressure in a long capillary tube of half-length L and radius a. At pressures for which the mean free path λ≫a, the result in the limit L→∞ reduces to that already obtained by M. Knudsen, the diffusion coefficient D being given by 2a¯v3, where ¯v is the mean molecular speed. For a capillary of finite length the diffusion coefficient is, to first order in aL, smaller than this by a factor 1−3a4L. In the opposite limit of high pressures, for which λ≪a, the result reduces to the elementary kinetic theory expression for the self diffusion coefficient, D=λ¯v3. One of the most significant features of the result is that in a long tube the diffusion coefficient drops very rapidly with increasing pressure from its initial value for λ≫L. Thus the initial slope of D as a function of pressure is given by dDd(aλ)≅−12¯va lnLa. It is shown that these results account for the anomalous low pressure minima observed by several investigators who have measured the specific flow GΔp through long capillary tubes as a function of mean pressure ¯p. The failure to observe such minima with porous media, for which effectively L≈a in each pore, is also explained by these results. The formulae obtained here represent a rigorous solution to the long capillary diffusion problem, valid at all pressures and subject only to the limitations of the mean free path type of treatment.},
	number = {7},
	urldate = {2022-05-06},
	journal = {Physical Review},
	author = {Pollard, W. G. and Present, R. D.},
	month = apr,
	year = {1948},
	note = {Publisher: American Physical Society},
	pages = {762--774},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\AISKYQW8\\PhysRev.73.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\SCW4JFRV\\Pollard and Present - 1948 - On Gaseous Self-Diffusion in Long Capillary Tubes.pdf:application/pdf},
}

@article{ahmadi_diffusion_2017,
	title = {Diffusion in quasi-one-dimensional channels: {A} small system n, p, {T}, transition state theory for hopping times},
	volume = {146},
	issn = {0021-9606},
	shorttitle = {Diffusion in quasi-one-dimensional channels},
	url = {https://aip.scitation.org/doi/10.1063/1.4981010},
	doi = {10.1063/1.4981010},
	abstract = {Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric–isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs’ case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.},
	number = {15},
	urldate = {2022-05-06},
	journal = {The Journal of Chemical Physics},
	author = {Ahmadi, Sheida and Bowles, Richard K.},
	month = apr,
	year = {2017},
	note = {Publisher: American Institute of Physics},
	pages = {154505},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\RNLFMRSS\\Ahmadi and Bowles - 2017 - Diffusion in quasi-one-dimensional channels A sma.pdf:application/pdf},
}

@article{takeuchi_second_2018,
	title = {Second messenger molecules have a limited spread in olfactory cilia},
	volume = {150},
	issn = {0022-1295},
	url = {https://doi.org/10.1085/jgp.201812126},
	doi = {10.1085/jgp.201812126},
	abstract = {Odorants are detected by olfactory receptors on the sensory cilia of olfactory receptor cells (ORCs). These cylindrical cilia have a diameters of 100–200 nm, within which the components required for signal transduction by the adenylyl cyclase–cAMP system are located. The kinetics of odorant responses are determined by the lifetimes of active proteins as well as the production, diffusion, and extrusion/degradation of second messenger molecules (cAMP and Ca2+). However, there is limited information about the molecular kinetics of ORC responses, mostly because of the technical limitations involved in studying such narrow spaces and fine structures. In this study, using a combination of electrophysiology, photolysis of caged substances, and spot UV laser stimulation, we show that second messenger molecules work only in the vicinity of their site of generation in the olfactory cilia. Such limited spreading clearly explains a unique feature of ORCs, namely, the integer multiple of unitary events that they display in low Ca2+ conditions. Although the small ORC uses cAMP and Ca2+ for various functions in different regions of the cell, these substances seem to operate only in the compartment that has been activated by the appropriate stimulus. We also show that these substances remain in the same vicinity for a long time. This enables the ORC to amplify the odorant signal and extend the lifetime of Ca2+-dependent adaptation. Cytoplasmic buffers and extrusion/degradation systems seem to play a crucial role in limiting molecular spreading. In addition, binding sites on the cytoplasmic surface of the plasma membrane may limit molecular diffusion in such a narrow space because of the high surface/volume ratio. Such efficient energy conversion may also be broadly used in other biological systems that have not yet been subjected to systematic experiments.},
	number = {12},
	urldate = {2022-05-06},
	journal = {Journal of General Physiology},
	author = {Takeuchi, Hiroko and Kurahashi, Takashi},
	month = oct,
	year = {2018},
	pages = {1647--1659},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\P5LJLZ33\\Takeuchi and Kurahashi - 2018 - Second messenger molecules have a limited spread i.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\WTTZVD58\\Second-messenger-molecules-have-a-limited-spread.html:text/html},
}

@article{pattelli_experimental_2022,
	title = {Experimental imaging and {Monte} {Carlo} modeling of ultrafast pulse propagation in thin scattering slabs},
	volume = {27},
	issn = {1083-3668, 1560-2281},
	url = {https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-27/issue-8/083020/Experimental-imaging-and-Monte-Carlo-modeling-of-ultrafast-pulse-propagation/10.1117/1.JBO.27.8.083020.full},
	doi = {10.1117/1.JBO.27.8.083020},
	abstract = {Significance: Most radiative transport problems in turbid media are typically associated with mm or cm scales, leading to typical time scales in the range of hundreds of ps or more. In certain cases, however, much thinner layers can also be relevant, which can dramatically alter the overall transport properties of a scattering medium. Studying scattering in these thin layers requires ultrafast detection techniques and adaptations to the common Monte Carlo (MC) approach. Aim: We aim to discuss a few relevant aspects for the simulation of light transport in thin scattering membranes, and compare the obtained numerical results with experimental measurements based on an all-optical gating technique. Approach: A thin membrane with controlled scattering properties based on polymer-dispersed TiO2 nanoparticles is fabricated for experimental validation. Transmittance measurements are compared against a custom open-source MC implementation including specific pulse profiles for tightly focused femtosecond laser pulses. Results: Experimental transmittance data of ultrafast pulses through a thin scattering sample are compared with MC simulations in the spatiotemporal domain to retrieve its scattering properties. The results show good agreement also at short distances and time scales. Conclusions: When simulating light transport in scattering membranes with thicknesses in the orders of tens of micrometer, care has to be taken when describing the temporal, spatial, and divergence profiles of the source term, as well as the possible truncation of step length distributions, which could be introduced by simple strategies for the generation of random exponentially distributed variables.},
	number = {8},
	urldate = {2025-03-03},
	journal = {Journal of Biomedical Optics},
	author = {Pattelli, Lorenzo and Mazzamuto, Giacomo},
	month = jun,
	year = {2022},
	note = {Publisher: SPIE},
	pages = {083020},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\Y4NTQ9IE\\Pattelli and Mazzamuto - 2022 - Experimental imaging and Monte Carlo modeling of ultrafast pulse propagation in thin scattering slab.pdf:application/pdf},
}

@article{svensson_exploiting_2013,
	title = {Exploiting breakdown of the similarity relation for diffuse light transport: simultaneous retrieval of scattering anisotropy and diffusion constant},
	volume = {38},
	copyright = {© 2013 Optical Society of America},
	issn = {1539-4794},
	shorttitle = {Exploiting breakdown of the similarity relation for diffuse light transport},
	url = {https://opg.optica.org/ol/abstract.cfm?uri=ol-38-4-437},
	doi = {10.1364/OL.38.000437},
	abstract = {As manifested in the similarity relation of diffuse light transport, it is difficult to assess single scattering characteristics from multiply scattered light. We take advantage of the limited validity of the diffusion approximation of light transport and demonstrate, experimentally and numerically, that even deep into the multiple scattering regime, time-resolved detection of transmitted light allows simultaneous assessment of both single scattering anisotropy and scattering mean free path, and therefore also macroscopic parameters like the diffusion constant and the transport mean free path. This is achieved via careful assessment of early light and matching against Monte Carlo simulations of radiative transfer.},
	language = {EN},
	number = {4},
	urldate = {2025-03-03},
	journal = {Optics Letters},
	author = {Svensson, T. and Savo, R. and Alerstam, E. and Vynck, K. and Burresi, M. and Wiersma, D. S.},
	month = feb,
	year = {2013},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Turbid media, Optical properties, Absorption coefficient, Forward scattering, Anisotropy},
	pages = {437--439},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\RH5W4JSP\\Svensson et al. - 2013 - Exploiting breakdown of the similarity relation for diffuse light transport simultaneous retrieval.pdf:application/pdf},
}

@article{pini_non-self-similar_2024,
	title = {Non-self-similar light transport in scattering media},
	volume = {6},
	url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.L032026},
	doi = {10.1103/PhysRevResearch.6.L032026},
	abstract = {Transport processes underpin a wide variety of phenomena, ranging from chemistry, to physics and ecology. Despite their pervasiveness, however, several distinctive features of these processes are still elusive, making it difficult to recognize and classify the associated transport regimes. Using light scattering as a probe to explore different propagation regimes, we report on the experimental observation of non-self-similar light transport through turbid membranes. Our results show that a breakdown of self-similarity can arise for light waves even in the presence of isotropic and homogeneous disorder, and can be tuned by varying the turbidity of the system. By introducing the concept of self-similarity for light propagation, we provide a unified framework for the classification of light transport regimes—overcoming the dichotomy between normal and anomalous diffusion—and show that non-self-similar propagation is a common and experimentally accessible phenomenon. This insight can help to understand and model other scenarios where light transport is dominated by rare propagation events, such as in nonlinear and active media, but also in other fields of research beyond optics.},
	number = {3},
	urldate = {2025-03-03},
	journal = {Physical Review Research},
	author = {Pini, Ernesto and Mazzamuto, Giacomo and Riboli, Francesco and Wiersma, Diederik S. and Pattelli, Lorenzo},
	month = jul,
	year = {2024},
	note = {Publisher: American Physical Society},
	pages = {L032026},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\H999TNJY\\Pini et al. - 2024 - Non-self-similar light transport in scattering media.pdf:application/pdf},
}

@article{mazzamuto_deducing_2016,
	title = {Deducing effective light transport parameters in optically thin systems},
	volume = {18},
	issn = {1367-2630},
	url = {https://dx.doi.org/10.1088/1367-2630/18/2/023036},
	doi = {10.1088/1367-2630/18/2/023036},
	abstract = {We present an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation. We systematically characterize diffusive transport in this intermediate scattering regime, notably in terms of the spatial variance of the transmitted/reflected profile. Focusing on late, multiply scattered light, we test the validity of the prediction cast by diffusion theory that the spatial variance should grow independently of absorption and, to a first approximation, of the sample thickness and refractive index contrast. Based on a large set of simulated data, we build a freely available look-up table routine enabling reliable and precise determination of the microscopic transport parameters starting from robust observables which are independent from absolute intensity measurements. We also present the Monte Carlo software package that was developed for the purpose of this study.},
	language = {en},
	number = {2},
	urldate = {2025-03-03},
	journal = {New Journal of Physics},
	author = {Mazzamuto, G and Pattelli, L and Toninelli, C and Wiersma, D S},
	month = feb,
	year = {2016},
	note = {Publisher: IOP Publishing},
	pages = {023036},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\CLAD3RRD\\Mazzamuto et al. - 2016 - Deducing effective light transport parameters in optically thin systems.pdf:application/pdf},
}

@article{pattelli_role_2018,
	title = {Role of packing density and spatial correlations in strongly scattering {3D} systems},
	volume = {5},
	copyright = {© 2018 Optical Society of America},
	issn = {2334-2536},
	url = {https://opg.optica.org/optica/abstract.cfm?uri=optica-5-9-1037},
	doi = {10.1364/OPTICA.5.001037},
	abstract = {Discrete random media have been investigated extensively over the past century due to their ability to scatter light. Even so, the link between the three-dimensional (3D) spatial distribution of the scattering elements and the resulting opacity is still lively debated to date due to different experimental conditions, range of parameters explored, or sample formulations. On the other hand, a unified numerical survey with controlled parameters has been impractical up to date due to the sheer computational power required to address samples with representative size. In this work, we exploit a graphics processing unit implementation of the T-matrix method to investigate the complete range of particle volume concentration and packing-induced spatial correlations, allowing us to reveal and elucidate a twofold role played by spatial correlations in either enhancing or suppressing opacity. By applying these findings to the illustrative case of white paint, we determine the optimal combination of density and spatial correlations corresponding to the highest opacity.},
	language = {EN},
	number = {9},
	urldate = {2025-03-03},
	journal = {Optica},
	author = {Pattelli, Lorenzo and Egel, Amos and Lemmer, Uli and Wiersma, Diederik S.},
	month = sep,
	year = {2018},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Scattering media, Effective medium theory, Effective refractive index, Phase space analysis methods, Reflector design},
	pages = {1037--1045},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\7953HXT2\\Pattelli et al. - 2018 - Role of packing density and spatial correlations in strongly scattering 3D systems.pdf:application/pdf},
}

@article{rezvani_naraghi_near-field_2015,
	title = {Near-{Field} {Effects} in {Mesoscopic} {Light} {Transport}},
	volume = {115},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.115.203903},
	doi = {10.1103/PhysRevLett.115.203903},
	abstract = {In dense multiple scattering media, optical fields evolve through both homogeneous and evanescent waves. New regimes of light transport emerge because of the near-field coupling between individual scattering centers at mesoscopic scales. We present a novel propagation model that is developed in terms of measurable far- and near-field scattering cross sections. Our quantitative description explains the increase of total transmission in dense scattering media and its accuracy is established through both full-scale numerical calculations and enhanced backscattering experiments.},
	number = {20},
	urldate = {2025-03-03},
	journal = {Physical Review Letters},
	author = {Rezvani Naraghi, R. and Sukhov, S. and Sáenz, J. J. and Dogariu, A.},
	month = nov,
	year = {2015},
	note = {Publisher: American Physical Society},
	pages = {203903},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\W872Z8I3\\PhysRevLett.115.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\NU6IVPXE\\Rezvani Naraghi et al. - 2015 - Near-Field Effects in Mesoscopic Light Transport.pdf:application/pdf},
}

@article{einstein_uber_1905-1,
	title = {Über einen die {Erzeugung} und {Verwandlung} des {Lichtes} betreffenden heuristischen {Gesichtspunkt}},
	volume = {322},
	issn = {1521-3889},
	url = {https://onlinelibrary.wiley.com/doi/10.1002/andp.19053220607},
	doi = {https://doi.org/10.1002/andp.19053220607},
	language = {en},
	number = {6},
	urldate = {2025-03-03},
	journal = {Annalen der Physik},
	author = {Einstein, A.},
	year = {1905},
	pages = {132--148},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\ZUSBN7V3\\Einstein - 2005 - Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt [AdP 1.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\M5LGG37I\\andp.html:text/html},
}

@article{boltzmann_weitere_1872,
	title = {Weitere {Studien} über das {Warmegleichgewicht} unter {Gasmolekülen} ({Further} {Studies} on the {Thermal} {Equilibrium} of {Gas} {Molecules}, {The} {Kinetic} {Theory} of {Gases})},
	volume = {66},
	url = {https://link.springer.com/chapter/10.1007/978-3-322-84986-1_3},
	urldate = {2025-03-03},
	journal = {Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften},
	author = {Boltzmann, Ludwig},
	year = {1872},
	pages = {275--370},
}

@book{maxwell_theory_1908,
	title = {Theory of heat},
	url = {http://archive.org/details/theoryofheat00maxwrich},
	abstract = {xiv, 348 p. 18 cm},
	language = {eng},
	urldate = {2025-03-03},
	publisher = {London, New York [etc.] Longmans, Green},
	author = {Maxwell, James Clerk and Rayleigh, John William Strutt},
	collaborator = {{University of California Libraries}},
	year = {1908},
	keywords = {Heat},
}

@book{sadi_carnot_reflexions_1824,
	address = {Paris},
	title = {Réflexions sur la puissance motrice du feu et sur les machines propres à développer atte puissance},
	copyright = {http://creativecommons.org/publicdomain/mark/1.0/},
	url = {http://archive.org/details/bub_gb_QX9iIWF3yOMC},
	language = {French},
	urldate = {2025-03-03},
	publisher = {Bachelier Libraire},
	author = {{Sadi Carnot}},
	collaborator = {{Library of Catalonia}},
	year = {1824},
	keywords = {bub\_upload},
}

@book{joule_scientific_2011,
	address = {Cambridge},
	series = {Cambridge {Library} {Collection} - {Physical}  {Sciences}},
	title = {The {Scientific} {Papers} of {James} {Prescott} {Joule}},
	volume = {1},
	isbn = {978-1-108-02882-0},
	url = {https://www.cambridge.org/core/books/scientific-papers-of-james-prescott-joule/8CF41E4B18482E071294E510DAB3522F},
	abstract = {Sir James Prescott Joule (1818–1889) became one of the most significant physicists of the nineteenth century, although his original interest in science was as a hobby and for practical business purposes. The son of a brewer, he began studying heat while investigating how to increase the efficiency of electric motors. His discovery of the relationship between heat and energy contributed to the discovery of the conservation of energy and the first law of thermodynamics. Volume 1 of Joule's scientific papers was published in 1884. It is organised chronologically and reveals the range of Joule's interests and the development of his thought. The topics of the papers include the measurement of heat, voltaic batteries, electromagnets, specific heat, meteorology and thermodynamics. Joule's careful experiments in these areas were fundamental to the development of significant areas of twentieth-century physics, although he was slow to gain recognition from his contemporaries.},
	urldate = {2025-03-03},
	publisher = {Cambridge University Press},
	author = {Joule, James Prescott},
	year = {2011},
	doi = {10.1017/CBO9780511995170},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\X5428NJG\\8CF41E4B18482E071294E510DAB3522F.html:text/html},
}

@article{joule_iii_1997,
	title = {{III}. {On} the mechanical equivalent of heat},
	volume = {140},
	url = {https://royalsocietypublishing.org/doi/10.1098/rstl.1850.0004},
	doi = {10.1098/rstl.1850.0004},
	abstract = {“Heat is a very brisk agitation of the insensible parts of the object, which produces in us that sensation from whence we denominate the object hot; so what in our sensation is heat, in the object is nothing but motion.”—Locke. “The force of a moving body is proportional to the square of its velocity, or to the height to which it would rise against gravity.”— Leibnitz.},
	urldate = {2025-03-03},
	journal = {Philosophical Transactions of the Royal Society of London},
	author = {Joule, James Prescott and Faraday, Michael},
	month = jan,
	year = {1997},
	note = {Publisher: Royal Society},
	pages = {61--82},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\6YU794PS\\Joule and Faraday - 1997 - III. On the mechanical equivalent of heat.pdf:application/pdf},
}

@article{joule_iii_1857,
	title = {{III}. {On} the thermal effects of fluids in motion},
	volume = {8},
	url = {https://royalsocietypublishing.org/doi/10.1098/rspl.1856.0048},
	doi = {10.1098/rspl.1856.0048},
	urldate = {2025-03-03},
	journal = {Proceedings of the Royal Society of London},
	author = {Joule, James Prescott and Thomson, William},
	year = {1857},
	pages = {178--185},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\E9MZWC23\\Joule and Thomson - 1997 - III. On the thermal effects of fluids in motion.pdf:application/pdf},
}

@incollection{thomson_dynamical_1851,
	series = {Transactions of {The} {Royal} {Society} of {Edinburgh}},
	title = {On the dynamical theory of heat, with numerical results deduced from {Mr} {Joule}'s equivalent of a thermal unit, and {M}. {Regnault}'s {Observations} on steam.},
	volume = {20},
	isbn = {978-1-108-02898-1},
	url = {https://www.cambridge.org/core/books/mathematical-and-physical-papers/on-the-dynamical-theory-of-heat-with-numerical-results-deduced-from-mr-joules-equivalent-of-a-thermal-unit-and-m-regnaults-observations-on-steam/804E85646C55128B340A0F4D54EF2CF5},
	urldate = {2025-03-03},
	booktitle = {Mathematical and {Physical} {Papers}},
	publisher = {Royal Society of Edinburgh},
	editor = {Thomson, William},
	year = {1851},
	pages = {174--332},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\KVMSSHJH\\804E85646C55128B340A0F4D54EF2CF5.html:text/html},
}

@book{fourier_analytical_1878,
	address = {Cambridge},
	title = {The analytical theory of heat},
	abstract = {Includes bibliographical references.},
	language = {eng},
	publisher = {At the University Press},
	author = {Fourier, Jean-Baptiste-Joseph},
	translator = {Freeman, Alexander},
	year = {1878},
	keywords = {Heat},
}

@book{lomonosov_mikhail_1970,
	title = {Mikhail {Vasil}'evich {Lomonosov} on the {Corpuscular} {Theory}},
	url = {http://archive.org/details/mikhailvasilevic017733mbp},
	language = {eng},
	urldate = {2025-03-03},
	publisher = {Harvard University Press},
	author = {Lomonosov, Mikhail Vasil'evich},
	translator = {{Henry M. Leicester}},
	year = {1970},
}

@book{bernoulli_hydrodynamica_1738,
	title = {Hydrodynamica, sive de viribus et motibus fluidorum commentarii : opus academicum ab auctore, dum {Petropoli} ageret, congestum},
	shorttitle = {Hydrodynamica, sive de viribus et motibus fluidorum commentarii},
	url = {http://www.e-rara.ch/zut/1227730},
	abstract = {ETH-Bibliothek (NEBIS). Bernoulli, Daniel: Danielis Bernoulli ... Hydrodynamica, sive de viribus et motibus fluidorum commentarii : opus academicum ab auctore, dum Petropoli ageret, congestum. Argentorati : sumptibus Johannis Reinholdi Dulseckeri : Typis Joh. Deckeri, typographi Basiliensis, anno 1738},
	language = {Latin},
	urldate = {2025-03-03},
	author = {Bernoulli, Daniel},
	year = {1738},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\MAC3IPCV\\e-rara-3911.html:text/html},
}

@article{newton_vii_1997,
	title = {{VII}. {Scala} graduum caloris},
	volume = {22},
	url = {https://royalsocietypublishing.org/doi/10.1098/rstl.1700.0082},
	doi = {10.1098/rstl.1700.0082},
	abstract = {Calor aeris hyberni ubi aqua incipit glurigescere. Innotescit hic calor accurate locando Thermometrum in nive compressaquo tempore gelu solvitur.},
	number = {270},
	urldate = {2025-03-03},
	journal = {Philosophical Transactions of the Royal Society of London},
	author = {Newton},
	month = jan,
	year = {1997},
	note = {Publisher: Royal Society},
	pages = {824--829},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\G6V97C4D\\1997 - VII. Scala graduum caloris.pdf:application/pdf},
}

@article{halley_historical_1686,
	title = {An {Historical} {Account} of the {Trade} {Winds}, and {Monsoons}, {Observable} in the {Seas} between and {Near} the {Tropicks}, with an {Attempt} to {Assign} the {Phisical} {Cause} of the {Said} {Winds}, {By} {E}. {Halley}},
	volume = {16},
	issn = {0260-7085},
	language = {eng},
	journal = {Philosophical transactions (Royal Society (Great Britain) : 1683)},
	author = {Halley, E.},
	year = {1686},
	note = {Publisher: The Royal Society},
	keywords = {Air, Land, Monsoons, Nomber 183, Ocean navigation, Oceans, Rainy seasons, Seas, Serenity, Trade winds, Wind},
	pages = {153--168},
}

@book{boyle_new_1660,
	address = {Oxford},
	title = {New experiments physico-mechanicall, touching the spring of the air, and its effects (made, for the most part, in a new pneumatical engine): written by way of letter to the {Right} {Honorable} {Charles}, {Lord} {Vicount} of {Dungarvan}, eldest son to the {Earl} of {Corke}},
	shorttitle = {New experiments physico-mechanicall, touching the spring of the air, and its effects (made, for the most part, in a new pneumatical engine)},
	abstract = {Errata: p. [1] at end., Reproduction of original in Yale University Library., Imperfect: folded plate lacking.},
	language = {eng},
	publisher = {Printed by H. Hall ... for Tho. Robinson},
	author = {Boyle, Robert},
	year = {1660},
	keywords = {Air, Air-pump, Early works to 1800},
}

@book{bacon_novum_1902,
	address = {New York},
	title = {Novum {Organum}; {Or}, {True} {Suggestions} for the {Interpretation} of {Nature}},
	copyright = {Public domain in the USA.},
	url = {https://www.gutenberg.org/cache/epub/45988/pg45988-images.html},
	language = {en},
	urldate = {2025-03-03},
	publisher = {P. F. COLLIER \& SON},
	author = {Bacon, Francis},
	editor = {Devey, Joseph},
	year = {1902},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\BBN3539J\\pg45988-images.html:text/html},
}

@article{graham_xxvii_1833,
	title = {{XXVII}. {On} the law of the diffusion of gases},
	volume = {2},
	issn = {1941-5966},
	url = {https://doi.org/10.1080/14786443308648004},
	doi = {10.1080/14786443308648004},
	number = {9},
	urldate = {2025-03-03},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Graham, Thomas},
	month = mar,
	year = {1833},
	note = {Publisher: Taylor \& Francis
\_eprint: https://doi.org/10.1080/14786443308648004},
	pages = {175--190},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\CI3U3WP7\\Graham - 1833 - XXVII. On the law of the diffusion of gases.pdf:application/pdf},
}

@article{gombosi_telegraph_1993,
	title = {The {Telegraph} {Equation} in {Charged} {Particle} {Transport}},
	volume = {403},
	issn = {0004-637X},
	url = {https://ui.adsabs.harvard.edu/abs/1993ApJ...403..377G},
	doi = {10.1086/172209},
	abstract = {We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.},
	urldate = {2024-12-03},
	journal = {The Astrophysical Journal},
	author = {Gombosi, T. I. and Jokipii, J. R. and Kota, J. and Lorencz, K. and Williams, L. L.},
	month = jan,
	year = {1993},
	note = {Publisher: IOP},
	keywords = {ACCELERATION OF PARTICLES, Asymptotic Methods, Charged Particles, ISM: COSMIC RAYS, Numerical Analysis, Partial Differential Equations, Plasma Physics, RADIATIVE TRANSFER, Transport Properties, Transport Theory},
	pages = {377},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\YYYVYCWB\\Gombosi et al. - 1993 - The Telegraph Equation in Charged Particle Transport.pdf:application/pdf},
}

@article{schuster_radiation_1905,
	title = {Radiation {Through} a {Foggy} {Atmosphere}},
	volume = {21},
	issn = {0004-637X},
	url = {https://ui.adsabs.harvard.edu/abs/1905ApJ....21....1S},
	doi = {10.1086/141186},
	urldate = {2024-05-10},
	journal = {The Astrophysical Journal},
	author = {Schuster, Arthur},
	month = jan,
	year = {1905},
	note = {Publisher: IOP},
	pages = {1},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\EAZCAZVG\\Schuster - 1905 - Radiation Through a Foggy Atmosphere.pdf:application/pdf},
}

@inproceedings{taitelbaum_diagnosis_1999,
	address = {Berlin, Heidelberg},
	series = {Lecture {Notes} in {Physics}},
	title = {Diagnosis using photon diffusion: {From} brain oxygenation to the fat of the atlantic salmon},
	volume = {519},
	isbn = {978-3-540-49259-7},
	shorttitle = {Diagnosis using photon diffusion},
	doi = {10.1007/BFb0106840},
	abstract = {We present a new diagnostic method, based on optical measurements in the visible and near-infrared wavelength regime. This method has many advantages over current imaging and biopsy techniques. In order to understand and interpret the results of the measurements, a random-walk on a lattice is used to model photon diffusion in biological tissues. Applications of this method range from medicine (diagnosis of brain function (oxygenation) in neonates and early detection of breast tumors) to food science (non-destructive determination of fat and moisture content in Atlantic Salmon).},
	language = {en},
	booktitle = {Anomalous {Diffusion} {From} {Basics} to {Applications}},
	publisher = {Springer},
	author = {Taitelbaum, H.},
	editor = {Pękalski, Andrzej and Sznajd-Weron, Katarzyna},
	year = {1999},
	keywords = {Average Path Length, Biological Tissue, Optical Biopsy, Photon Trajectory, Turbid Medium},
	pages = {160--174},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\RQYXUFUL\\Taitelbaum - 1999 - Diagnosis using photon diffusion From brain oxyge.pdf:application/pdf},
}

@article{heizler_asymptotic_2012,
	title = {The {Asymptotic} {Telegrapher}’s {Equation} ({P1}) {Approximation} for {Time}-{Dependent}, {Thermal} {Radiative} {Transfer}},
	volume = {41},
	issn = {0041-1450},
	url = {https://doi.org/10.1080/00411450.2012.671205},
	doi = {10.1080/00411450.2012.671205},
	abstract = {We develop the asymptotic P 1 approximation for the time-dependent thermal radiative transfer equation for a multidimensional general geometry. Careful derivation of the asymptotic P 1 equations, directly from the time-dependent Boltzmann equation, yields a particle velocity that is closer (v≈0.91c) to the exact value of c but is based on an asymptotic analysis rather than diffusion theory (infinite velocity) or conventional P 1 theory (which gives rise to the Telegrapher’s equation, ). While this approach does not match the exact value of c as does the P 1/3 method, the latter method is an ad hoc approach that has not been justified on theoretical grounds. This article provides the theoretical justification for the almost-correct value of c that yields improved results for the well-known (one-dimensional) Su-Olson benchmark for radiative transfer, for which we obtain a semi-analytic solution in the case of local thermodynamic equilibrium. We found that the asymptotic P 1 approximation yields a better solution than the diffusion, the classic P 1, and the P 1/3 approximations, yielding the correct steady-state behavior for the energy density and the (almost) correct particle velocity.},
	number = {3-4},
	urldate = {2024-09-23},
	journal = {Transport Theory and Statistical Physics},
	author = {Heizler, Shay I.},
	month = may,
	year = {2012},
	note = {Publisher: Taylor and Francis},
	keywords = {Boltzmann equation, diffusion equation, kinetic theory, radiative transfer, transport theory},
	pages = {175--199},
}

@article{goldstein_diffusion_1951,
	title = {On {Diffusion} by {Discontinuous} {Movements}, and on the {Telegraph} {Equation}},
	volume = {4},
	issn = {0033-5614},
	url = {https://doi.org/10.1093/qjmam/4.2.129},
	doi = {10.1093/qjmam/4.2.129},
	abstract = {At time t=0 a large number of non-interacting particles start from an origin and move with a uniform velocity υ along a straight line for an interval of time τ. To begin with, half move in each direction. Thereafter, and at the end of each successive interval of time τ, each particle starts a new partial path; it still moves with speed υ, and there is a probability p that it will continue to move in the same direction as in its previous path, and a probability q (= 1−p) that the direction of its velocity will be reversed, so the directions in any two consecutive intervals are correlated with a correlation coefficient c=p−q. The partial correlations for non-consecutive intervals are zero. The difference equation is found for the fraction γ(n,ν) of the number of particles at a distance y=νυτ from the origin after a time t=nτ; it is shown how γ(n,ν) may be computed; asymptotic formulae for large n are found, both for a fixed value p/q and for a fixed value of nq/p. The limiting density distribution (and the limiting characteristic function) are found when n→∞, τ→0, with nτ=t, νυτ=y, and in the limiting operation c=1−τ/A, with A constant, so that c→1, and the speed υ is kept constant; the limiting form of the difference equation is the telegraph equation, with υ2=(LC)−1, A=L/R, where L, C, and R are the self-inductance, capacitance, and resistance per unit length; and the limiting density distribution is the solution of this equation for an instantaneous source. If p+q≠1, and there is, at the end of each interval of time τ, a non-zero probability, 1−p−q, that a particle will escape from the system, then the same limiting operation, with T/(1−p−q)=G, G constant, leads to the telegraph equation with leakage, the leakage resistance being G/C. The solution of the telegraph equation is further considered (and in particular is given in terms of Lommel's function of two variables) when one end of a long cable is held at a constant potential for t≥0.},
	number = {2},
	urldate = {2024-08-13},
	journal = {The Quarterly Journal of Mechanics and Applied Mathematics},
	author = {Goldstein, S.},
	month = jan,
	year = {1951},
	pages = {129--156},
	file = {GOLDSTEIN - 1951 - ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON TH.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\N2TZ2WCL\\GOLDSTEIN - 1951 - ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON TH.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\P2NM5ELK\\1874849.html:text/html},
}

@book{redner_guide_2001,
	address = {Cambridge},
	title = {A {Guide} to {First}-{Passage} {Processes}},
	isbn = {978-0-521-65248-3},
	url = {https://www.cambridge.org/core/books/guide-to-firstpassage-processes/59066FD9754B42D22B028E33726D1F07},
	abstract = {First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems and the kinetics of diffusion-controlled reactions. First-passage processes provide an appealing way for graduate students and researchers in physics, chemistry, theoretical biology, electrical engineering, chemical engineering, operations research and finance to understand all of these systems.},
	urldate = {2025-01-10},
	publisher = {Cambridge University Press},
	author = {Redner, Sidney},
	year = {2001},
	doi = {10.1017/CBO9780511606014},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\2PLCYWU7\\Redner - 2001 - A Guide to First-Passage Processes.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\LYNH9XZ2\\59066FD9754B42D22B028E33726D1F07.html:text/html},
}

@book{lakowicz_principles_2006,
	address = {Boston, MA},
	title = {Principles of {Fluorescence} {Spectroscopy}},
	copyright = {https://www.springernature.com/gp/researchers/text-and-data-mining},
	isbn = {978-0-387-31278-1 978-0-387-46312-4},
	url = {https://link.springer.com/10.1007/978-0-387-46312-4},
	language = {en},
	urldate = {2025-01-06},
	publisher = {Springer US},
	editor = {Lakowicz, Joseph R.},
	year = {2006},
	doi = {10.1007/978-0-387-46312-4},
	keywords = {Biophysics, DNA, fluorescence, biochemistry, bioengineering, biology, Biopolymer, biotechnology, Fluorophore, imaging, microscopy},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\9L7DPESN\\Lakowicz - 2006 - Principles of Fluorescence Spectroscopy.pdf:application/pdf},
}

@incollection{lakowicz_instrumentation_2006,
	address = {Boston, MA},
	title = {Instrumentation for {Fluorescence} {Spectroscopy}},
	isbn = {978-0-387-46312-4},
	url = {https://doi.org/10.1007/978-0-387-46312-4_2},
	abstract = {The success of fluorescence experiments requires attention to experimental details and an understanding of the instrumentation. There are also many potential artifacts that can distort the data. Light can be detected with high sensitivity. As a result, the gain or amplification of instruments can usually be increased to obtain observable signals, even if the sample is nearly nonfluorescent. These signals seen at high amplification may not originate with the fluorophore of interest. Instead, the interference can be due to background fluorescence from the solvents, light leaks in the instrumentation, emission from the optical components, stray light passing through the optics, light scattered by turbid solutions, and Rayleigh and/or Raman scatter, to name a few interference sources.},
	language = {en},
	urldate = {2025-01-06},
	booktitle = {Principles of {Fluorescence} {Spectroscopy}},
	publisher = {Springer US},
	editor = {Lakowicz, Joseph R.},
	year = {2006},
	doi = {10.1007/978-0-387-46312-4_2},
	keywords = {Emission Spectrum, Fluorescence Quantum Yield, Fluorescence Spectroscopy, Stray Light, Xenon Lamp},
	pages = {27--61},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\CSK5P6NA\\Lakowicz - 2006 - Instrumentation for Fluorescence Spectroscopy.pdf:application/pdf},
}

@article{toublanc_henyeygreenstein_1996,
	title = {Henyey–{Greenstein} and {Mie} phase functions in {Monte} {Carlo} radiative transfer computations},
	volume = {35},
	copyright = {© 1996 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-35-18-3270},
	doi = {10.1364/AO.35.003270},
	abstract = {Monte Carlo radiative transfer simulation of light scattering in planetary atmospheres is not a simple problem, especially the study of angular distribution of light intensity. Approximate phase functions such as Henyey–Greenstein, modified Henyey–Greenstein, or Legendre polynomial decomposition are often used to simulate the Mie phase function. An alternative solution using an exact calculation alleviates these approximations.},
	language = {EN},
	number = {18},
	urldate = {2024-12-06},
	journal = {Applied Optics},
	author = {Toublanc, Dominique},
	month = jun,
	year = {1996},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Mie scattering, Refractive index, Aerosols, Geometric optics, Phase},
	pages = {3270--3274},
}

@incollection{pu_basic_2019,
	series = {Nanophotonics},
	title = {Basic {Optical} {Scattering} {Parameter} of the {Brain} and {Prostate} {Tissues} in the {Spectral} {Range} of 400–2400   nm},
	isbn = {978-0-323-48067-3},
	url = {https://www.sciencedirect.com/science/article/pii/B9780323480673000111},
	abstract = {The scattering coefficient, μs, the anisotropy factor, g, the scattering phase function, p(θ), and the angular and wavelength dependences of scattering intensity distributions of discrete particles in different size were systematically investigated from spectral range of 400 to 2400nm as a function of wavelength, scattering angle, and scattering particle size using Mie theory and experimental parameters. The MATLAB-based codes using Mie theory for both spherical and cylindrical models were developed and applied for studying the light propagation and the key scattering properties of the discrete particles. The optical and structural parameters of tissue such as the index of refraction of cytoplasm, size of nuclei, and the diameter of the nucleoli for cancerous and normal human tissues obtained from the previous biological, biomedical, and bio-optic studies were used for Mie theory simulation and calculation. The wavelength dependence of scattering coefficient, anisotropy factor, and reduced scattering coefficients were investigated in the wide spectral range from 300 to 2400nm. The scattering particle size dependence of μs, g, and scattering angular distributions was studied. The results show that larger size scattering particles have more contribution to the forward scattering in comparison with the smaller particles. In addition to the conventional simulation model that approximately considers the scattering particles as spheres, the cylinder model that is more suitable for fiber-like tissue frame components such as collagen and elastin was used for developing a computation code to study angular dependence of light scattering in turbid particle media and tissue for the first time.},
	urldate = {2024-12-06},
	booktitle = {Neurophotonics and {Biomedical} {Spectroscopy}},
	publisher = {Elsevier},
	author = {Pu, Yang and Chen, Jun and Wang, Wubao and Alfano, Robert R.},
	editor = {Alfano, Robert R. and Shi, Lingyan},
	month = jan,
	year = {2019},
	doi = {10.1016/B978-0-323-48067-3.00011-1},
	keywords = {Absorption coefficient, Anisotropy factor, Brain and prostate tissues, Discrete particles, Mie theory, Near-infrared spectroscopy, Reduced scattering coefficient, Scattering coefficient},
	pages = {229--252},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\TTBY53KV\\B9780323480673000111.html:text/html},
}

@book{ishimaru_wave_1997,
	title = {Wave {Propagation} and {Scattering} in {Random} {Media}},
	isbn = {978-0-7803-4717-5},
	url = {https://ieeexplore.ieee.org/book/5270963},
	urldate = {2023-02-25},
	author = {Ishimaru, Akira},
	year = {1997},
	file = {Ishimaru - Wave Propagation and Scattering in Random Media  .pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\GV75QISR\\Ishimaru - Wave Propagation and Scattering in Random Media  .pdf:application/pdf;Wave Propagation and Scattering in Random Media | IEEE eBooks | IEEE Xplore:C\:\\Users\\centrifuge\\Zotero\\storage\\WGDSS2T2\\5270963.html:text/html},
}

@article{amendola_accuracy_2021,
	title = {Accuracy of homogeneous models for photon diffusion in estimating neonatal cerebral hemodynamics by {TD}-{NIRS}},
	volume = {12},
	copyright = {© 2021 Optical Society of America},
	issn = {2156-7085},
	url = {https://opg.optica.org/boe/abstract.cfm?uri=boe-12-4-1905},
	doi = {10.1364/BOE.417357},
	abstract = {We assessed the accuracy of homogenous (semi-infinite, spherical) photon diffusion models in estimating absolute hemodynamic parameters of the neonatal brain in realistic scenarios (ischemia, hyperoxygenation, and hypoventilation) from 1.5 cm interfiber distance TD NIRS measurements. Time-point-spread-functions in 29- and 44-weeks postmenstrual age head meshes were simulated by the Monte Carlo method, convoluted with a real instrument response function, and then fitted with photon diffusion models. The results show good accuracy in retrieving brain oxygen saturation, and severe underestimation of total cerebral hemoglobin, suggesting the need for more complex models of analysis or of larger interfiber distances to precisely monitor all hemodynamic parameters.},
	language = {EN},
	number = {4},
	urldate = {2024-12-03},
	journal = {Biomedical Optics Express},
	author = {Amendola, Caterina and Spinelli, Lorenzo and Contini, Davide and Carli, Agnese De and Martinelli, Cesare and Fumagalli, Monica and Torricelli, Alessandro},
	month = apr,
	year = {2021},
	note = {Publisher: Optica Publishing Group},
	keywords = {Optical properties, Absorption coefficient, Light propagation, Magnetic resonance imaging, Near infrared, Point spread function},
	pages = {1905--1921},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\NTWVQRSF\\Amendola et al. - 2021 - Accuracy of homogeneous models for photon diffusion in estimating neonatal cerebral hemodynamics by.pdf:application/pdf},
}

@article{contini_photon_1997,
	title = {Photon migration through a turbid slab described by a model based on diffusion approximation. {I}. {Theory}},
	volume = {36},
	copyright = {© 1997 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-36-19-4587},
	doi = {10.1364/AO.36.004587},
	abstract = {The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.},
	language = {EN},
	number = {19},
	urldate = {2024-12-03},
	journal = {Applied Optics},
	author = {Contini, Daniele and Martelli, Fabrizio and Zaccanti, Giovanni},
	month = jul,
	year = {1997},
	note = {Publisher: Optica Publishing Group},
	keywords = {Refractive index, Turbid media, Optical properties, Absorption coefficient, Light propagation, Tissue optics},
	pages = {4587--4599},
}

@article{sassaroli_performance_2001,
	title = {Performance of fitting procedures in curved geometry for retrieval of the optical properties of tissue from time-resolved measurements},
	volume = {40},
	copyright = {© 2001 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-40-1-185},
	doi = {10.1364/AO.40.000185},
	abstract = {By use of the solution of the diffusion equation for cylindrical and spherical geometry, two fitting procedures for retrieval of the optical properties from time-resolved measurements have been implemented. The fitting procedures are based on the Levenberg–Marquardt algorithm, in which the fitting parameters are the absorption coefficient, the reduced scattering coefficient, and an amplitude factor. Monte Carlo data generated for cylindrical and spherical geometry were fitted by these fitting procedures, and the retrieved optical properties were compared with those obtained from the inversion procedure with a mismatched geometry of a semi-infinite medium. The effects of refractive-index mismatch and of different boundary conditions of the diffusion equation were also studied, together with the effects of several sources of error that are typically found in time-resolved measurements. The advantages and drawbacks of these fitting procedures, including many details in several situations of interest in the field of tissue optics, are discussed. The results also offer a guideline to understanding the effects of mismatching in curved geometry as functions of source–detector distance and radii of cylinders or spheres.},
	language = {EN},
	number = {1},
	urldate = {2024-12-03},
	journal = {Applied Optics},
	author = {Sassaroli, Angelo and Martelli, Fabrizio and Zaccanti, Giovanni and Yamada, Yukio},
	month = jan,
	year = {2001},
	note = {Publisher: Optica Publishing Group},
	keywords = {Optical properties, Absorption coefficient, Tissue optics, Near infrared spectroscopy, Neural networks, Transmittance},
	pages = {185--197},
}

@article{bucher_experiments_1973,
	title = {Experiments on {Light} {Pulse} {Communication} and {Propagation} {Through} {Atmospheric} {Clouds}},
	volume = {12},
	copyright = {© 1973 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-12-10-2401},
	doi = {10.1364/AO.12.002401},
	abstract = {This paper describes the facilities and results in an experiment to investigate light pulse propagation through atmospheric clouds. The experiments were conducted with the transmitter and receiver located on two mountain peaks in a naturally cloudy area. The transmitter was a Q-switched ruby laser producing 30 nsec light pulses. The received pulses were 1–10 μsec in duration when there was a cloud in the propagation path. The multipath time lengthening of the received pulse resulted from multiple scattering inside the cloud. The extent of this multipath pulse spreading can be shown to be comparable to that predicted from computer simulation models. We also observed a number of effects in which relatively small changes in the gross cloud shape produced a change in the received signal intensity of an order of magnitude or so.},
	language = {EN},
	number = {10},
	urldate = {2024-12-03},
	journal = {Applied Optics},
	author = {Bucher, Edward A. and Lerner, Robert M.},
	month = oct,
	year = {1973},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Scattering media, Forward scattering, Light propagation, Pulse propagation, Q switched lasers},
	pages = {2401--2414},
}

@article{hass_first-passage_2024,
	title = {First-passage time for many-particle diffusion in space-time random environments},
	volume = {109},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.109.054101},
	doi = {10.1103/PhysRevE.109.054101},
	abstract = {The first-passage time for a single diffusing particle has been studied extensively, but the first-passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently. We consider two models for many-particle diffusion—one treats each particle as independent simple random walkers while the other treats them as coupled to a common space-time random forcing field that biases particles nearby in space and time in similar ways. The first-passage time of a single diffusing particle under both models shows the same statistics and scaling behavior. However, for many-particle diffusions, the first-passage time among all particles (the extreme first-passage time) is very different between the two models, effected in the latter case by the randomness of the common forcing field. We develop an asymptotic (in the number of particles and location where first passage is being probed) theoretical framework to separate the impact of the random environment with that of the sampling trajectories within it. We identify a power law describing the impact of the environment on the variance of the extreme first-passage time. Through numerical simulations, we verify that the predictions from this asymptotic theory hold even for systems with widely varying numbers of particles, all the way down to 100 particles. This shows that measurements of the extreme first-passage time for many-particle diffusions provide an indirect measurement of the underlying environment in which the diffusion is occurring.},
	number = {5},
	urldate = {2024-10-13},
	journal = {Physical Review E},
	author = {Hass, Jacob B. and Corwin, Ivan and Corwin, Eric I.},
	month = may,
	year = {2024},
	note = {Publisher: American Physical Society},
	pages = {054101},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\H62R3CRQ\\PhysRevE.109.html:text/html;https\://journals.aps.org/pre/pdf/10.1103/PhysRevE.109.054101:C\:\\Users\\centrifuge\\Zotero\\storage\\TWDG6HD5\\PhysRevE.109.pdf:application/pdf;PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\EQFXHZYL\\Hass et al. - 2024 - First-passage time for many-particle diffusion in space-time random environments.pdf:application/pdf},
}

@article{mayerhofer_bouguer-beer-lambert_2020,
	title = {The {Bouguer}-{Beer}-{Lambert} {Law}: {Shining} {Light} on the {Obscure}},
	volume = {21},
	copyright = {© 2020 The Authors. Published by Wiley-VCH GmbH},
	issn = {1439-7641},
	shorttitle = {The {Bouguer}-{Beer}-{Lambert} {Law}},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cphc.202000464},
	doi = {10.1002/cphc.202000464},
	abstract = {The Beer-Lambert law is unquestionably the most important law in optical spectroscopy and indispensable for the qualitative and quantitative interpretation of spectroscopic data. As such, every spectroscopist should know its limits and potential pitfalls, arising from its application, by heart. It is the goal of this work to review these limits and pitfalls, as well as to provide solutions and explanations to guide the reader. This guidance will allow a deeper understanding of spectral features, which cannot be explained by the Beer-Lambert law, because they arise from electromagnetic effects/the wave nature of light. Those features include band shifts and intensity changes based exclusively upon optical conditions, i. e. the method chosen to record the spectra, the substrate and the form of the sample. As such, the review will be an essential tool towards a full understanding of optical spectra and their quantitative interpretation based not only on oscillator positions, but also on their strengths and damping constants.},
	language = {en},
	number = {18},
	urldate = {2024-11-13},
	journal = {ChemPhysChem},
	author = {Mayerhöfer, Thomas G. and Pahlow, Susanne and Popp, Jürgen},
	year = {2020},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/cphc.202000464},
	keywords = {absorbance, Bouguer-Beer-Lambert law, dispersion theory, electromagnetic theory, Lorentz-Lorenz relation},
	pages = {2029--2046},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\4CVYCVZA\\Mayerhöfer et al. - 2020 - The Bouguer-Beer-Lambert Law Shining Light on the Obscure.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\E7ISKSNW\\cphc.html:text/html},
}

@article{collis_lidar_1966,
	title = {Lidar: {A} new atmospheric probe},
	volume = {92},
	copyright = {Copyright © 1966 Royal Meteorological Society},
	issn = {1477-870X},
	shorttitle = {Lidar},
	doi = {10.1002/qj.49709239205},
	abstract = {Pulsed-light techniques of probing the atmosphere have been greatly extended by employing lasers as energy sources in instruments called ‘lidars.’ Because of the nature of laser energy and the manner in which it is used in current and proposed systems, lidar is best discussed in terms of radar. Apart from the basic capabilities of lidar for detecting backscattering from atmospheric constituents, possibilities exist for more sophisticated techniques based on the wave nature of the energy. The basic capabilities of lidar, however, make it possible to observe the atmosphere with previously unknown resolution and sensitivity. Apart from providing new information about clouds, lidar has shown that the concentration of the particulate matter content of clear air is highly variable and that such variations can indicate the structure and motion of the clear atmosphere. These capabilities have applications in atmospheric and meteorological research and various operational activities.},
	language = {en},
	number = {392},
	urldate = {2024-08-08},
	journal = {Quarterly Journal of the Royal Meteorological Society},
	author = {Collis, R. T. H.},
	year = {1966},
	pages = {220--230},
	file = {19720017707.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\MAP5MXFM\\19720017707.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\W5CT4KZ7\\qj.html:text/html},
}

@book{bohren_absorption_1983,
	title = {Absorption and {Scattering} of {Light} by {Small} {Particles}},
	isbn = {978-0-471-05772-7},
	abstract = {Absorption and Scattering of Light by Small Particles  Treating absorption and scattering in equal measure, this self-contained, interdisciplinary study examines and illustrates how small particles absorb and scatter light. The authors emphasize that any discussion of the optical behavior of small particles is inseparable from a full understanding of the optical behavior of the parent material--bulk matter. To divorce one concept from the other is to render any study on scattering theory seriously incomplete.  Special features and important topics covered in this book include: ∗ Classical theories of optical properties based on idealized models ∗ Measurements for three representative materials: magnesium oxide, aluminum, and water ∗ An extensive discussion of electromagnetic theory ∗ Numerous exact and approximate solutions to various scattering problems ∗ Examples and applications from physics, astrophysics, atmospheric physics, and biophysics ∗ Some 500 references emphasizing work done since Kerker′s 1969 work on scattering theory ∗ Computer programs for calculating scattering by spheres, coated spheres, and infinite cylinders},
	language = {en},
	publisher = {Wiley},
	author = {Bohren, Craig F. and Huffman, Donald R.},
	month = apr,
	year = {1983},
	keywords = {Science / Physics / Atomic \& Molecular, Science / Physics / General, Science / Physics / Optics \& Light},
	file = {scattering.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\7MA4L2T9\\scattering.pdf:application/pdf},
}

@article{polizzi_mean_2016,
	title = {Mean {First}-{Passage} {Times} in {Biology}},
	volume = {56},
	copyright = {© 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
	issn = {1869-5868},
	doi = {10.1002/ijch.201600040},
	abstract = {Many biochemical processes, such as charge hopping or protein folding, can be described by an average timescale to reach a final state, starting from an initial state. Here, we provide a pedagogical treatment of the mean first-passage time (MFPT) of a physical process, which depends on the number of intervening states between the initial state and the target state. Our aim in this tutorial review is to provide a clear development of the mean first-passage time formalism and to show some of its practical utility. The MFPT treatment can provide a useful link between microscopic rates and the average timescales often probed by experiment.},
	language = {en},
	number = {9-10},
	urldate = {2024-10-13},
	journal = {Israel Journal of Chemistry},
	author = {Polizzi, Nicholas F. and Therien, Michael J. and Beratan, David N.},
	year = {2016},
	keywords = {electron transfer, Markov chains, mean first-passage time, protein folding},
	pages = {816--824},
	file = {Accepted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\HSLZMTWU\\Polizzi et al. - 2016 - Mean First-Passage Times in Biology.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\PFKSSJGC\\ijch.html:text/html},
}

@article{meerson_mortality_2015,
	title = {Mortality, {Redundancy}, and {Diversity} in {Stochastic} {Search}},
	volume = {114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.198101},
	doi = {10.1103/PhysRevLett.114.198101},
	abstract = {We investigate a stochastic search process in one dimension under the competing roles of mortality, redundancy, and diversity of the searchers. This picture represents a toy model for the fertilization of an oocyte by sperm. A population of 𝑁 independent and mortal diffusing searchers all start at 𝑥=𝐿 and attempt to reach the target at 𝑥=0. When mortality is irrelevant, the search time scales as 𝜏𝐷/ln⁡𝑁 for ln⁡𝑁≫1, where 𝜏𝐷∼𝐿2/𝐷 is the diffusive time scale. Conversely, when the mortality rate 𝜇 of the searchers is sufficiently large, the search time scales as √𝜏𝐷/𝜇, independent of 𝑁. When searchers have distinct and high mortalities, a subpopulation with a nontrivial optimal diffusivity is most likely to reach the target. We also discuss the effect of chemotaxis on the search time and its fluctuations.},
	number = {19},
	urldate = {2024-11-11},
	journal = {Physical Review Letters},
	author = {Meerson, Baruch and Redner, S.},
	month = may,
	year = {2015},
	note = {Publisher: American Physical Society},
	pages = {198101},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\5JYVSW5G\\PhysRevLett.114.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\JJTPWEQ2\\Meerson and Redner - 2015 - Mortality, Redundancy, and Diversity in Stochastic Search.pdf:application/pdf},
}

@article{schuss_redundancy_2019,
	title = {Redundancy principle and the role of extreme statistics in molecular and cellular biology},
	volume = {28},
	issn = {1571-0645},
	url = {https://www.sciencedirect.com/science/article/pii/S1571064519300090},
	doi = {10.1016/j.plrev.2019.01.001},
	abstract = {The paradigm of chemical activation rates in cellular biology has been shifted from the mean arrival time of a single particle to the mean of the first among many particles to arrive at a small activation site. The activation rate is set by extremely rare events, which have drastically different time scales from the mean times between activations, and depends on different structural parameters. This shift calls for reconsideration of physical processes used in deterministic and stochastic modeling of chemical reactions that are based on the traditional forward rate, especially for fast activation processes in living cells. Consequently, the biological activation time is not necessarily exponentially distributed. We review here the physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes. We provide examples in cellular transduction, gene activation, cell senescence activation or spermatozoa selection during fertilization, where the rate depends on numbers. We conclude that the statistics of the minimal time to activation set kinetic laws in biology, which can be very different from the ones associated to average times.},
	urldate = {2024-11-11},
	journal = {Physics of Life Reviews},
	author = {Schuss, Z. and Basnayake, K. and Holcman, D.},
	month = mar,
	year = {2019},
	keywords = {Diffusion, Calcium dynamics, Extreme statistics, First Passage Times, Optimal trajectories, Transduction},
	pages = {52--79},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\2VIUCGR5\\S1571064519300090.html:text/html},
}

@article{zsurkis_first_2024,
	title = {First passage times in portfolio optimization: {A} novel nonparametric approach},
	volume = {312},
	issn = {0377-2217},
	shorttitle = {First passage times in portfolio optimization},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221723006033},
	doi = {10.1016/j.ejor.2023.07.044},
	abstract = {This paper introduces a portfolio optimization procedure that aims to minimize the intra-horizon (IH) risk subject to a minimum expected time to achieve a target cumulative return. To estimate the first passage probabilities and the expected time a novel nonparametric method and a new Markov chain order determination approach are developed. The optimization framework proposed allows us to include novel path-dependent measures of risk and return in the asset allocation problem. An empirical application to S\&P 100 companies, a risk-free asset and stock indices is provided. Our empirical results suggest that the proposed framework exhibits more consistency between in-sample and out-of-sample performance than the mean-variance model and an alternative optimization problem that minimizes the MaxVaR measure of Boudoukh et al. (2004). Overall, the portfolio optimization approach we introduce results in higher out-of-sample annualized returns for relatively low levels of IH risk.},
	number = {3},
	urldate = {2024-11-08},
	journal = {European Journal of Operational Research},
	author = {Zsurkis, Gabriel and Nicolau, João and Rodrigues, Paulo M. M.},
	month = feb,
	year = {2024},
	keywords = {Markov chains, First-passage probability, Intra-horizon risk, Portfolio optimization},
	pages = {1074--1085},
}

@article{barney_first-passage-time_2017,
	title = {First-{Passage}-{Time} {Distribution} for {Variable}-{Diffusion} {Processes}},
	volume = {167},
	issn = {1572-9613},
	url = {https://doi.org/10.1007/s10955-017-1758-2},
	doi = {10.1007/s10955-017-1758-2},
	abstract = {First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically—often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time—and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221–233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra- and inter-day behavior similar to those of empirical first-passage-time distributions.},
	language = {en},
	number = {3},
	urldate = {2024-11-08},
	journal = {Journal of Statistical Physics},
	author = {Barney, Liberty and Gunaratne, Gemunu H.},
	month = may,
	year = {2017},
	keywords = {First-passage-time distributions, Investment horizon, Stochastic processes},
	pages = {878--891},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\LNU9RQTB\\Barney and Gunaratne - 2017 - First-Passage-Time Distribution for Variable-Diffusion Processes.pdf:application/pdf},
}

@misc{noauthor_how_nodate,
	title = {How {Viruses} {Spread} {Among} {Computers} and {People} {\textbar} {Science}},
	url = {https://www.science.org/doi/10.1126/science.1061076},
	urldate = {2024-11-08},
}

@book{noauthor_stochastic_2007,
	title = {Stochastic {Processes} in {Physics} and {Chemistry}},
	isbn = {978-0-444-52965-7},
	url = {https://shop.elsevier.com/books/stochastic-processes-in-physics-and-chemistry/van-kampen/978-0-444-52965-7},
	abstract = {The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived applic},
	language = {en-US},
	urldate = {2024-11-08},
	month = mar,
	year = {2007},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\4U28NUN3\\978-0-444-52965-7.html:text/html},
}

@article{ishimaru_diffusion_1978,
	title = {Diffusion of a pulse in densely distributed scatterers},
	volume = {68},
	copyright = {© 1978 Optical Society of America},
	url = {https://opg.optica.org/josa/abstract.cfm?uri=josa-68-8-1045},
	doi = {10.1364/JOSA.68.001045},
	abstract = {This paper presents a theoretical study on propagation and scattering characteristics of a short optical pulse in a dense distribution of scatterers. Examples include pulse diffusion in whole blood and in a dense distribution of particulate matter in the atmosphere and the ocean. The parabolic equation technique is applicable to the forward-scatter region where the angular spread is confined within narrow forward angles. When the angular spread becomes comparable to the order of unit steradian, there is as much backscattering as forward scattering and diffusion phenomena take place. We start with the integral and differential equations for the two-frequency mutual coherence function under the first-order smoothing approximation, and a general diffusion equation and boundary conditions are obtained. As examples, we present solutions for diffusion of a pulse from a point source and a plane wave incident on a slab of scatterers.},
	language = {EN},
	number = {8},
	urldate = {2023-02-26},
	journal = {JOSA},
	author = {Ishimaru, Akira},
	month = aug,
	year = {1978},
	note = {Publisher: Optica Publishing Group},
	keywords = {Diffusion, Backscattering, Multiple scattering, Forward scattering, Pulse propagation, Light beams, Optical fibers, Optical turbulence, Pulse shaping},
	pages = {1045--1050},
}

@article{ishimaru_diffusion_1989,
	title = {Diffusion of light in turbid material},
	volume = {28},
	copyright = {© 1989 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-28-12-2210},
	doi = {10.1364/AO.28.002210},
	abstract = {This paper discusses some of the present knowledge of the mathematical techniques used to describe light diffusion in turbid material such as tissues. Attention will be paid to the usefulness and limitations of various techniques. First, we review the transport theory, radiance, radiant energy fluence rate, phase functions, boundary conditions, and measurement techniques. We then discuss the first-order solution, multiple scattering, diffusion approximation, and their limitations. The plane wave, spherical wave, beam wave, and pulse wave excitations are discussed followed by a brief review of the surface scattering effects due to rough interfaces.},
	language = {EN},
	number = {12},
	urldate = {2024-08-09},
	journal = {Applied Optics},
	author = {Ishimaru, Akira},
	month = jun,
	year = {1989},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Turbid media, Scattering media, Scattering theory, Mathematical methods, Rough surface scattering},
	pages = {2210--2215},
}

@article{polishchuk_photon-density_1997,
	title = {Photon-density modes beyond the diffusion approximation: scalar wave-diffusion equation},
	volume = {14},
	copyright = {© 1997 Optical Society of America},
	issn = {1520-8532},
	shorttitle = {Photon-density modes beyond the diffusion approximation},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-14-1-230},
	doi = {10.1364/JOSAA.14.000230},
	abstract = {Various modifications of the diffusion model designed to describe photon migration in scattering and absorbing media are analyzed and compared in the nondiffusion region. A more accurate modified diffusion equation that has a broader region of applicability is introduced. The radiative-transfer equation is solved numerically to assess the validity range of different models tested and to select the best one.},
	language = {EN},
	number = {1},
	urldate = {2024-10-16},
	journal = {JOSA A},
	author = {Polishchuk, A. Ya and Gutman, S. and Lax, M. and Alfano, R. R.},
	month = jan,
	year = {1997},
	note = {Publisher: Optica Publishing Group},
	keywords = {Spatial resolution, Fourier transforms, Scattering media, Femtosecond pulses, Photon counting, Random lasers},
	pages = {230--234},
	file = {Polishchuk et al. - 1997 - Photon-density modes beyond the diffusion approxim.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\B77FFDVI\\Polishchuk et al. - 1997 - Photon-density modes beyond the diffusion approxim.pdf:application/pdf},
}

@article{serva_random_2020,
	title = {Random {Motion} of {Light}-{Speed} {Particles}},
	volume = {181},
	issn = {1572-9613},
	url = {https://doi.org/10.1007/s10955-020-02638-5},
	doi = {10.1007/s10955-020-02638-5},
	abstract = {In 1956 Mark Kac proposed a process related to the telegrapher equation where the particle travels at constant speed (say the speed of light c) and randomly inverts its velocity. This process had important applications concerning the path-integral solution and the probabilistic interpretation of the 1\$\$+\$\$1 dimensions Dirac equation. The extension to 3\$\$+\$\$1 dimensions requires that the particle only moves at light-speed, which implies that velocity can be represented as a point on the surface of a sphere of radius c. The realizations of the process for the velocity only may connect these points, and, by strict analogy with the Kac model, it can be assumed that the velocity jumps from one value to another. In this paper we follow a new and different strategy assuming that the velocity performs continuous trajectories (velocity changes direction in a continuous way) which are the realization of a Wiener process on the surface. The processes which emerge transform one in the other by Lorentz boost. The associate Forward Kolmogorov Equation for the joint probability density of position and velocity, which is the (3\$\$+\$\$1) dimensional analogous of the telegrapher equation, is examined and a simplification is performed by means of variables separation.},
	language = {en},
	number = {5},
	urldate = {2024-10-16},
	journal = {Journal of Statistical Physics},
	author = {Serva, Maurizio},
	month = dec,
	year = {2020},
	keywords = {Brownian motion, Ito calculus, Lorentz boost, Relativity, Wiener process},
	pages = {1603--1608},
	file = {Serva - 2020 - Random Motion of Light-Speed Particles.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\M4UZPNN8\\Serva - 2020 - Random Motion of Light-Speed Particles.pdf:application/pdf},
}

@article{fujii_characteristic_2020,
	title = {Characteristic {Length} and {Time} {Scales} of the {Highly} {Forward} {Scattering} of {Photons} in {Random} {Media}},
	volume = {10},
	copyright = {http://creativecommons.org/licenses/by/3.0/},
	issn = {2076-3417},
	url = {https://www.mdpi.com/2076-3417/10/1/93},
	doi = {10.3390/app10010093},
	abstract = {Background: Elucidation of the highly forward scattering of photons in random media such as biological tissue is crucial for further developments of optical imaging using photon transport models. We evaluated length and time scales of the photon scattering in three-dimensional media. Methods: We employed analytical solutions of the time-dependent radiative transfer, M-th order delta-Eddington, and photon diffusion equations (RTE, dEM, and PDE). We calculated the fluence rates at different source-detector distances and optical properties. Results: We found that the zeroth order dEM and PDE, which approximate the highly forward scattering to the isotropic scattering, are valid in longer length and time scales than approximately     10 /  μ t ′      and     40 /  μ t ′  v    , respectively, where     μ t ′     is the reduced transport coefficient and v the speed of light in a medium. The first and second order dEM, which approximate the highly forward-peaked phase function by the first two and three Legendre moments, are valid in the longer scales than approximately     4.0 /  μ t ′      and     6.3 /  μ t ′  v    ;     2.8 /  μ t ′      and     3.5 /  μ t ′  v    , respectively. The boundary conditions less influence the length scales, while they reduce the times scales from those for bulk at the longer length scale than approximately     4.0 /  μ t ′     . Conclusion: Our findings are useful for constructions of accurate and efficient photon transport models. We evaluated length and time scales of the highly forward scattering of photons in various kinds of three-dimensional random media by analytical solutions of the radiative transfer, M-th order delta-Eddington, and photon diffusion equations.},
	language = {en},
	number = {1},
	urldate = {2024-10-15},
	journal = {Applied Sciences},
	author = {Fujii, Hiroyuki and Ueno, Moegi and Kobayashi, Kazumichi and Watanabe, Masao},
	month = jan,
	year = {2020},
	note = {Number: 1
Publisher: Multidisciplinary Digital Publishing Institute},
	keywords = {characteristic length and time scales of photon transport, diffusion and delta-Eddington approximations, highly forward scattering of photons, radiative transfer equation},
	pages = {93},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\GCY6QKIC\\Fujii et al. - 2020 - Characteristic Length and Time Scales of the Highl.pdf:application/pdf},
}

@misc{buglia_introduction_1986,
	title = {Introduction to the {Theory} of {Atmospheric} {Radiative} {Transfer}},
	url = {https://ntrs.nasa.gov/citations/19860018367},
	abstract = {The fundamental physical and mathematical principles governing the transmission of radiation through the atmosphere are presented, with emphasis on the scattering of visible and near-IR radiation. The classical two-stream, thin-atmosphere, and Eddington approximations, along with some of their offspring, are developed in detail, along with the discrete ordinates method of Chandrasekhar. The adding and doubling methods are discussed from basic principles, and references for further reading are suggested.},
	urldate = {2024-10-15},
	author = {Buglia, J. J.},
	month = jul,
	year = {1986},
	note = {NTRS Author Affiliations: NASA Langley Research Center
NTRS Report/Patent Number: NAS 1.61:1156
NTRS Document ID: 19860018367
NTRS Research Center: Legacy CDMS (CDMS)},
	keywords = {Geophysics},
	file = {19860018367.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\5K4JGUE6\\Buglia - 1986 - Introduction to the Theory of Atmospheric Radiativ.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\EGPLL8LH\\19860018367.html:text/html},
}

@article{madsen_experimental_1992,
	title = {Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements},
	volume = {31},
	copyright = {© 1992 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-31-18-3509},
	doi = {10.1364/AO.31.003509},
	abstract = {When a picosecond light pulse is incident upon a turbid medium such as tissue, the temporal distribution of diffusely reflected and transmitted photons depends on the optical absorption and scattering properties of the medium. From diffusion theory it is possible to derive analytic expressions for the pulse shape in terms of the optical interaction coefficients of a homogeneous semi-infinite medium. Experimental tests of this simple model in tissue-simulating liquid phantoms of different geometries are presented here. The results of these tests show that, in a semi-infinite phantom, the application of the diffusion model provides estimates of the absorption and transport-scattering coefficients that are accurate to better than 10\%. Comparable accuracy was also obtained with this simple model for finite slab, cylindrical, and spherical volumes as long as the objects were of sufficient size. For smaller volumes the absorption coefficient was overestimated because of the significant loss of photons at the boundaries of the object.},
	language = {EN},
	number = {18},
	urldate = {2024-10-13},
	journal = {Applied Optics},
	author = {Madsen, Steen J. and Wilson, Brian C. and Patterson, Michael S. and Park, Young D. and Jacques, Steven L. and Hefetz, Yaron},
	month = jun,
	year = {1992},
	note = {Publisher: Optica Publishing Group},
	keywords = {Turbid media, Optical properties, Absorption coefficient, Diffuse reflectance, Optical absorption, Picosecond pulses},
	pages = {3509--3517},
	file = {Madsen et al. - 1992 - Experimental tests of a simple diffusion model for.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\7QL2DYGK\\Madsen et al. - 1992 - Experimental tests of a simple diffusion model for.pdf:application/pdf},
}

@article{tarvainen_hybrid_2005,
	title = {Hybrid radiative-transfer–diffusion model for optical tomography},
	volume = {44},
	copyright = {© 2005 Optical Society of America},
	issn = {2155-3165},
	url = {https://opg.optica.org/ao/abstract.cfm?uri=ao-44-6-876},
	doi = {10.1364/AO.44.000876},
	abstract = {A hybrid radiative-transfer–diffusion model for optical tomography is proposed. The light propagation is modeled with the radiative-transfer equation in the vicinity of the laser sources, and the diffusion approximation is used elsewhere in the domain. The solution of the radiative-transfer equation is used to construct a Dirichlet boundary condition for the diffusion approximation on a fictitious interface within the object. This boundary condition constitutes an approximative distributed source model for the diffusion approximation in the remaining area. The results from the proposed approach are compared with finite-element solutions of the radiative-transfer equation and the diffusion approximation and Monte Carlo simulation. The results show that the method improves the accuracy of the forward model compared with the conventional diffusion model.},
	language = {EN},
	number = {6},
	urldate = {2024-10-13},
	journal = {Applied Optics},
	author = {Tarvainen, Tanja and Vauhkonen, Marko and Kolehmainen, Ville and Kaipio, Jari P.},
	month = feb,
	year = {2005},
	note = {Publisher: Optica Publishing Group},
	keywords = {Optical properties, Scattering media, Light propagation, Diffuse optical tomography, Laser sources, Optical constants},
	pages = {876--886},
}

@article{martelli_theres_2016,
	title = {There’s plenty of light at the bottom: statistics of photon penetration depth in random media},
	volume = {6},
	copyright = {2016 The Author(s)},
	issn = {2045-2322},
	shorttitle = {There’s plenty of light at the bottom},
	url = {https://www.nature.com/articles/srep27057},
	doi = {10.1038/srep27057},
	abstract = {We propose a comprehensive statistical approach describing the penetration depth of light in random media. The presented theory exploits the concept of probability density function f(z{\textbar}ρ, t) for the maximum depth reached by the photons that are eventually re-emitted from the surface of the medium at distance ρ and time t. Analytical formulas for f, for the mean maximum depth 〈zmax〉 and for the mean average depth reached by the detected photons at the surface of a diffusive slab are derived within the framework of the diffusion approximation to the radiative transfer equation, both in the time domain and the continuous wave domain. Validation of the theory by means of comparisons with Monte Carlo simulations is also presented. The results are of interest for many research fields such as biomedical optics, advanced microscopy and disordered photonics.},
	language = {en},
	number = {1},
	urldate = {2024-10-13},
	journal = {Scientific Reports},
	author = {Martelli, Fabrizio and Binzoni, Tiziano and Pifferi, Antonio and Spinelli, Lorenzo and Farina, Andrea and Torricelli, Alessandro},
	month = jun,
	year = {2016},
	note = {Publisher: Nature Publishing Group},
	keywords = {Near-infrared spectroscopy, Fluorescence spectroscopy, Raman spectroscopy, Statistics},
	pages = {27057},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\5I96SY2K\\Martelli et al. - 2016 - There’s plenty of light at the bottom statistics .pdf:application/pdf},
}

@article{xu_photon_2002,
	title = {Photon migration in turbid media using a cumulant approximation to radiative transfer},
	volume = {65},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.65.066609},
	doi = {10.1103/PhysRevE.65.066609},
	abstract = {A photon transport model for light migration in turbid media based on a cumulant approximation to radiative transfer is presented for image reconstruction inside an infinite medium or a bounded medium with a planar geometry. This model treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation and uses the second-order cumulant solution of photon density to the Boltzmann equation as the Green’s function for the uniform background. It provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. At early times, it agrees much better with the result from the Monte Carlo simulation than the diffusion approximation. Both approximations agree well with the Monte Carlo simulation at later times. The weight function for image reconstruction under this proposed model is shown to have a strong dependence at both early and later times on absorption and/or scattering inhomogeneities located in the propagation direction of and close to the source, or in the field of view of and close to the detector. This effect originates from the initial ballistic motion of incident photons, which is substantially underestimated by the diffusion approximation.},
	number = {6},
	urldate = {2024-10-13},
	journal = {Physical Review E},
	author = {Xu, M. and Cai, W. and Lax, M. and Alfano, R. R.},
	month = jun,
	year = {2002},
	note = {Publisher: American Physical Society},
	pages = {066609},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\9VQBT7EI\\PhysRevE.65.html:text/html},
}

@article{condamin_first-passage_2007,
	title = {First-passage times in complex scale-invariant media},
	volume = {450},
	copyright = {2007 Springer Nature Limited},
	issn = {1476-4687},
	url = {https://www.nature.com/articles/nature06201},
	doi = {10.1038/nature06201},
	abstract = {How long does it take a random walker to reach a given target point? This quantity, called first-passage time (FPT), is important because of its role in real situations such as transport in disordered media, neuron firing, spread of diseases and target search processes. Previous methods of determining FPT properties were effectively limited to one-dimensional geometries or to homogeneous media. Condamin et al. have developed a general theory that allows the accurate evaluation of the mean FPT in complex media. The predictions are confirmed by numerical simulations of several models of disordered media, fractals, anomalous diffusion and scale-free networks, including a yeast protein interaction network.},
	language = {en},
	number = {7166},
	urldate = {2024-10-13},
	journal = {Nature},
	author = {Condamin, S. and Bénichou, O. and Tejedor, V. and Voituriez, R. and Klafter, J.},
	month = nov,
	year = {2007},
	note = {Publisher: Nature Publishing Group},
	keywords = {Humanities and Social Sciences, multidisciplinary, Science},
	pages = {77--80},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\936VIALV\\Condamin et al. - 2007 - First-passage times in complex scale-invariant med.pdf:application/pdf},
}

@article{havlin_diffusion_2002,
	title = {Diffusion in disordered media},
	volume = {51},
	issn = {0001-8732},
	url = {https://doi.org/10.1080/00018730110116353},
	doi = {10.1080/00018730110116353},
	abstract = {Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.},
	number = {1},
	urldate = {2024-10-13},
	journal = {Advances in Physics},
	author = {Havlin, Shlomo and Ben-Avraham, Daniel},
	month = jan,
	year = {2002},
	note = {Publisher: Taylor \& Francis
\_eprint: https://doi.org/10.1080/00018730110116353},
	pages = {187--292},
	file = {Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\L3XA8GKP\\Havlin and Ben-Avraham - 2002 - Diffusion in disordered media.pdf:application/pdf},
}

@article{long_particle_2001,
	title = {Particle sizing and optical constant measurement in granular samples using statistical descriptors of photon time-of-flight distributions},
	volume = {434},
	issn = {0003-2670},
	url = {https://www.sciencedirect.com/science/article/pii/S0003267001008145},
	doi = {10.1016/S0003-2670(01)00814-5},
	abstract = {A method is described for optical constant estimation and particle sizing in granular samples using diffuse reflectance measurements. Statistical descriptors of the time-resolved photon distributions were used to obtain information inherent to absorption and scattering processes in a sample. Changes in a sample’s absorption and scattering properties and apparent particle diameter were simultaneously estimated using stepwise multi-linear regression (SMLR) and partial least squares regression (PLS). Models were constructed using time-distributions taken at both single and multiple radial displacements between source and detector. SMLR estimates of absorption and particle diameter required descriptors related to the trailing and rising edges of the time profiles, respectively. The inclusion of multi-perspective information allowed for improved estimates for all quantities. Using statistical descriptors, a robust means for simplifying complex photon time-distributions into measurable parameters was found. It was found that the SMLR model gave slightly better results compared with the PLS model. The absorption coefficient, scattering coefficient and apparent particle diameter were estimated to within 10, 9 and 7\% of their respective reference values with SMLR. In the future, this approach may be used as a means in which to develop practical instrumentation for on-line, real-time characterisation of absorbing granular media.},
	number = {1},
	urldate = {2024-10-13},
	journal = {Analytica Chimica Acta},
	author = {Long, William F and Burns, David H},
	month = apr,
	year = {2001},
	keywords = {Scattering, Absorption, Descriptors, Granular samples, Particle sizing},
	pages = {113--123},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\PBEUP3YV\\S0003267001008145.html:text/html},
}

@article{calba_ultrashort_2008,
	title = {Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments},
	volume = {25},
	copyright = {© 2008 Optical Society of America},
	issn = {1520-8532},
	shorttitle = {Ultrashort pulse propagation through a strongly scattering medium},
	url = {https://opg.optica.org/josaa/abstract.cfm?uri=josaa-25-7-1541},
	doi = {10.1364/JOSAA.25.001541},
	abstract = {Forward light scattering of femtosecond pulses through strongly scattering media is investigated experimentally and numerically. Computations are based on a semi-Monte Carlo method including polarization effects when experiments depend on a Ti:sapphire regenerative amplifier (100 fs, 1 kHz, 1 mJ@ 800 nm). The temporal separation between ballistic light and scattered light is exhibited and used to perform optical depth measurements up to 22 (transmission factor of ≈10−10). Quantitative comparisons between experiments and Monte Carlo simulations show a good agreement. Temporal forward scattered light evolutions with concentration and particle size are presented. Numerical results show that the early scattered light contains information on particle size, opening the way to particle sizing in strongly scattering media.},
	language = {EN},
	number = {7},
	urldate = {2024-10-13},
	journal = {JOSA A},
	author = {Calba, Cécile and Méès, Loïc and Rozé, Claude and Girasole, Thierry},
	month = jul,
	year = {2008},
	note = {Publisher: Optica Publishing Group},
	keywords = {Multiple scattering, Scattering media, Forward scattering, Pulse propagation, Femtosecond pulses, Optical media},
	pages = {1541--1550},
	file = {Calba et al. - 2008 - Ultrashort pulse propagation through a strongly sc.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\4AXTY6IE\\Calba et al. - 2008 - Ultrashort pulse propagation through a strongly sc.pdf:application/pdf},
}

@article{lee_using_2007,
	title = {Using ultra-short pulses to determine particle size and density distributions},
	volume = {15},
	copyright = {\&\#169; 2007 Optical Society of America},
	issn = {1094-4087},
	url = {https://opg.optica.org/oe/abstract.cfm?uri=oe-15-19-12483},
	doi = {10.1364/OE.15.012483},
	abstract = {We analyze the time dependent response of strongly scattering media (SSM) to ultra-short pulses of light. A random walk technique is used to model the optical scattering of ultra-short pulses of light propagating through media with random shapes and various packing densities. The pulse spreading was found to be strongly dependent on the average particle size, particle size distribution, and the packing fraction. We also show that the intensity as a function of time-delay can be used to analyze the particle size distribution and packing fraction of an optically thick sample independently of the presence of absorption features. Finally, we propose an all new way to measure the shape of ultra-short pulses that have propagated through a SSM.},
	language = {EN},
	number = {19},
	urldate = {2024-10-13},
	journal = {Optics Express},
	author = {Lee, Chris J. and Slot, Peter J. M. van der and Boller, Klaus-J.},
	month = sep,
	year = {2007},
	note = {Publisher: Optica Publishing Group},
	pages = {12483--12497},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\Z9E8SIY2\\Lee et al. - 2007 - Using ultra-short pulses to determine particle siz.pdf:application/pdf},
}

@article{kervella_picosecond_2012,
	title = {Picosecond time scale modification of forward scattered light induced by absorption inside particles},
	volume = {20},
	copyright = {© 2011 OSA},
	issn = {1094-4087},
	url = {https://opg.optica.org/oe/abstract.cfm?uri=oe-20-1-32},
	doi = {10.1364/OE.20.000032},
	abstract = {The aim of this work is to evaluate the influence of absorption processes on the Time Of Flight (TOF) of the light scattered out of a thick medium in the forward direction. We use a Monte-Carlo simulation with temporal phase function and Debye modes. The main result of our study is that absorption inside the particle induces a decrease of the TOF on a picosecond time scale, measurable with a femtosecond laser apparatus. This decrease, which exhibits a neat sensitivity to the absorption coefficient of particles, could provide an efficient way to measure this absorption.},
	language = {EN},
	number = {1},
	urldate = {2024-10-13},
	journal = {Optics Express},
	author = {Kervella, Myriam and d’Abzac, Françoix-Xavier and Hache, François and Hespel, Laurent and Dartigalongue, Thibault},
	month = jan,
	year = {2012},
	note = {Publisher: Optica Publishing Group},
	keywords = {Absorption coefficient, Scattering media, Forward scattering, Femtosecond lasers, Laser beams, Ultrafast lasers},
	pages = {32--41},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\3CXZV88Y\\Kervella et al. - 2012 - Picosecond time scale modification of forward scat.pdf:application/pdf},
}

@article{gributs_multiresolution_2003,
	series = {Papers presented at the 8th {International} {Conference} on {Chemometrics} and {Analytical} {Chemistry}},
	title = {Multiresolution analysis for quantification of optical properties in scattering media using pulsed photon time-of-flight measurements},
	volume = {490},
	issn = {0003-2670},
	url = {https://www.sciencedirect.com/science/article/pii/S0003267003005348},
	doi = {10.1016/S0003-2670(03)00534-8},
	abstract = {A simplified photon time-of-flight (TOF) instrument based on a nanosecond rise-time diode laser at 635nm was used for the quantification of optical properties of samples. A series of transmittance photon time-of-flight measurements were acquired from absorbing/scattering Intralipid™ samples of known composition (0{\textless}μa{\textless}0.0014mm−1; 13{\textless}μs{\textless}24mm−1). Time-of-flight distributions were analyzed using Haar transform with selection of the most parsimonious set of wavelets by genetic algorithm optimization. Results showed that the scattering coefficient could be estimated with a coefficient of variation (CV) of 4.4\% and r2=0.95 using wavelets of frequency up to 400MHz. Absorption coefficients were estimated with a CV of 6.9\% and r2=0.99 using steady-state intensity of blank- and scatter-corrected data. Furthermore, it was shown that quantification using simplified electronics can estimate scattering to within 7.2\% (r2=0.88) and absorption with an error of 8.3\% (r2=0.99). The above findings suggest that a simplified instrument based on a pulsed laser diode and low frequency switches could be developed to quantify absorption in highly scattering media.},
	number = {1},
	urldate = {2024-10-13},
	journal = {Analytica Chimica Acta},
	author = {Gributs, Claudia E. W. and Burns, David H.},
	month = aug,
	year = {2003},
	keywords = {Optical properties, Scattering media, Haar transform, Laser diode, Time-correlated single photon counting},
	pages = {185--195},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\LI59H8PQ\\S0003267003005348.html:text/html},
}

@article{serrano_characterization_2023,
	title = {Characterization of the {Mean} {First}-{Passage} {Time} {Function} {Subject} to {Advection} in {Annular}-like {Domains}},
	volume = {11},
	url = {https://ideas.repec.org//a/gam/jmathe/v11y2023i24p4998-d1302400.html},
	abstract = {Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations.},
	language = {en},
	number = {24},
	urldate = {2024-10-13},
	journal = {Mathematics},
	author = {Serrano, Hélia and Álvarez-Estrada, Ramón F.},
	year = {2023},
	note = {Publisher: MDPI},
	keywords = {mean first-passage time, annular cylinder, annulus, diffusion–advection equation, Dirichlet and Robin boundary conditions},
	pages = {1--17},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\TX8FRZQW\\v11y2023i24p4998-d1302400.html:text/html},
}

@article{chun_heterogeneous_2023,
	title = {Heterogeneous {Mean} {First}-{Passage} {Time} {Scaling} in {Fractal} {Media}},
	volume = {131},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.131.227101},
	doi = {10.1103/PhysRevLett.131.227101},
	abstract = {The mean first passage time (MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.},
	number = {22},
	urldate = {2024-10-13},
	journal = {Physical Review Letters},
	author = {Chun, Hyun-Myung and Hwang, Sungmin and Kahng, Byungnam and Rieger, Heiko and Noh, Jae Dong},
	month = nov,
	year = {2023},
	note = {Publisher: American Physical Society},
	pages = {227101},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\4AQVH9NV\\PhysRevLett.131.html:text/html},
}

@article{benichou_zero_2008,
	title = {Zero {Constant} {Formula} for {First}-{Passage} {Observables} in {Bounded} {Domains}},
	volume = {101},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.101.130601},
	doi = {10.1103/PhysRevLett.101.130601},
	abstract = {In this Letter, we develop an analytical approach which provides an explicit determination of mean first-passage times (MFPTs) for random walks in bounded domains for a wide class of transport processes. In particular, we derive for the first time explicit expressions of MFPTs for emblematic models of transport in complex media, such as diffusion on deterministic and random fractals. This approach relies on a scale-invariance hypothesis and a large volume expansion of the MFPT, which actually proves to be very accurate even for small system sizes as shown by numerical simulations. This explicit determination of MFPTs can be straightforwardly generalized to further useful first-passage observables such as occupation times and splitting probabilities.},
	number = {13},
	urldate = {2024-10-13},
	journal = {Physical Review Letters},
	author = {Bénichou, O. and Meyer, B. and Tejedor, V. and Voituriez, R.},
	month = sep,
	year = {2008},
	note = {Publisher: American Physical Society},
	pages = {130601},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\LU77ACXL\\PhysRevLett.101.html:text/html},
}

@article{condamin_first-passage_2005,
	title = {First-{Passage} {Times} for {Random} {Walks} in {Bounded} {Domains}},
	volume = {95},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.95.260601},
	doi = {10.1103/PhysRevLett.95.260601},
	abstract = {We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical simulations. Their range of validity is discussed. We also consider the case of a starting site and two targets. In addition, we present the extension to continuous Brownian motion. These results are of great relevance to any system involving diffusion in confined media.},
	number = {26},
	urldate = {2024-10-13},
	journal = {Physical Review Letters},
	author = {Condamin, S. and Bénichou, O. and Moreau, M.},
	month = dec,
	year = {2005},
	note = {Publisher: American Physical Society},
	pages = {260601},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\UQZEA7U2\\PhysRevLett.95.html:text/html},
}

@article{koren_leapover_2007,
	title = {Leapover {Lengths} and {First} {Passage} {Time} {Statistics} for {L}{\textbackslash}'evy {Flights}},
	volume = {99},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.99.160602},
	doi = {10.1103/PhysRevLett.99.160602},
	abstract = {Exact results for the first passage time and leapover statistics of symmetric and one-sided Lévy flights (LFs) are derived. LFs with a stable index 𝛼 are shown to have leapover lengths that are asymptotically power law distributed with an index 𝛼 for one-sided LFs and, surprisingly, with an index 𝛼/2 for symmetric LFs. The first passage time distribution scales like a power law with an index 1/2 as required by the Sparre-Andersen theorem for symmetric LFs, whereas one-sided LFs have a narrow distribution of first passage times. The exact analytic results are confirmed by extensive simulations.},
	number = {16},
	urldate = {2024-10-13},
	journal = {Physical Review Letters},
	author = {Koren, Tal and Lomholt, Michael A. and Chechkin, Aleksei V. and Klafter, Joseph and Metzler, Ralf},
	month = oct,
	year = {2007},
	note = {Publisher: American Physical Society},
	pages = {160602},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\Y7Y4G5VA\\PhysRevLett.99.html:text/html;Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\NR2XA2S5\\Koren et al. - 2007 - Leapover Lengths and First Passage Time Statistics.pdf:application/pdf},
}

@article{noskowicz_average_1988,
	title = {Average versus {Typical} {Mean} {First}-{Passage} {Time} in a {Random} {Random} {Walk}},
	volume = {61},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.500},
	doi = {10.1103/PhysRevLett.61.500},
	abstract = {Random walk in a one-dimensional random medium of length 𝑁 is analyzed. It is rigorously shown that in most realizations of the medium, the mean first-passage time, ¯𝑡, bears the following relation to 𝑁, for large 𝑁:log⁡¯𝑡∝√𝑁. The average of √𝑡 over the realizations of the medium, 〈𝑡〉, satisfies log⁡〈𝑡〉∝𝑁. Our formalism, though being exact, employs only elementary means and makes transparent the physics of the delay experienced by the random walker: It is due to the existence of subsegments in which the bias against motion towards the desired end is largest. Some implications of these results concerning the replica method are briefly discussed.},
	number = {5},
	urldate = {2024-10-13},
	journal = {Physical Review Letters},
	author = {Noskowicz, S. H. and Goldhirsch, I.},
	month = aug,
	year = {1988},
	note = {Publisher: American Physical Society},
	pages = {500--502},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\A9YYI7TJ\\PhysRevLett.61.html:text/html;Noskowicz and Goldhirsch - 1988 - Average versus Typical Mean First-Passage Time in .pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\S3IPDW2I\\Noskowicz and Goldhirsch - 1988 - Average versus Typical Mean First-Passage Time in .pdf:application/pdf},
}

@article{hoenders_telegraphers_2005,
	title = {Telegrapher’s equation for light derived from the transport equation},
	volume = {255},
	issn = {0030-4018},
	url = {https://www.sciencedirect.com/science/article/pii/S0030401805005985},
	doi = {10.1016/j.optcom.2005.06.024},
	abstract = {Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher’s equations in the well known P1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapher’s equations were derived, restricted to the case of isotropic scattering, and their properties are discussed. A correct diffusion coefficient for the stationary case could be obtained. However, this solution did not lead to the correct phase velocity. Correct phase velocities in combination with a correct diffusion coefficient were found for a dispersion relation that corresponds with anisotropic Henyey–Greenstein scattering with g=0.22. It provides a time-dependent description of the fluence rate with validity for all values of the albedo.},
	number = {4},
	urldate = {2024-10-13},
	journal = {Optics Communications},
	author = {Hoenders, Bernhard J. and Graaff, Reindert},
	month = nov,
	year = {2005},
	keywords = {Radiative transfer, Diffusion approximation, Dispersion relation},
	pages = {184--195},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\3ZHF7T6D\\Hoenders and Graaff - 2005 - Telegrapher’s equation for light derived from the .pdf:application/pdf;ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\3SLJ2G2S\\S0030401805005985.html:text/html},
}

@article{hass_anomalous_2023,
	title = {Anomalous fluctuations of extremes in many-particle diffusion},
	volume = {107},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.107.L022101},
	doi = {10.1103/PhysRevE.107.L022101},
	abstract = {In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of Einstein's treatment of single-particle diffusion, has each particle taking independent homogeneous random walks. This, however, neglects the fact that all particles diffuse in a common and often inhomogeneous environment that can affect their motion. A more sophisticated model treats this common environment as a space-time random biasing field which influences each particle's independent motion. While the bulk (or typical particle) behavior of these two models has been found to match to high degree, recent theoretical work of G. Barraquand and I. Corwin, Probab. Theory Relat. Fields 167, 1057 (2017) and G. Barraquand and P. Le Doussal, J. Phys. A: Math. Theor. 53, 215002 (2020) on a one-dimensional exactly solvable version of this random environment model suggests that the extreme behavior is quite different between the two models. We transform these asymptotic (in system size and time) results into physically applicable predictions. Using high-precision numerical simulations we reconcile different asymptotic phases in a manner that matches numerics down to realistic system sizes, amenable to experimental confirmation. We characterize the behavior of extreme diffusion in the random environment model by the presence of a new phase with anomalous fluctuations related to the Kardar-Parisi-Zhang universality class and equation.},
	number = {2},
	urldate = {2024-10-13},
	journal = {Physical Review E},
	author = {Hass, Jacob B. and Carroll-Godfrey, Aileen N. and Corwin, Ivan and Corwin, Eric I.},
	month = feb,
	year = {2023},
	note = {Publisher: American Physical Society},
	pages = {L022101},
	file = {[2308.01267] First Passage Time for Many Particle Diffusion in Space-Time Random Environments:C\:\\Users\\centrifuge\\Zotero\\storage\\ILI37FBD\\2308.html:text/html;APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\8NVHHG2A\\PhysRevE.107.html:text/html;Submitted Version:C\:\\Users\\centrifuge\\Zotero\\storage\\82T4M2V3\\Hass et al. - 2023 - Anomalous fluctuations of extremes in many-particl.pdf:application/pdf},
}

@article{yodh_spectroscopy_1995,
	title = {Spectroscopy and {Imaging} with {Diffusing} {Light}},
	volume = {48},
	issn = {0031-9228, 1945-0699},
	url = {https://pubs.aip.org/physicstoday/article/48/3/34/408499/Spectroscopy-and-Imaging-with-Diffusing},
	doi = {10.1063/1.881445},
	abstract = {Visually opaque media are ubiquitous in nature. While some materials are opaque because they strongly absorb visible light, others, such as loam, white paint, biological tissue and milk, are opaque because photons traveling within them are predominantly scattered rather than absorbed. A vanishingly small number of photons travel straight through such substances. Instead, light is transported through these materials in a process similar to heat diffusion (figure 1).},
	language = {en},
	number = {3},
	urldate = {2024-10-13},
	journal = {Physics Today},
	author = {Yodh, Arjun and Chance, Britton},
	month = mar,
	year = {1995},
	pages = {34--40},
	file = {Yodh and Chance - 1995 - Spectroscopy and Imaging with Diffusing Light.pdf:C\:\\Users\\centrifuge\\Zotero\\storage\\2QTBZ4WM\\Yodh and Chance - 1995 - Spectroscopy and Imaging with Diffusing Light.pdf:application/pdf},
}

@article{yoo_photon_1989,
	title = {Photon localization in a disordered multilayered system},
	volume = {39},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.39.5806},
	doi = {10.1103/PhysRevB.39.5806},
	abstract = {Classical wave propagation in random multilayered media has been studied by numerical simulation in terms of interface reflectance, fluctuation of layer thickness, and number of layers. Several interesting features on wave propagation in finite media were obtained.},
	number = {9},
	urldate = {2024-10-02},
	journal = {Physical Review B},
	author = {Yoo, K. M. and Alfano, R. R.},
	month = mar,
	year = {1989},
	note = {Publisher: American Physical Society},
	pages = {5806--5809},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\XVNVRRHH\\PhysRevB.39.html:text/html},
}

@article{godoy_generalized_1998,
	title = {Generalized two stream theory for photon migration},
	volume = {261},
	issn = {0378-4371},
	url = {https://www.sciencedirect.com/science/article/pii/S037843719800329X},
	doi = {10.1016/S0378-4371(98)00329-X},
	abstract = {Recent work has indicated that a telegrapher’s type equation may accurately describe the diffusion of photons in highly turbid media, specially during the ballistic regime of the process. On the other hand, calculations that have been made using the persistent random walk model (PRW) appear to contradict this result since the telegrapher’s equation, for the case of very simple lattice geometries does not exist using PRW in 2 and 3 dimensions. In the present work we show how the continuous diffusion equations in 2D and 3D of PRW, in the weak coupling limit, provide an alternative theory for mesoscopic photon diffusion, showing that this problem can be studied using either the traditional telegrapher’s equation or by the new approach provided by the continuum and discrete versions of PRW.},
	number = {3},
	urldate = {2024-09-30},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Godoy, Salvador and Garcı́a-Colı́n, L. S. and Olivares-Robles, M. A.},
	month = dec,
	year = {1998},
	pages = {435--450},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\E8WFY2AY\\S037843719800329X.html:text/html},
}

@article{yoo_time-resolved_1990,
	title = {Time-resolved coherent and incoherent components of forward light scattering in random media},
	volume = {15},
	copyright = {© 1990 Optical Society of America},
	issn = {1539-4794},
	url = {https://opg.optica.org/ol/abstract.cfm?uri=ol-15-6-320},
	doi = {10.1364/OL.15.000320},
	abstract = {Angle- and time-resolved studies are presented for an ultrafast laser pulse propagating through a slab of random media in the intermediate scattering regime, where a coherent (ballistic) component coexists with a incoherent (diffusive) component in the forward-scattered light. The incoherent component can be approximated by diffusion theory when the thickness of the slab is greater than 10 transport mean free paths. The theoretical results from the two-frequency coherence function in the Rytov approximation are in qualitative but not quantitative agreement with the experimental results.},
	language = {EN},
	number = {6},
	urldate = {2024-09-30},
	journal = {Optics Letters},
	author = {Yoo, K. M. and Alfano, R. R.},
	month = mar,
	year = {1990},
	note = {Publisher: Optica Publishing Group},
	keywords = {Mie scattering, Scattering media, Forward scattering, Laser beams, Ultrafast lasers, Streak cameras},
	pages = {320--322},
}

@article{masoliver_finite-velocity_1996,
	title = {Finite-velocity diffusion},
	volume = {17},
	issn = {0143-0807},
	url = {https://dx.doi.org/10.1088/0143-0807/17/4/008},
	doi = {10.1088/0143-0807/17/4/008},
	abstract = {The phenomenon of diffusion modelled as Brownian motion or in terms of the diffusion equation is deficient in that it permits an infinite speed of signal propagation. The simplest diffusion-like equation with a bounded speed of signal propagation is the so-called telegrapher's equation which implicitly contains a type of momentum. We discuss some properties, solutions and problems related to this equation. These are generally more complicated in form than corresponding ones for the diffusion equation, exhibiting wave-like properties at short times and diffusion-like properties in the long-time limit. Resumen. El fenómeno de la difusión, modelado tanto como movimiento Browniano como mediante la ecuación de difusión, es deficiente en el sentido que permite una velocidad de propagación infinita. La denominada ecuación del telegrafista es una de las ecuaciones más simples con una velocidad de propagación acotada y que contiene de forma implícita un cierto tipo momento. En este trabajo se discuten algunas propiedades, soluciones y cuestiones relacionadas con esta ecuación. Estas propiedades y soluciones son generalmente más complicadas que las correspondientes a la ecuación de difusión ordinaria, presentando, a tiempos cortos, propiedades de tipo ondulatorio y propiedades difusivas en el límite asintótico.},
	language = {en},
	number = {4},
	urldate = {2024-09-23},
	journal = {European Journal of Physics},
	author = {Masoliver, Jaume and Weiss, George H.},
	month = jul,
	year = {1996},
	pages = {190},
	file = {IOP Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\XY5JZPRY\\Masoliver and Weiss - 1996 - Finite-velocity diffusion.pdf:application/pdf},
}

@article{masoliver_telegraphers_1994,
	title = {Telegrapher's equations with variable propagation speeds},
	volume = {49},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.49.3852},
	doi = {10.1103/PhysRevE.49.3852},
	abstract = {All derivations of the one-dimensional telegrapher’s equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.},
	number = {5},
	urldate = {2024-09-23},
	journal = {Physical Review E},
	author = {Masoliver, Jaume and Weiss, George H.},
	month = may,
	year = {1994},
	note = {Publisher: American Physical Society},
	pages = {3852--3854},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\T6684AYW\\PhysRevE.49.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\7HPFEBQ8\\Masoliver and Weiss - 1994 - Telegrapher's equations with variable propagation .pdf:application/pdf},
}

@article{weiss_applications_2002,
	title = {Some applications of persistent random walks and the telegrapher's equation},
	volume = {311},
	issn = {0378-4371},
	url = {https://www.sciencedirect.com/science/article/pii/S0378437102008051},
	doi = {10.1016/S0378-4371(02)00805-1},
	abstract = {A persistent random walk can be regarded as a multidimensional Markov process. The bias-free telegraphers equation is∂2p∂t2+1T∂p∂t=v2∇2p.It can be regarded as interpolating between the wave equation (T→∞) and the diffusion equation (T→0). Previously, it has found application in thermodynamics (cf. the review in Rev. Mod. Phys. 61 (1989) 41; 62 (1990) 375). More recent applications are reviewed in the present article.},
	number = {3},
	urldate = {2024-09-23},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Weiss, George H},
	month = aug,
	year = {2002},
	keywords = {Ballistic transport, Diffusive transport, Optical imaging},
	pages = {381--410},
	file = {ScienceDirect Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\YEFENJRE\\S0378437102008051.html:text/html},
}

@article{serva_brownian_2021,
	title = {Brownian {Motion} at the {Speed} of {Light}: {A} {New} {Lorentz} {Invariant} {Family} of {Processes}.},
	volume = {182},
	issn = {00224715},
	shorttitle = {Brownian {Motion} at the {Speed} of {Light}},
	url = {https://go.gale.com/ps/i.do?p=AONE&sw=w&issn=00224715&v=2.1&it=r&id=GALE%7CA656388842&sid=googleScholar&linkaccess=abs},
	doi = {10.1007/s10955-021-02734-0},
	abstract = {{\textless}em{\textgreater}Gale{\textless}/em{\textgreater} Academic OneFile includes Brownian Motion at the Speed of Light: A New Lorentz In by Maurizio Serva. Click to explore.},
	language = {English},
	number = {3},
	urldate = {2024-09-23},
	journal = {Journal of Statistical Physics},
	author = {Serva, Maurizio},
	month = mar,
	year = {2021},
	note = {Publisher: Springer},
	pages = {NA--NA},
	file = {Full Text:C\:\\Users\\centrifuge\\Zotero\\storage\\ALHBLFFF\\Serva - 2021 - Brownian Motion at the Speed of Light A New Loren.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\LXU79HYF\\i.html:text/html},
}

@book{du_chatelet_dissertation_1744,
	address = {Paris},
	title = {Dissertation sur la nature et la propagation du feu},
	copyright = {domaine public},
	url = {https://gallica.bnf.fr/ark:/12148/bpt6k756786},
	abstract = {Dissertation sur la nature et la propagation du feu / [par la Mise Du Châtelet] -- 1744 -- livre},
	language = {EN},
	urldate = {2025-03-10},
	publisher = {Prault fils},
	author = {Du Châtelet, Gabrielle-Émilie Le Tonnelier de Breteuil (1706-1749 ; marquise) Auteur du texte},
	year = {1744},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\SJF2IPIU\\bpt6k756786.html:text/html},
}

@book{rudolf_clausius_mechanical_1867,
	address = {London},
	title = {The {Mechanical} {Theory} of {Heat}: {With} {Its} {Applications} to the {Steam}-engine and to the {Physical} {Properties} of {Bodies}},
	shorttitle = {The {Mechanical} {Theory} of {Heat}},
	url = {http://archive.org/details/mechanicaltheor04claugoog},
	abstract = {Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.},
	language = {English},
	urldate = {2025-03-10},
	publisher = {J. Van Voorst},
	author = {{Rudolf Clausius}},
	collaborator = {{Harvard University}},
	year = {1867},
}

@article{bachelier_theorie_1900,
	title = {Théorie de la spéculation},
	volume = {17},
	url = {https://archive.org/details/bachelier-theorie-de-la-speculation/page/n5/mode/2up},
	urldate = {2025-03-10},
	journal = {Annales scientifiques de l'École Normale Supérieure},
	author = {Bachelier, Louis},
	year = {1900},
	file = {Théorie de la spéculation \: Bachelier, Louis, 1870-1946 \: Free Download, Borrow, and Streaming \: Internet Archive:C\:\\Users\\centrifuge\\Zotero\\storage\\ZNG69VKG\\2up.html:text/html},
}

@article{ingenhousz_new_1785,
	title = {New {Experiments} and {Observations} on {Diverse} {Physical} {Objects}},
	url = {https://scholar.googleusercontent.com/scholar.bib?q=info:VhT3YDCVQyEJ:scholar.google.com/&output=citation&scisdr=ClEwtjnsENCEinVfngs:AFWwaeYAAAAAZ89ZhgtIDi2Pa5xyO2qO4VEj-vc&scisig=AFWwaeYAAAAAZ89Zhk9a-wz5V6cBNMh8P8HgGtA&scisf=4&ct=citation&cd=-1&hl=en},
	urldate = {2025-03-10},
	journal = {T. Barrois le jeune, Paris},
	author = {Ingenhousz, Jan},
	year = {1785},
	file = {scholar.googleusercontent.com/scholar.bib?q=info\:VhT3YDCVQyEJ\:scholar.google.com/&output=citation&scisdr=ClEwtjnsENCEinVfngs\:AFWwaeYAAAAAZ89ZhgtIDi2Pa5xyO2qO4VEj-vc&scisig=AFWwaeYAAAAAZ89Zhk9a-wz5V6cBNMh8P8HgGtA&scisf=4&ct=citation&cd=-1&hl=en:C\:\\Users\\centrifuge\\Zotero\\storage\\AW55VCHP\\scholar.html:text/html},
}

@article{van_der_pas_discovery_1971,
	title = {The {Discovery} of the {Brownian} {Motion}},
	volume = {13},
	url = {https://resources.huygens.knaw.nl/retroboeken/scientiarumhistoria/#page=25&accessor=toc&source=source_volume_13},
	number = {1},
	urldate = {2025-03-10},
	journal = {Scientiarum Historia: Journal of the History of Science and Medicine},
	author = {van der Pas, Peter W.},
	year = {1971},
	pages = {27--35},
	file = {Scientiarum Historia\: Journal of the History of Science and Medicine (1959-2006):C\:\\Users\\centrifuge\\Zotero\\storage\\2XIZEYDK\\scientiarumhistoria.html:text/html},
}

@article{sutherland_lxxv_1905,
	title = {{LXXV}. {A} dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin},
	volume = {9},
	issn = {1941-5982},
	url = {https://doi.org/10.1080/14786440509463331},
	doi = {10.1080/14786440509463331},
	number = {54},
	urldate = {2025-03-11},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Sutherland, William},
	month = jun,
	year = {1905},
	pages = {781--785},
}

@article{alberts_intermediate_2010,
	title = {Intermediate {Disorder} {Regime} for {Directed} {Polymers} in {Dimension} 1+1},
	volume = {105},
	doi = {10.1103/PhysRevLett.105.090603},
	abstract = {We introduce a new disorder regime for directed polymers in dimension 1+1 by scaling the inverse temperature β with the length of the polymer n. We scale βn:=βn-α for {\textbackslash}alpha{\textbackslash}geq0. This scaling interpolates between the weak disorder (β=0) and strong disorder regimes ({\textbackslash}beta{\textgreater}0). The fluctuation exponents ζ for the polymer end point and χ for the free energy depend on α in this regime, with α=0 corresponding to the Kardar-Parisi-Zhang polymer exponents ζ=2/3, χ=1/3, and {\textbackslash}alpha{\textbackslash}geq1/4 corresponding to the simple random walk exponents ζ=1/2, χ=0. For {\textbackslash}alphaın(0,1/4) the exponents interpolate linearly between these two extremes. At α=1/4 we exactly identify the limiting distribution of the free energy and the end point of the polymer.},
	number = {9},
	journal = {Physical Review Letters},
	author = {Alberts, Tom and Khanin, Kostya and Quastel, Jeremy},
	month = aug,
	year = {2010},
	note = {Publisher: American Physical Society},
	pages = {090603},
}

@article{amir_probability_2011,
	title = {Probability {Distribution} of the {Free} {Energy} of the {Continuum} {Directed} {Random} {Polymer} in 1+1 {Dimensions}},
	volume = {64},
	issn = {00103640},
	doi = {10.1002/cpa.20347},
	abstract = {We consider the solution of the stochastic heat equation {\textbackslash}textbackslash partial\_T {\textbackslash}textbackslash mathcal\{Z\} = 1/2 {\textbackslash}textbackslash partial\_X{\textasciicircum}2 {\textbackslash}textbackslash mathcal\{Z\} - {\textbackslash}textbackslash mathcal\{Z\} {\textbackslash}textbackslash dot\{{\textbackslash}textbackslash mathscr\{W\}\} with delta function initial condition {\textbackslash}textbackslash mathcal\{Z\} (T=0)= {\textbackslash}textbackslash delta\_0 whose logarithm, with appropriate normalizations, is the free energy of the continuum directed polymer, or the solution of the Kardar-Parisi-Zhang equation with narrow wedge initial conditions. We obtain explicit formulas for the one-dimensional marginal distributions – the \{{\textbackslash}textbackslash it crossover distributions\} – which interpolate between a standard Gaussian distribution (small time) and the GUE Tracy-Widom distribution (large time). The proof is via a rigorous steepest descent analysis of the Tracy-Widom formula for the asymmetric simple exclusion with anti-shock initial data, which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit. The limit also describes the crossover behaviour between the symmetric and asymmetric exclusion processes.},
	number = {4},
	journal = {Communications on Pure and Applied Mathematics},
	author = {Amir, Gideon and Corwin, Ivan and Quastel, Jeremy},
	month = apr,
	year = {2011},
	note = {arXiv: 1003.0443},
	keywords = {Condensed Matter - Statistical Mechanics, 82C22, Mathematics - Probability, Mathematical Physics, 60H15},
	pages = {466--537},
}

@article{balazs_large_2019,
	title = {Large {Deviations} and {Wandering} {Exponent} for {Random} {Walk} in a {Dynamic} {Beta} {Environment}},
	volume = {47},
	issn = {0091-1798, 2168-894X},
	doi = {10.1214/18-AOP1306},
	abstract = {Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution, the transformed walk obeys the wandering exponent {\textbackslash}2/3{\textbackslash} that agrees with Kardar– Parisi– Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.},
	number = {4},
	journal = {The Annals of Probability},
	author = {Balázs, Márton and Rassoul-Agha, Firas and Seppäläinen, Timo},
	month = jul,
	year = {2019},
	note = {Publisher: Institute of Mathematical Statistics},
	keywords = {large deviations, 60K35, 60K37, Random walk, KPZ, Beta distribution, Doob transform, hypergeometric function, Kardar–Parisi–Zhang, random environment, RWRE, wandering exponent},
	pages = {2186--2229},
}

@article{balazs_random_2006,
	title = {The {Random} {Average} {Process} and {Random} {Walk} in a {Space}-{Time} {Random} {Environment} in {One} {Dimension}},
	volume = {266},
	issn = {0010-3616, 1432-0916},
	doi = {10.1007/s00220-006-0036-y},
	abstract = {We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n{\textasciicircum}\{1/4\} where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form equilibria, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n{\textasciicircum}\{1/4\} and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.},
	number = {2},
	journal = {Communications in Mathematical Physics},
	author = {Balazs, Marton and Rassoul-Agha, Firas and Seppalainen, Timo},
	month = sep,
	year = {2006},
	note = {arXiv: math/0507226},
	keywords = {60K35, 60K37, Mathematics - Probability, 60F05},
	pages = {499--545},
}

@article{balkovsky_intermittent_2001,
	title = {Intermittent {Distribution} of {Inertial} {Particles} in {Turbulent} {Flows}},
	volume = {86},
	doi = {10.1103/PhysRevLett.86.2790},
	abstract = {We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.},
	number = {13},
	journal = {Physical Review Letters},
	author = {Balkovsky, E. and Falkovich, G. and Fouxon, A.},
	month = mar,
	year = {2001},
	note = {Publisher: American Physical Society},
	pages = {2790--2793},
}

@article{barraquand_large_2020,
	title = {Large {Deviations} for {Sticky} {Brownian} {Motions}},
	volume = {25},
	issn = {1083-6489, 1083-6489},
	doi = {10.1214/20-EJP515},
	abstract = {We consider {\textbackslash}n{\textbackslash}-point sticky Brownian motions: a family of {\textbackslash}n{\textbackslash} diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive probability. These diffusions can also be seen as {\textbackslash}n{\textbackslash} random motions in a random environment whose distribution is given by so-called stochastic flows of kernels. For a specific type of sticky interaction, we prove exact formulas characterizing the stochastic flow and show that in the large deviations regime, the random fluctuations of these stochastic flows are Tracy-Widom GUE distributed. An equivalent formulation of this result states that the extremal particle among {\textbackslash}n{\textbackslash} sticky Brownian motions has Tracy-Widom distributed fluctuations in the large {\textbackslash}n{\textbackslash} and large time limit. These results are proved by viewing sticky Brownian motions as a (previously known) limit of the exactly solvable beta random walk in random environment.},
	number = {none},
	journal = {Electronic Journal of Probability},
	author = {Barraquand, Guillaume and Rychnovsky, Mark},
	month = jan,
	year = {2020},
	note = {Publisher: Institute of Mathematical Statistics and Bernoulli Society},
	keywords = {60B20, 60F10, 82B21, 82B23, 82C22, Bethe ansatz, continuum models, interacting particle systems, large deviations, random matrices},
	pages = {1--52},
}

@article{bernard_anomalous_1996,
	title = {Anomalous {Scaling} in the {N}-{Point} {Functions} of {Passive} {Scalar}},
	volume = {54},
	issn = {1063-651X, 1095-3787},
	doi = {10.1103/PhysRevE.54.2564},
	abstract = {A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.},
	number = {3},
	journal = {Physical Review E},
	author = {Bernard, Denis and Gawedzki, Krzysztof and Kupiainen, Antti},
	month = sep,
	year = {1996},
	note = {arXiv: chao-dyn/9601018},
	keywords = {Condensed Matter, High Energy Physics - Theory, Nonlinear Sciences - Chaotic Dynamics},
	pages = {2564--2572},
}

@article{bernard_entanglement_2019,
	title = {Entanglement {Entropy} {Growth} in {Stochastic} {Conformal} {Field} {Theory} and the {KPZ} {Class}},
	abstract = {We introduce a model of effective conformal quantum field theory in dimension {\textbackslash}d=1+1{\textbackslash} coupled to stochastic noise, where Kardar-Parisi-Zhang (KPZ) class fluctuations can be observed. The analysis of the quantum dynamics of the scaling operators reduces to the study of random trajectories in a random environment, modeled by Brownian vector fields. We use recent results on random walks in random environments to calculate the time-dependent entanglement entropy of a subsystem interval, starting from a factorized state. We find that the fluctuations of the entropy in the large deviation regime are governed by the universal Tracy-Widom distribution. This enlarges the KPZ class, previously observed in random circuit models, to a family of interacting many body quantum systems.},
	author = {Bernard, Denis and Doussal, Pierre Le},
	month = dec,
	year = {2019},
	keywords = {0540, 8265Dp, numbers: 6460Fr},
}

@book{bolthausen_ten_2002,
	title = {Ten {Lectures} on {Random} {Media}},
	isbn = {978-3-7643-6703-9},
	abstract = {The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon{\textbackslash}- sible for these two very enjoyable visits, Laurent Miclo for his comments on an earlier version of these notes, and last but not least Erwin Bolthausen who was my accomplice during the DMV-Seminar. A Brief Introduction The main theme of this series of lectures are "Random motions in random me{\textbackslash}- dia". The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics . . . , in which typically some diffusion mechanism takes place in an inho{\textbackslash}- mogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place.},
	publisher = {Birkhäuser Basel},
	author = {Bolthausen, Erwin and Sznitman, Alain-Sol},
	year = {2002},
}

@article{bouchaud_classical_1990,
	title = {Classical {Diffusion} of a {Particle} in a {One}-{Dimensional} {Random} {Force} {Field}},
	volume = {201},
	issn = {0003-4916},
	doi = {10.1016/0003-4916(90)90043-N},
	abstract = {We present a comprehensive study of the motion of a damped Brownian particle evolving in a static, one dimensional gaussian random force field. We provide both a clear physical picture of the process and a variety of analytical techniques. As the average bias μ is increased, a succession of different “diffusion laws” is observed: Sinai's diffusion (μ = 0, x2 {\textbackslash}backsimeq ln4t), anomalous drift (x {\textbackslash}backsimeq tμ, μ {\textless} 1), anomalous dispersion (x - Vt {\textbackslash}backsimeq {\textbackslash}pmt1μ, 1 {\textless} μ {\textless} 2), and finally normal diffusion (μ {\textgreater} 2), apart from algebraic tails outside the scaling region. We show that all those results can be understood in simple terms through a large scale description of the problem as a directed walk among traps characterized by a broad distribution of release time. From this analysis, the full asymptotic probability distributions (averaged over disorder) are precisely determined, in terms of Lévy stable laws. Sample to sample fluctuations are discussed. The probability of presence at the initial point is more specifically adressed. It amounts to computing the density of states of a Schrödinger equation with a special type of random potential. We obtain exactly the average over disorder of this quantity, using the following two different approaches: the “Dyson-Schmidt” technique, and the replica method. Both reveal interesting technical features, and the latter can be used to obtain information on the full probability distribution (and Green function). Some physical applications of this model are discussed.},
	number = {2},
	journal = {Annals of Physics},
	author = {Bouchaud, J. P and Comtet, A and Georges, A and Le Doussal, P},
	month = aug,
	year = {1990},
	pages = {285--341},
}

@article{bouchaud_diffusion_1990,
	title = {Diffusion and {Localization} of {Waves} in a {Time}-{Varying} {Random} {Environment}},
	volume = {11},
	issn = {0295-5075},
	doi = {10.1209/0295-5075/11/6/004},
	abstract = {We investigate the diffusion properties of a quantum particle or wave in a time-evolving random environment. We argue that the problem is equivalent to a classical random walk among traps with a release time distribution given by the time correlation function of the disorder. For a slowly decaying correlation function, we exhibit a new form of localization, characterized by a zero diffusion constant but a nonzero probability of escaping from any region of space. When the correlation time is finite, we argue that, for intermediate disorder, the diffusion constant of the particle will be of the same order of magnitude as the diffusion constant of the impurities.},
	number = {6},
	journal = {Europhysics Letters (EPL)},
	author = {Bouchaud, J. P.},
	month = mar,
	year = {1990},
	note = {Publisher: IOP Publishing},
	pages = {505--510},
}

@article{bouchaud_relaxation-time_1987,
	title = {The {Relaxation}-{Time} {Spectrum} of {Diffusion} in a {One}-{Dimensional} {Random} {Medium}: {An} {Exactly} {Solvable} {Case}},
	volume = {3},
	issn = {0295-5075},
	shorttitle = {The {Relaxation}-{Time} {Spectrum} of {Diffusion} in a {One}-{Dimensional} {Random} {Medium}},
	doi = {10.1209/0295-5075/3/6/002},
	abstract = {The asymmetric diffusion of a particle in a random one-dimensional medium can be described by a model of random potential with positive spectrum closely linked to supersymmetric quantum mechanics. We obtain analytical expressions for the density of states ρ(ϵ) (inverse relaxation time spectrum). This allows us to compute the averaged probability of return at any time. At zero energy ρ(ϵ) exhibits a variety of singular behaviours with a continuously varying exponent. This corresponds to the different phases of the diffusion problem at large time, including Sinaï's behaviour łanglex2(t){\textbackslash}rangle = C ln4t. The validity of the dynamical-scaling assumption is discussed.},
	number = {6},
	journal = {Europhysics Letters (EPL)},
	author = {Bouchaud, J. P. and Comtet, A. and Georges, A. and Doussal, P. Le},
	month = mar,
	year = {1987},
	note = {Publisher: IOP Publishing},
	pages = {653--660},
}

@article{brockington_bethe_2021,
	title = {The {Bethe} {Ansatz} for {Sticky} {Brownian} {Motions}},
	abstract = {We consider a diffusion in {\textbackslash}textbackslash mathbb\{R\}{\textasciicircum}n{\textbackslash} whose coordinates each behave as one-dimensional Brownian motions, that behave independently when apart, but have a sticky interaction when they meet. The diffusion in {\textbackslash}textbackslash mathbb\{R\}{\textasciicircum}n{\textbackslash} can be viewed as the {\textbackslash}n{\textbackslash}-point motion of a stochastic flow of kernels. We derive the Kolmogorov backwards equation and show that for a specific choice of interaction it can be solved exactly with the Bethe ansatz. We then use our formulae to study the behaviour of the flow of kernels for the exactly solvable choice of interaction.},
	journal = {arXiv:2104.06482 [math]},
	author = {Brockington, Dom and Warren, Jon},
	month = apr,
	year = {2021},
	note = {arXiv: 2104.06482},
	keywords = {Mathematics - Probability},
}

@article{burlatsky_transient_1998,
	title = {Transient {Relaxation} of a {Charged} {Polymer} {Chain} {Subject} to an {External} {Field} in a {Random} {Tube}},
	volume = {109},
	issn = {0021-9606},
	doi = {10.1063/1.476831},
	number = {6},
	journal = {The Journal of Chemical Physics},
	author = {Burlatsky, S. F. and Deutch, John M.},
	month = aug,
	year = {1998},
	note = {Publisher: American Institute of Physics},
	pages = {2572--2578},
}

@article{calabrese_free-energy_2010,
	title = {Free-{Energy} {Distribution} of the {Directed} {Polymer} at {High} {Temperature}},
	volume = {90},
	issn = {0295-5075},
	doi = {10.1209/0295-5075/90/20002},
	abstract = {We study the directed polymer of length t in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature T is described, upon scaling “time”t{\textbackslash}simT5/κ and space x=T3/κ (with κ=T for the discrete model) by a continuum model with δ-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free-energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy-Widom distribution (TW) which describes the fixed-T infinite-t limit. The exact free-energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.},
	number = {2},
	journal = {EPL (Europhysics Letters)},
	author = {Calabrese, P. and Doussal, P. Le and Rosso, A.},
	month = apr,
	year = {2010},
	note = {Publisher: IOP Publishing},
	pages = {20002},
}

@article{chernov_replication_1967,
	title = {Replication of a {Multicomponent} {Chain} by the "{Lightning}" {Mechanism}},
	volume = {12},
	issn = {0006-3509, 1555-6654},
	number = {2},
	journal = {Biophysics},
	author = {Chernov, A. A.},
	year = {1967},
}

@article{chertkov_anomalous_1996,
	title = {Anomalous {Scaling} {Exponents} of a {White}-{Advected} {Passive} {Scalar}},
	volume = {76},
	doi = {10.1103/PhysRevLett.76.2706},
	abstract = {For Kraichnan's problem of passive scalar advection by a velocity field delta correlated in time, the limit of large space dimensionality d{\textbackslash}gg1 is considered. Scaling exponents of the scalar field are analytically found to be ζ2n=nζ2-2(2-ζ2)n(n-1)/d, while those of the dissipation field are μn=-2(2-ζ2)n(n-1)/d for orders nłld. The refined similarity hypothesis ζ2n=nζ2+μn is thus established by a straightforward calculation for the case considered.},
	number = {15},
	journal = {Physical Review Letters},
	author = {Chertkov, M. and Falkovich, G.},
	month = apr,
	year = {1996},
	note = {Publisher: American Physical Society},
	pages = {2706--2709},
}

@article{corwin_kardar_2012,
	title = {The {Kardar}– {Parisi}– {Zhang} {Equation} and {Universality} {Class}},
	volume = {01},
	issn = {2010-3263},
	doi = {10.1142/S2010326311300014},
	abstract = {Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past 25 years a new universality class has emerged to describe a host of important physical and probabilistic models (including one-dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar– Parisi– Zhang (KPZ) universality class and underlying it is, again, a continuum object — a non-linear stochastic partial differential equation — known as the KPZ equation. The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media. As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.},
	number = {01},
	journal = {Random Matrices: Theory and Applications},
	author = {Corwin, Ivan},
	month = jan,
	year = {2012},
	note = {Publisher: World Scientific Publishing Co.},
	keywords = {anomalous fluctuations, asymmetric exclusion process, directed polymers, Kardar–Parisi–Zhang equation, random growth, stochastic Burgers equation, stochastic heat equation},
	pages = {1130001},
}

@article{noskowicz_average_1988-1,
	title = {Average versus {Typical} {Mean} {First}-{Passage} {Time} in a {Random} {Random} {Walk}},
	volume = {61},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.500},
	doi = {10.1103/PhysRevLett.61.500},
	number = {5},
	journal = {Phys. Rev. Lett.},
	author = {Noskowicz, S. H. and Goldhirsch, I.},
	month = aug,
	year = {1988},
	note = {Publisher: American Physical Society},
	pages = {500--502},
}

@article{le_doussal_first-passage_1989,
	title = {First-passage time for random walks in random environments},
	volume = {62},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.3097},
	doi = {10.1103/PhysRevLett.62.3097},
	number = {26},
	journal = {Phys. Rev. Lett.},
	author = {Le Doussal, Pierre},
	month = jun,
	year = {1989},
	note = {Publisher: American Physical Society},
	pages = {3097--3097},
}

@article{chechkin_brownian_2017,
	title = {Brownian yet {Non}-{Gaussian} {Diffusion}: {From} {Superstatistics} to {Subordination} of {Diffusing} {Diffusivities}},
	volume = {7},
	url = {https://link.aps.org/doi/10.1103/PhysRevX.7.021002},
	doi = {10.1103/PhysRevX.7.021002},
	number = {2},
	journal = {Phys. Rev. X},
	author = {Chechkin, Aleksei V. and Seno, Flavio and Metzler, Ralf and Sokolov, Igor M.},
	month = apr,
	year = {2017},
	note = {Publisher: American Physical Society},
	pages = {021002},
}

@article{corwin_kardarparisizhang_2017,
	title = {Kardar–{Parisi}–{Zhang} {Equation} and {Large} {Deviations} for {Random} {Walks} in {Weak} {Random} {Environments}},
	volume = {166},
	issn = {1572-9613},
	doi = {10.1007/s10955-016-1693-7},
	abstract = {We consider the transition probabilities for random walks in {\textbackslash}1+1{\textbackslash}dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.},
	number = {1},
	journal = {Journal of Statistical Physics},
	author = {Corwin, Ivan and Gu, Yu},
	month = jan,
	year = {2017},
	pages = {150--168},
}

@article{deuschel_quenched_2016,
	title = {Quenched {Invariance} {Principle} for {Random} {Walk} in {Time}-{Dependent} {Balanced} {Random} {Environment}},
	abstract = {We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments which is not necessarily nearest-neigbhor. We assume that the environment satisfies appropriate ergodicity and ellipticity conditions. The proof is based on the use of a maximum principle for parabolic difference operators.},
	journal = {arXiv:1503.01964 [math]},
	author = {Deuschel, Jean-Dominique and Guo, Xiaoqin and Ramirez, Alejandro F.},
	month = sep,
	year = {2016},
	note = {arXiv: 1503.01964},
	keywords = {60K37, Mathematics - Probability, 35K10 (Secondary), 82D30 (Primary)},
}

@article{dotsenko_bethe_2010,
	title = {Bethe {Ansatz} {Derivation} of the {Tracy}-{Widom} {Distribution} for {One}-{Dimensional} {Directed} {Polymers}},
	volume = {90},
	issn = {0295-5075},
	doi = {10.1209/0295-5075/90/20003},
	abstract = {The distribution function of the free-energy fluctuations in one-dimensional directed polymers with δ-correlated random potential is studied by mapping the replicated problem to a many-body quantum boson system with attractive interactions. Performing the summation over the entire spectrum of excited states the problem is reduced to the Fredholm determinant with the Airy kernel which is known to yield the Tracy-Widom distribution.},
	number = {2},
	journal = {EPL (Europhysics Letters)},
	author = {Dotsenko, V.},
	month = apr,
	year = {2010},
	note = {Publisher: IOP Publishing},
	pages = {20003},
}

@article{duclaux_mouvement_1940,
	title = {Le {Mouvement} {Brownien} et {La} {Formule} d'{Einstein}},
	volume = {1},
	doi = {10.1051/jphysrad:019400010308100},
	abstract = {Le problème du mouvement brownien d'une particule au sein d'un liquide visqueux est considéré comme résolu par la formule d'Einstein. Cependant la signification de cette formule est autre. Elle résulte d'une combinaison entre le principe d'équipartition de l'énergie et l'hydrodynamique, et ne suppose pas la nature moléculaire du liquide. Ce n'est donc pas en réalité une formule du mouvement brownien. La relation qu'elle établit semble être un cas particulier d'une loi générale, d'après laquelle la trajectoire moyenne d'une particule, ou sa position moyenne d'équilibre, est indépendante de la présence et de la nature du liquide environnant. La véritable formule du mouvement brownien sera celle qui donnera la viscosité d'un liquide en fonction de sa constitution moléculaire. Les vérifications expérimentales connues de la formule d'Einstein sont incomplètes par leur principe, et ne permettent pas de conclure à l'exactitude de la théorie du mouvement brownien.},
	number = {3},
	journal = {Journal de Physique et le Radium},
	author = {Duclaux, J.},
	year = {1940},
	pages = {81--84},
}

@article{einstein_theoretische_1907,
	title = {Theoretische {Bemerkungen} Über {Die} {Brownsche} {Bewegung}},
	volume = {13},
	issn = {0005-9021},
	doi = {10.1002/bbpc.19070130602},
	number = {6},
	journal = {Zeitschrift für Elektrochemie und angewandte physikalische Chemie},
	author = {Einstein, A.},
	year = {1907},
	pages = {41--42},
}

@article{einstein_zur_1906,
	title = {Zur {Theorie} {Der} {Brownschen} {Bewegung}},
	volume = {324},
	issn = {1521-3889},
	doi = {10.1002/andp.19063240208},
	number = {2},
	journal = {Annalen der Physik},
	author = {Einstein, A.},
	year = {1906},
	pages = {371--381},
}

@book{ewens_mathematical_2012,
	title = {Mathematical {Population} {Genetics}, {I}. {Theoretical} {Introduction}},
	volume = {27},
	isbn = {978-0-387-21822-9},
	abstract = {It has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, e.g., the theory of molecular ...},
	author = {Ewens, Warren John},
	year = {2012},
	doi = {10.1007/978-0-387-21822-9},
}

@article{feller_diffusion_1951,
	title = {Diffusion {Processes} in {Genetics}},
	volume = {2},
	abstract = {Berkeley Symposium on Mathematical Statistics and Probability},
	journal = {Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability},
	author = {Feller, William},
	month = jan,
	year = {1951},
	note = {Publisher: University of California Press},
	pages = {227--247},
}

@article{fisher_nonequilibrium_2001,
	title = {Nonequilibrium {Dynamics} of {Random} {Field} {Ising} {Spin} {Chains}: {Exact} {Results} via {Real} {Space} {Renormalization} {Group}},
	volume = {64},
	shorttitle = {Nonequilibrium {Dynamics} of {Random} {Field} {Ising} {Spin} {Chains}},
	doi = {10.1103/PhysRevE.64.066107},
	abstract = {The nonequilibrium dynamics of classical random Ising spin chains with nonconserved magnetization are studied using an asymptotically exact real space renormalization group (RSRG). We focus on random field Ising model (RFIM) spin chains with and without a uniform applied field, as well as on Ising spin glass chains in an applied field. For the RFIM we consider a universal regime where the random field and the temperature are both much smaller than the exchange coupling. In this regime, the Imry-Ma length that sets the scale of the equilibrium correlations is large and the coarsening of domains from random initial conditions (e.g., a quench from high temperature) occurs over a wide range of length scales. The two types of domain walls that occur diffuse in opposite random potentials, of the form studied by Sinai, and domain walls annihilate when they meet. Using the RSRG we compute many universal asymptotic properties of both the nonequilibrium dynamics and the equilibrium limit. We find that the configurations of the domain walls converge rapidly toward a set of system-specific time-dependent positions that are independent of the initial conditions. Thus the behavior of this nonequilibrium system is pseudodeterministic at long times because of the broad distributions of barriers that occur on the long length scales involved. Specifically, we obtain the time dependence of the energy, the magnetization, and the distribution of domain sizes (found to be statistically independent). The equilibrium limits agree with known exact results. We obtain the exact scaling form of the two-point equal time correlation function ¯łangleS0(t)Sx(t){\textbackslash}rangle and the two-time autocorrelations ¯łangleS0(t')S0(t){\textbackslash}rangle. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the {\textbackslash}pmJ Ising spin glass in an applied field are obtained from the RFIM via a gauge transformation. In addition to these we compute the two-point two-time correlation function ¯łangleS0(t)Sx(t){\textbackslash}ranglełangleS0(t')Sx(t'){\textbackslash}rangle which can in principle be measured by experiments on spin-glass-like systems. The thermal fluctuations are studied and found to be dominated by rare events; in particular all moments of truncated equal time correlations are computed. Physical properties which are typically measured in aging experiments are also studied, focusing on the response to a small magnetic field which is applied after waiting for the system to equilibrate for a time tw. The nonequilibrium fluctuation-dissipation ratio X(t,tw) is computed. We find that for (t-tw){\textbackslash}simt{\textasciicircum}αw with {\textasciicircum}{\textbackslash}alpha{\textless}1, the ratio equal to its equilibrium value X=1, although time translational invariance does not hold in this regime. For t-tw{\textbackslash}simtw the ratio exhibits an aging regime with a nontrivial X=X(t/tw){\textbackslash}neq1, but the behavior is markedly different from mean field theory. Finally the distribution of the total magnetization and of the number of domains is computed for large finite size systems. General issues about convergence toward equilibrium and the possibilities of weakly history-dependent evolution in other random systems are discussed.},
	number = {6},
	journal = {Physical Review E},
	author = {Fisher, Daniel S. and Le Doussal, Pierre and Monthus, Cécile},
	month = nov,
	year = {2001},
	note = {Publisher: American Physical Society},
	pages = {066107},
}

@article{ghosh_non-universal_2015,
	title = {Non-{Universal} {Tracer} {Diffusion} in {Crowded} {Media} of {Non}-{Inert} {Obstacles}},
	volume = {17},
	doi = {10.1039/c4cp03599b},
	abstract = {We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.},
	number = {3},
	journal = {Physical Chemistry Chemical Physics},
	author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf},
	month = jan,
	year = {2015},
	pages = {1847--1858},
}

@article{halpin-healy_kpz_2015,
	title = {A {KPZ} {Cocktail}-{Shaken}, {Not} {Stirred}...},
	volume = {160},
	issn = {1572-9613},
	doi = {10.1007/s10955-015-1282-1},
	abstract = {The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we (i) pay debts to heroic predecessors, (ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, (iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, (iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of {\textbackslash}d={\textbackslash}textbackslash infty {\textbackslash}KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.},
	number = {4},
	journal = {Journal of Statistical Physics},
	author = {Halpin-Healy, Timothy and Takeuchi, Kazumasa A.},
	month = aug,
	year = {2015},
	pages = {794--814},
}

@article{krug_amplitude_1992,
	title = {Amplitude universality for driven interfaces and directed polymers in random media},
	volume = {45},
	url = {https://link.aps.org/doi/10.1103/PhysRevA.45.638},
	doi = {10.1103/PhysRevA.45.638},
	number = {2},
	journal = {Phys. Rev. A},
	author = {Krug, Joachim and Meakin, Paul and Halpin-Healy, Timothy},
	month = jan,
	year = {1992},
	note = {Publisher: American Physical Society},
	pages = {638--653},
}

@article{hartmann_probing_2020,
	title = {Probing {Large} {Deviations} of the {Kardar}-{Parisi}-{Zhang} {Equation} at {Short} {Times} with an {Importance} {Sampling} of {Directed} {Polymers} in {Random} {Media}},
	volume = {101},
	doi = {10.1103/PhysRevE.101.012134},
	abstract = {The one-point distribution of the height for the continuum Kardar-Parisi-Zhang equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10-1000 in the tails. The short-time behavior is investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations, showing a spectacular agreement with the analytical expressions. The flat and stationary initial conditions are studied in the full space, together with the droplet initial condition in the half-space.},
	number = {1},
	journal = {Physical Review E},
	author = {Hartmann, Alexander K. and Krajenbrink, Alexandre and Le Doussal, Pierre},
	month = jan,
	year = {2020},
	pages = {012134--012134},
}

@article{hentschel_relative_1984,
	title = {Relative {Diffusion} in {Turbulent} {Media}: {The} {Fractal} {Dimension} of {Clouds}},
	volume = {29},
	shorttitle = {Relative {Diffusion} in {Turbulent} {Media}},
	doi = {10.1103/PhysRevA.29.1461},
	abstract = {A recent experiment indicates that clouds in the atmosphere have fractal surfaces which are characterized by a fractal dimension D{\textbackslash}sim2.35. Here we present a theory of the fractal dimension of clouds. We show that the fractal dimension of clouds is calculable from the theory of relative turbulent diffusion. We claim that previous approaches to the theory of relative diffusion are in contradiction with this experiment and that a newly developed theory gives D{\textbackslash}sim2.35 as a natural consequence. The new theory of relative diffusion is simultaneously in agreement with the intermittency-modified "43 (power) law" [i.e., the (4+2μ)3 (power) law, where μ is the intermittency exponent].},
	number = {3},
	journal = {Physical Review A},
	author = {Hentschel, H. G. E. and Procaccia, Itamar},
	month = mar,
	year = {1984},
	note = {Publisher: American Physical Society},
	pages = {1461--1470},
}

@article{hinrichsen_non-equilibrium_2000,
	title = {Non-{Equilibrium} {Critical} {Phenomena} and {Phase} {Transitions} into {Absorbing} {States}},
	volume = {49},
	doi = {10.1080/00018730050198152},
	abstract = {This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states. © 2000 Taylor \& Francis Group, LLC.},
	number = {7},
	journal = {Advances in Physics},
	author = {Hinrichsen, Haye},
	month = nov,
	year = {2000},
	pages = {815--958},
}

@article{hofling_anomalous_2013,
	title = {Anomalous {Transport} in the {Crowded} {World} of {Biological} {Cells}},
	volume = {76},
	doi = {10.1088/0034-4885/76/4/046602},
	abstract = {A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation. © 2013 IOP Publishing Ltd.},
	number = {4},
	journal = {Reports on Progress in Physics},
	author = {Höfling, Felix and Franosch, Thomas},
	year = {2013},
	keywords = {Animals, Humans, Biological Transport, Biological, Cells / metabolism*, doi:10.1088/0034-4885/76/4/046602, Felix Höfling, MEDLINE, Models, Movement, National Center for Biotechnology Information, National Institutes of Health, National Library of Medicine, NCBI, NIH, NLM, Non-U.S. Gov't, pmid:23481518, PubMed Abstract, Research Support, Review, Thomas Franosch},
}

@article{lukic_direct_2005,
	title = {Direct {Observation} of {Nondiffusive} {Motion} of a {Brownian} {Particle}},
	volume = {95},
	doi = {10.1103/PhysRevLett.95.160601},
	abstract = {The thermal position fluctuations of a single micron-sized sphere immersed in a fluid were recorded by optical trapping interferometry with nanometer spatial and microsecond temporal resolution. We find, in accord with the theory of Brownian motion including hydrodynamic memory effects, that the transition from ballistic to diffusive motion is delayed to significantly longer times than predicted by the standard Langevin equation. This delay is a consequence of the inertia of the fluid. On the shortest time scales investigated, the sphere's inertia has a small, but measurable, effect.},
	number = {16},
	journal = {Physical Review Letters},
	author = {Lukić, B. and Jeney, S. and Tischer, C. and Kulik, A. J. and Forró, L. and Florin, E.-L.},
	month = oct,
	year = {2005},
	pages = {160601},
}

@article{franosch_resonances_2011,
	title = {Resonances {Arising} from {Hydrodynamic} {Memory} in {Brownian} {Motion}},
	volume = {478},
	copyright = {© 2011 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {0028-0836},
	doi = {10.1038/nature10498},
	abstract = {Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations. This hydrodynamic /`memory/' translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin/'s pioneering experiments on Brownian motion, direct experimental observation of this colour is still elusive. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere/'s positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors, our results reveal that the particle-fluid-trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications.},
	number = {7367},
	journal = {Nature},
	author = {Franosch, Thomas and Grimm, Matthias and Belushkin, Maxim and Mor, Flavio M. and Foffi, Giuseppe and Forró, László and Jeney, Sylvia},
	month = oct,
	year = {2011},
	keywords = {physics, Particle physics, Statistical mechanics},
	pages = {85--88},
}

@article{kheifets_observation_2014,
	title = {Observation of {Brownian} {Motion} in {Liquids} at {Short} {Times}: {Instantaneous} {Velocity} and {Memory} {Loss}},
	volume = {343},
	issn = {0036-8075, 1095-9203},
	shorttitle = {Observation of {Brownian} {Motion} in {Liquids} at {Short} {Times}},
	doi = {10.1126/science.1248091},
	abstract = {Measurement of the instantaneous velocity of Brownian motion of suspended particles in liquid probes the microscopic foundations of statistical mechanics in soft condensed matter. However, instantaneous velocity has eluded experimental observation for more than a century since Einstein's prediction of the small length and time scales involved. We report shot-noise– limited, high-bandwidth measurements of Brownian motion of micrometer-sized beads suspended in water and acetone by an optical tweezer. We observe the hydrodynamic instantaneous velocity of Brownian motion in a liquid, which follows a modified energy equipartition theorem that accounts for the kinetic energy of the fluid displaced by the moving bead. We also observe an anticorrelated thermal force, which is conventionally assumed to be uncorrelated. Beyond Brownian Motion On long time scales, the random Brownian motion of particles diffusing in a liquid is well described by theories developed by Einstein and others, but the instantaneous or short time scale behavior has been much harder to observe or analyze. Kheifets et al. (p. 1493) combined ultrasensitive position detection with sufficient data collection to probe the Brownian motion of microbeads in fluids on time scales that are shorter than the characteristic bead-fluid interaction time.},
	number = {6178},
	journal = {Science},
	author = {Kheifets, Simon and Simha, Akarsh and Melin, Kevin and Li, Tongcang and Raizen, Mark G.},
	month = mar,
	year = {2014},
	pmid = {24675957},
	pages = {1493--1496},
}

@book{hughes_random_1995,
	title = {Random {Walks} and {Random} {Environments}: {Random} {Walks}},
	isbn = {978-0-19-853788-5},
	shorttitle = {Random {Walks} and {Random} {Environments}},
	abstract = {This is the first of two volumes devoted to probability theory in physics, physical chemistry, and engineering, providing an introduction to the problem of the random walk and its applications. In its simplest form, the random walk describes the motion of an idealized drunkard and is a discreet analogy of the diffusion process. A thorough account is given of the theory of random walks on discreet spaces (lattices or networks) and in continuous spaces, including those processed with random waiting time between steps. Applications discussed include dielectric relaxation, charge transport in the xerographic process, turbulent dispersion, diffusion through a medium with traps, laser speckle and the conformations of polymers in dilute solution. Prior knowledge of probability theory would be helpful, but not assumed. An extensive bibliography concludes the book.},
	publisher = {Clarendon Press},
	author = {Hughes, Barry D.},
	year = {1995},
	keywords = {Mathematics / Probability \& Statistics / General, Mathematics / Applied, Science / Physics / Mathematical \& Computational, Social Science / Sociology / Urban},
}

@article{huang_direct_2011,
	title = {Direct {Observation} of the {Full} {Transition} from {Ballistic} to {Diffusive} {Brownian} {Motion} in a {Liquid}},
	volume = {7},
	copyright = {© 2011 Nature Publishing Group},
	issn = {1745-2473},
	doi = {10.1038/nphys1953},
	abstract = {At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-å ngström spatial precision and the determination of the particle's velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects.},
	number = {7},
	journal = {Nature Physics},
	author = {Huang, Rongxin and Chavez, Isaac and Taute, Katja M. and Lukić, Branimir and Jeney, Sylvia and Raizen, Mark G. and Florin, Ernst-Ludwig},
	month = jul,
	year = {2011},
	keywords = {Statistical physics, Atomic, Classical and Continuum Physics, Complex Systems, Condensed Matter Physics, general, Mathematical and Computational Physics, Molecular, Optical and Plasma Physics, Physics, Theoretical, Fluid dynamics, thermodynamics and nonlinear dynamics},
	pages = {576--580},
}

@article{jullien_richardson_1999,
	title = {Richardson {Pair} {Dispersion} in {Two}-{Dimensional} {Turbulence}},
	volume = {82},
	doi = {10.1103/PhysRevLett.82.2872},
	abstract = {We report the first experimental study of the dispersion of pairs of passive particles, performed in a controlled two-dimensional turbulent flow, in which Kolmogorov-Kraichnan scaling E(k){\textbackslash}simk-5/3 holds. The Richardson t3 law is observed, and strongly non-Gaussian behavior is obtained for the Lagrangian distributions of separations. The process is shown to be isotropic, and self-similar in time. The observations, which fit well in the Kolmogorov framework, jeopardize the relevance of the Lévy walk approach.},
	number = {14},
	journal = {Physical Review Letters},
	author = {Jullien, Marie-Caroline and Paret, Jérôme and Tabeling, Patrick},
	month = apr,
	year = {1999},
	note = {Publisher: American Physical Society},
	pages = {2872--2875},
}

@article{kac_random_1947,
	title = {Random {Walk} and the {Theory} of {Brownian} {Motion}},
	volume = {54},
	doi = {10.1080/00029890.1947.11990189},
	number = {7P1},
	journal = {The American Mathematical Monthly},
	author = {Kac, Mark},
	month = aug,
	year = {1947},
	pages = {369--391},
}

@article{kanazawa_loopy_2020-1,
	title = {Loopy {Lévy} {Flights} {Enhance} {Tracer} {Diffusion} in {Active} {Suspensions}},
	volume = {579},
	issn = {1476-4687},
	doi = {10.1038/s41586-020-2086-2},
	abstract = {Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3-10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15.},
	number = {7799},
	journal = {Nature},
	author = {Kanazawa, Kiyoshi and Sano, Tomohiko G. and Cairoli, Andrea and Baule, Adrian},
	month = mar,
	year = {2020},
	pmid = {32188948},
	pages = {364--367},
}

@article{kao_virus_2006,
	title = {Virus {Diffusion} in {Isolation} {Rooms}},
	volume = {62},
	issn = {0195-6701},
	doi = {10.1016/j.jhin.2005.07.019},
	abstract = {In hospitals, the ventilation of isolation rooms operating under closed-door conditions is vital if the spread of viruses and infection is to be contained. Engineering simulation, which employs computational fluid dynamics, provides a convenient means of investigating airflow behaviour in isolation rooms for various ventilation arrangements. A cough model was constructed to permit the numerical simulation of virus diffusion inside an isolation room for different ventilation system configurations. An analysis of the region of droplet fallout and the dilution time of virus diffusion of coughed gas in the isolation room was also performed for each ventilation arrangement. The numerical results presented in this paper indicate that the parallel-directional airflow pattern is the most effective means of controlling flows containing virus droplets. Additionally, staggering the positions of the supply vents at the door end of the room relative to the exhaust vents on the wall behind the bed head provides effective infection control and containment. These results suggest that this particular ventilation arrangement enhances the safety of staff when performing medical treatments within isolation rooms.},
	number = {3},
	journal = {Journal of Hospital Infection},
	author = {Kao, P. H. and Yang, R. J.},
	month = mar,
	year = {2006},
	keywords = {Computational fluid dynamics (CFD), Infection control and containment, Isolation rooms, Virus diffusion},
	pages = {338--345},
}

@article{kardar_dynamic_1986-1,
	title = {Dynamic {Scaling} of {Growing} {Interfaces}},
	volume = {56},
	doi = {10.1103/PhysRevLett.56.889},
	abstract = {A model is proposed for the evolution of the profile of a growing interface. The deterministic growth is solved exactly, and exhibits nontrivial relaxation patterns. The stochastic version is studied by dynamic renormalization-group techniques and by mappings to Burgers's equation and to a random directed-polymer problem. The exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations. Predictions are made for more dimensions.},
	number = {9},
	journal = {Physical Review Letters},
	author = {Kardar, Mehran and Parisi, Giorgio and Zhang, Yi-Cheng},
	month = mar,
	year = {1986},
	note = {Publisher: American Physical Society},
	pages = {889--892},
}

@article{kesten_limit_1975,
	title = {A limit law for random walk in a random environment},
	volume = {30},
	number = {2},
	journal = {Compositio Mathematica},
	author = {Kesten, H. and Kozlov, M. V. and Spitzer, F.},
	year = {1975},
	pages = {145--168},
}

@article{korotkikh_hidden_2022,
	title = {Hidden {Diagonal} {Integrability} of {Q}-{Hahn} {Vertex} {Model} and {Beta} {Polymer} {Model}},
	issn = {1432-2064},
	doi = {10.1007/s00440-022-01117-0},
	abstract = {We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for q-deformed moments of the (colored) height functions of the model. Following known techniques our model can be interpreted as a q-discretization of the Beta polymer model from (Probab Theory Relat Fields 167(3):1057– 1116 (2017). arXiv:1503.04117) with a new family of parameters, also attached to diagonals. To demonstrate how integrability with respect to the new diagonal parameters works, we extend the known results about Tracy– Widom large-scale fluctuations of the Beta polymer model.},
	journal = {Probability Theory and Related Fields},
	author = {Korotkikh, Sergei},
	month = mar,
	year = {2022},
}

@article{krajenbrink_crossover_2022,
	title = {The {Crossover} from the {Macroscopic} {Fluctuation} {Theory} to the {Kardar}-{Parisi}-{Zhang} {Equation} {Controls} the {Large} {Deviations} beyond {Einstein}'s {Diffusion}},
	abstract = {We study the crossover from the macroscopic fluctuation theory (MFT) which describes 1D stochastic diffusive systems at late times, to the weak noise theory (WNT) which describes the Kardar-Parisi-Zhang (KPZ) equation at early times. We focus on the example of the diffusion in a time-dependent random field, observed in an atypical direction which induces an asymmetry. The crossover is described by a non-linear system which interpolates between the derivative and the standard non-linear Schrodinger equations in imaginary time. We solve this system using the inverse scattering method for mixed-time boundary conditions introduced by us to solve the WNT. We obtain the rate function which describes the large deviations of the sample-to-sample fluctuations of the cumulative distribution of the tracer position. It exhibits a crossover as the asymmetry is varied, recovering both MFT and KPZ limits. We sketch how it is consistent with extracting the asymptotics of a Fredholm determinant formula, recently derived for sticky Brownian motions. The crossover mechanism studied here should generalize to a larger class of models described by the MFT. Our results apply to study extremal diffusion beyond Einstein's theory.},
	journal = {arXiv:2204.04720 [cond-mat, physics:math-ph, physics:nlin]},
	author = {Krajenbrink, Alexandre and Doussal, Pierre Le},
	month = apr,
	year = {2022},
	note = {arXiv: 2204.04720},
	keywords = {Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks, Mathematics - Probability, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems},
}

@article{langevin_sur_1908,
	title = {Sur {La} {Theorie} {Du} {Mouvement} {Brownien}},
	volume = {146},
	journal = {Compt. Rendus},
	author = {Langevin, Paul},
	year = {1908},
	pages = {530--533},
}

@article{lanoiselee_diffusion-limited_2018,
	title = {Diffusion-{Limited} {Reactions} in {Dynamic} {Heterogeneous} {Media}},
	volume = {9},
	copyright = {2018 The Author(s)},
	issn = {2041-1723},
	doi = {10.1038/s41467-018-06610-6},
	abstract = {Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatiotemporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.},
	number = {1},
	journal = {Nature Communications},
	author = {Lanoiselée, Yann and Moutal, Nicolas and Grebenkov, Denis S.},
	month = oct,
	year = {2018},
	note = {Publisher: Nature Publishing Group},
	keywords = {Statistical physics, Biological physics, Permeation and transport, Reaction kinetics and dynamics},
	pages = {4398},
}

@article{le_doussal_diffusion_2017-1,
	title = {Diffusion in {Time}-{Dependent} {Random} {Media} and the {Kardar}-{Parisi}-{Zhang} {Equation}},
	volume = {96},
	doi = {10.1103/PhysRevE.96.010102},
	abstract = {Although time-dependent random media with short-range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in one-dimensional (1D) lattice random walks, where statistics related to the 1D Kardar-Parisi-Zhang (KPZ) universality class, i.e., the Gaussian unitary ensemble Tracy-Widom distribution, were shown to arise. Here, we provide a simple picture for this correspondence, directly in the continuum, which allows one to study arbitrary space dimensions and to predict a variety of universal distributions. In d=1, we predict and verify numerically the emergence of the Gaussian orthogonal ensemble Tracy-Widom distribution for fluctuations of the transition probability. In d=3, we predict a phase transition from Gaussian fluctuations to three-dimensional KPZ-type fluctuations as the bias is increased. We predict KPZ universal distributions for the arrival time of a first particle from a cloud diffusing in such media.},
	number = {1},
	journal = {Physical Review E},
	author = {Le Doussal, Pierre and Thiery, Thimothée},
	month = jul,
	year = {2017},
	pages = {010102(R)},
}

@article{le_doussal_random_1999,
	title = {Random {Walkers} in {One}-{Dimensional} {Random} {Environments}: {Exact} {Renormalization} {Group} {Analysis}},
	volume = {59},
	shorttitle = {Random {Walkers} in {One}-{Dimensional} {Random} {Environments}},
	doi = {10.1103/PhysRevE.59.4795},
	abstract = {Sinai's model of diffusion in one dimension with random local bias is studied by a real space renormalization group, which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We obtain analytically the scaling form of the distribution of the position x(t) of a particle, the probability of it not returning to the origin, and the distributions of first passage times, in an infinite sample as well as in the presence of a boundary and in a finite but large sample. We compute the distribution of the meeting time of two particles in the same environment. We also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward. These quantities obey multifractal scaling, characterized by generalized persistence exponents {\textbackslash}texttheta (g) which we compute. In the presence of a small bias, the number of returns to the origin becomes finite, characterized by a universal scaling function which we obtain. The full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained, as well as detailed analytical information about correlations between directions and times of successive jumps. The two-time distribution of the positions of a particle, x(t) and x(t') with t{\textgreater}t', is also computed exactly. It is found to exhibit “aging” with several time regimes characterized by different behaviors. In the unbiased case, for t-t'{\textbackslash}simt'α with {\textbackslash}alpha{\textgreater}1, it exhibits a lnt/lnt' scaling, with a singularity at coinciding rescaled positions x(t)=x(t'). This singularity is a novel feature, and corresponds to particles that remain in a renormalized valley. For closer times {\textbackslash}alpha{\textless}1, the two-time diffusion front exhibits a quasiequilibrium regime with a ln(t-t')/lnt' behavior which we compute. The crossover to a t/t' aging form in the presence of a small bias is also obtained analytically. Rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail. Connections with the Green function of a one-dimensional Schrödinger problem and quantum spin chains are discussed.},
	number = {5},
	journal = {Physical Review E},
	author = {Le Doussal, Pierre and Monthus, Cécile and Fisher, Daniel S.},
	month = may,
	year = {1999},
	note = {Publisher: American Physical Society},
	pages = {4795--4840},
}

@article{le_doussal_velocity_2020,
	title = {Velocity and {Diffusion} {Constant} of an {Active} {Particle} in a {One}-{Dimensional} {Force} {Field}},
	volume = {130},
	doi = {10.1209/0295-5075/130/40002},
	abstract = {We consider a run-and-tumble particle with two velocity states {\textbackslash}pmv0, in an inhomogeneous force field f(x) in one dimension. We obtain exact formulae for its velocity V L and diffusion constant D L for arbitrary periodic f(x) of period L. They involve the "active potential"which allows to define a global bias. Upon varying parameters, such as an external force F, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non-analyticities in the V L vs. F curve. A random landscape in the presence of a bias leads, for large L, to anomalous diffusion x {\textbackslash}sim tμ, μ {\textless} 1, or to a phase with a finite velocity that we calculate.},
	number = {4},
	journal = {EPL},
	author = {Le Doussal, Pierre and Majumdar, Satya N. and Schehr, Grégory},
	month = jun,
	year = {2020},
	pages = {40002--40002},
}

@article{lemons_paul_1997,
	title = {Paul {Langevin}'s 1908 {Paper} “{On} the {Theory} of {Brownian} {Motion}” [“{Sur} {La} {Théorie} {Du} {Mouvement} {Brownien},” {C}. {R}. {Acad}. {Sci}. ({Paris}) 146 , 530– 533 (1908)]},
	volume = {65},
	doi = {10.1119/1.18725},
	abstract = {We present a translation of Paul Langevin's landmark paper. In it Langevin successfully applied Newtonian dynamics to a Brownian particle and so invented an analytical approach to random processes which has remained useful to this day.},
	number = {11},
	journal = {American Journal of Physics},
	author = {Lemons, Don S. and Gythiel, Anthony},
	month = nov,
	year = {1997},
	keywords = {Brownian motion, 01.30, 01.65, 05.40, teaching},
	pages = {1079--1081},
}

@article{liu_anchoring_2017-1,
	title = {Anchoring {Effect} on {First} {Passage} {Process} in {Taiwan} {Financial} {Market}},
	volume = {477},
	issn = {0378-4371},
	doi = {10.1016/j.physa.2017.02.043},
	abstract = {Empirical analysis of the price fluctuations of financial markets has received extensive attention because a substantial amount of financial market data has been collected and because of advances in data-mining techniques. Price fluctuation trends can help investors to make informed trading decisions, but such decisions may also be affected by a psychological factors— the anchoring effect. This study explores the intraday price time series of Taiwan futures, and applies diffusion model and quantitative methods to analyze the relationship between the anchoring effect and price fluctuations during first passage process. Our results indicate that power-law scaling and anomalous diffusion for stock price fluctuations are related to the anchoring effect. Moreover, microscopic price fluctuations before switching point in first passage process correspond with long-term price fluctuations of Taiwan's stock market. We find that microscopic trends could provide useful information for understanding macroscopic trends in stock markets.},
	journal = {Physica A: Statistical Mechanics and its Applications},
	author = {Liu, Hsing and Liao, Chi-Yo and Ko, Jing-Yuan and Lih, Jiann-Shing},
	month = jul,
	year = {2017},
	keywords = {Anchoring effect, Anomalous diffusion, First passage process, First return time, Switching point},
	pages = {114--127},
}

@article{manzo_review_2015,
	title = {A {Review} of {Progress} in {Single} {Particle} {Tracking}: {From} {Methods} to {Biophysical} {Insights}},
	volume = {78},
	doi = {10.1088/0034-4885/78/12/124601},
	abstract = {Optical microscopy has for centuries been a key tool to study living cells with minimum invasiveness. The advent of single molecule techniques over the past two decades has revolutionized the field of cell biology by providing a more quantitative picture of the complex and highly dynamic organization of living systems. Amongst these techniques, single particle tracking (SPT) has emerged as a powerful approach to study a variety of dynamic processes in life sciences. SPT provides access to single molecule behavior in the natural context of living cells, thereby allowing a complete statistical characterization of the system under study. In this review we describe the foundations of SPT together with novel optical implementations that nowadays allow the investigation of single molecule dynamic events with increasingly high spatiotemporal resolution using molecular densities closer to physiological expression levels. We outline some of the algorithms for the faithful reconstruction of SPT trajectories as well as data analysis, and highlight biological examples where the technique has provided novel insights into the role of diffusion regulating cellular function. The last part of the review concentrates on different theoretical models that describe anomalous transport behavior and ergodicity breaking observed from SPT studies in living cells.},
	number = {12},
	journal = {Reports on Progress in Physics},
	author = {Manzo, Carlo and Garcia-Parajo, Maria F.},
	year = {2015},
	keywords = {anomalous diffusion, cell biophysics, nonergodicity, single molecule fluorescence, transport in living systems},
}

@article{mehrer_diffusion_2007,
	title = {Diffusion in {Solids}: {Fundamentals}, {Methods}, {Materials}, {Diffusion}-{Controlled} {Processes}},
	issn = {978-3-540-71486-6},
	doi = {10.1007/978-3-540-71488-0},
	abstract = {Diffusion is a vital topic in solid-state physics and chemistry, physical{\textbackslash}textbackslash nmetallurgy and materials science. Diffusion processes are ubiquitous{\textbackslash}textbackslash nin solids at elevated temperatures. A thorough understanding of diffusion{\textbackslash}textbackslash nin materials is crucial for materials development and engineering.{\textbackslash}textbackslash nThis book first gives an account of the central aspects of diffusion{\textbackslash}textbackslash nin solids, for which the necessary background is a course in solid{\textbackslash}textbackslash nstate physics. It then provides easy access to important information{\textbackslash}textbackslash nabout diffusion in metals, alloys, semiconductors, ion-conducting{\textbackslash}textbackslash nmaterials, glasses and nanomaterials. Several diffusion-controlled{\textbackslash}textbackslash nphenomena, including ionic conduction, grain-boundary and dislocation{\textbackslash}textbackslash npipe diffusion, are considered as well.Graduate students in solid-state{\textbackslash}textbackslash nphysics, physical metallurgy, materials science, physical and inorganic{\textbackslash}textbackslash nchemistry or geophysics will benefit from this book as will physicists,{\textbackslash}textbackslash nchemists, metallurgists, materials engineers in academic and industrial{\textbackslash}textbackslash nresearch laboratories.},
	journal = {Springer series in solid-state sciences},
	author = {Mehrer, Helmut},
	year = {2007},
	pages = {--},
}

@article{metzler_brownian_2019-1,
	title = {Brownian {Motion} and beyond: {First}-{Passage}, {Power} {Spectrum}, {Non}-{Gaussianity}, and {Anomalous} {Diffusion}},
	volume = {2019},
	doi = {10.1088/1742-5468/ab4988},
	abstract = {Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exists a very large range of applications of stochastic processes in various disciplines. Here we provide a summary of some of the recent developments in the field of stochastic processes, highlighting both the experimental findings and theoretical frameworks.},
	number = {11},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	author = {Metzler, Ralf},
	month = nov,
	year = {2019},
	keywords = {Brownian motion, diffusion},
	pages = {114003--114003},
}

@book{metzler_first-passage_2014-1,
	title = {First-{Passage} {Phenomena} and {Their} {Applications}},
	isbn = {978-981-4590-29-7},
	abstract = {The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic.},
	publisher = {World Scientific Publishing Co.},
	author = {Metzler, Ralf and Oshanin, Gleb and Redner, Sidney},
	month = jan,
	year = {2014},
	doi = {10.1142/9104},
}

@article{metzler_non-brownian_2016,
	title = {Non-{Brownian} {Diffusion} in {Lipid} {Membranes}: {Experiments} and {Simulations}},
	volume = {1858},
	issn = {0006-3002},
	shorttitle = {Non-{Brownian} {Diffusion} in {Lipid} {Membranes}},
	doi = {10.1016/j.bbamem.2016.01.022},
	abstract = {The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.},
	number = {10},
	journal = {Biochimica Et Biophysica Acta},
	author = {Metzler, R. and Jeon, J.-H. and Cherstvy, A. G.},
	month = oct,
	year = {2016},
	pmid = {26826272},
	keywords = {Anomalous diffusion, Diffusion, Gels, Lipid bilayer, Lipid Bilayers, Membrane Lipids, Membrane Proteins, Molecular Dynamics Simulation, Non-Gaussian processes, Protein crowding, Simulations, Static Electricity, Stochastic modelling},
	pages = {2451--2467},
}

@article{moran_random_1958,
	title = {Random {Processes} in {Genetics}},
	volume = {54},
	issn = {1469-8064, 0305-0041},
	doi = {10.1017/S0305004100033193},
	abstract = {Wright's model of a random process in genetica is modified by supposing that births and deaths occur individually at random so that the generations are no longer simultaneous. An exact solution is then obtained for the distribution of the number of a-genes in a haploid organism when mutation is occurring in both directions. When there is no mutation, the rate of approach to homozygosity is found in more complicated models with two sexes and diploid individuate. This rate is twice that occurring in Wright's models.},
	number = {1},
	journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
	author = {Moran, P. a. P.},
	month = jan,
	year = {1958},
	note = {Publisher: Cambridge University Press},
	pages = {60--71},
}

@book{nelson_photon_2017,
	title = {From {Photon} to {Neuron} {\textbar} {Princeton} {University} {Press}},
	isbn = {978-0-691-17518-8},
	publisher = {Princeton University Press},
	author = {Nelson, Philip},
	year = {2017},
}

@article{nicholson_diffusion_2001,
	title = {Diffusion and {Related} {Transport} {Mechanisms} in {Brain} {Tissue}},
	volume = {64},
	issn = {0034-4885},
	doi = {10.1088/0034-4885/64/7/202},
	abstract = {Diffusion plays a crucial role in brain function. The spaces between cells can be likened to the water phase of a foam and many substances move within this complicated region. Diffusion in this interstitial space can be accurately modelled with appropriate modifications of classical equations and quantified from measurements based on novel micro-techniques. Besides delivering glucose and oxygen from the vascular system to brain cells, diffusion also moves informational substances between cells, a process known as volume transmission. Deviations from expected results reveal how local uptake, degradation or bulk flow may modify the transport of molecules. Diffusion is also essential to many therapies that deliver drugs to the brain. The diffusion-generated concentration distributions of well-chosen molecules also reveal the structure of brain tissue. This structure is represented by the volume fraction (void space) and the tortuosity (hindrance to diffusion imposed by local boundaries or local viscosity). Analysis of these parameters also reveals how the local geometry of the brain changes with time or under pathological conditions. Theoretical and experimental approaches borrow from classical diffusion theory and from porous media concepts. Earlier studies were based on radiotracers but the recent methods use a point-source paradigm coupled with micro-sensors or optical imaging of macromolecules labelled with fluorescent tags. These concepts and methods are likely to be applicable elsewhere to measure diffusion properties in very small volumes of highly structured but delicate material.},
	number = {7},
	journal = {Reports on Progress in Physics},
	author = {Nicholson, Charles},
	month = jun,
	year = {2001},
	note = {Publisher: IOP Publishing},
	pages = {815--884},
}

@article{nicholson_reports_2001,
	title = {Reports on {Progress} in {Physics} {Related} {Content} {Diffusion} and {Related} {Transport} {Mechanisms} in {Brain} {Tissue}},
	volume = {64},
	number = {2001},
	journal = {Reports on Progress in Physics},
	author = {Nicholson, Charles},
	year = {2001},
	pages = {815--884},
}

@incollection{ofer_random_2004,
	address = {Berlin},
	series = {Math},
	title = {Random {Walks} in {Random} {Environment}},
	volume = {1837},
	booktitle = {Lectures on {Probability} {Thorey} and {Statistics}, {Lecture} {Notes}},
	publisher = {Springer},
	author = {Ofer, Zeitouni},
	year = {2004},
	pages = {189--312},
}

@article{oviedo_second_2021,
	title = {Second {Order} {Fluctuations} of {Large} {Deviations} for {Perturbed} {Random} {Walks}},
	abstract = {We prove that the Beta random walk has second order cubic fluctuations from the large deviation principle of the GUE Tracy-Widom type for arbitrary values {\textbackslash}textbackslash upalpha{\textgreater}0{\textbackslash} and {\textbackslash}textbackslash upbeta{\textgreater}0{\textbackslash} of the parameters of the Beta distribution, removing previous restrictions on their values. Furthermore, we prove that the GUE Tracy-Widom fluctuations still hold in the intermediate disorder regime. We also show that any random walk in space-time random environment that matches certain moments with the Beta random walk also has GUE Tracy-Widom fluctuations in the intermediate disorder regime. As a corollary we show the emergence of GUE Tracy-Widom fluctuations from the large deviation principle for trajectories ending at boundary points for random walks in space (time-independent) i.i.d. Dirichlet random environment in dimension {\textbackslash}d=2{\textbackslash} for a class of asymptotic behavior of the parameters.},
	journal = {arXiv:2108.02877 [math]},
	author = {Oviedo, Giancarlos and Panizo, Gonzalo and Ramírez, Alejandro F.},
	month = aug,
	year = {2021},
	note = {arXiv: 2108.02877},
	keywords = {60K37, Mathematics - Probability, 82D30, 82C23, 82C41},
}

@article{perrin_mouvement_1910,
	title = {Mouvement brownien et molécules},
	volume = {8},
	copyright = {© Paris : Société de Chimie Physique, 1910},
	issn = {0021-7689},
	doi = {10.1051/jcp/1910080057},
	abstract = {Journal de Chimie Physique et de Physico-Chimie Biologique},
	journal = {Journal de Chimie Physique},
	author = {Perrin, Jean},
	year = {1910},
	note = {Publisher: EDP Sciences},
	pages = {57--91},
}

@article{perrin_mouvement_1909-1,
	title = {Le {Mouvement} {Brownien} et {La} {Réalité} {Moleculaire}},
	volume = {18},
	number = {8},
	journal = {Ann. Chimi. Phys.},
	author = {Perrin, Jean Baptiste},
	year = {1909},
	pages = {5--114},
}

@book{phillips_physical_2012,
	title = {Physical {Biology} of the {Cell}},
	abstract = {4th ed. CD-ROM contains: Video clips – Animations – Molecular structures – High-resolution micrographs. CD-ROM contains: Video clips – Animations – Molecular structures – High-resolution micrographs. Part I – Introduction to the cell : Cells and genomes – Cell chemistry and biosynthesis – Proteins Part II – Basic genetic mechanisms : DNA and chromosomes – DNA replication, repair, and recombination – How cells read the genome: from DNA to Protein – Control of gene expression Part III – Methods : Manipulating proteins, DNA, and RNA – Visualizing cells Part IV – Internal organization of the cell : Membrane structure – Membrane transport of small molecules and the electrical properties of membranes – Intracellular compartments and protein sorting – Intracellular vesicular traffic – Energy conversion: mitochondria and chloroplasts – Cell communication – Cytoskeleton – Cell cycle and programmed cell death – Mechanics of cell division Part V – Cells in their social context : Cell junctions, cell adhesion, and the extracellular matrix – Germ cells and fertilzation – Development of multicellular organisms – Histology: the lives and deaths of cells in tissues – Cancer – Adaptive Immune system – Pathogens, infection, and innate immunity.},
	publisher = {Garland Science},
	author = {Phillips, Rob and Kondev, Jane and Theriot, Julie and Garcia, Hernan G. and Orme, Nigel},
	month = oct,
	year = {2012},
	doi = {10.1201/9781134111589},
}

@article{pinto_physics_2000,
	title = {The {Physics} of {Type} {Ia} {Supernova} {Light} {Curves}. {II}. {Opacity} and {Diffusion}},
	volume = {530},
	doi = {10.1086/308380},
	abstract = {We examine the nature of the opacity and radiation transport in Type Ia supernovae. The dominant opacity arises from line transitions. We discuss the nature of line opacities and di usion in expanding media and the appropriateness of various mean and expansion opacities used in light-curve calculations. Fluorescence is shown to be the dominant physical process governing the rate at which energy escapes the supernova. We present a sample light curve that was obtained using a time-dependent solution of the radiative transport equation with a spectral resolution of 80 km s{\textbackslash}textasciitilde 1 and employing an LTE equation of state. The result compares favorably with light curves and spectra of typical supernovae and is used to illustrate the physics controlling the evolution of the light curve and especially the secondary maxima seen in infrared photometry.},
	number = {2},
	journal = {The Astrophysical Journal},
	author = {Pinto, Philip A. and Eastman, Ronald G.},
	month = feb,
	year = {2000},
	keywords = {general, distance scale È radiative transfer È supernovae, Subject headings},
	pages = {757--776},
}

@article{pollard_gaseous_1948-1,
	title = {On {Gaseous} {Self}-{Diffusion} in {Long} {Capillary} {Tubes}},
	volume = {73},
	doi = {10.1103/PhysRev.73.762},
	abstract = {A calculation is made of the rate of diffusion of "tagged" molecules in a pure gas at uniform pressure in a long capillary tube of half-length L and radius a. At pressures for which the mean free path łambda{\textbackslash}gga, the result in the limit L→ınfty reduces to that already obtained by M. Knudsen, the diffusion coefficient D being given by 2a¯ v3, where ¯ v is the mean molecular speed. For a capillary of finite length the diffusion coefficient is, to first order in aL, smaller than this by a factor 1-3a4L. In the opposite limit of high pressures, for which łambdałla, the result reduces to the elementary kinetic theory expression for the self diffusion coefficient, D=λ¯ v3. One of the most significant features of the result is that in a long tube the diffusion coefficient drops very rapidly with increasing pressure from its initial value for łambda{\textbackslash}ggL. Thus the initial slope of D as a function of pressure is given by dDd(aλ){\textbackslash}cong-12¯ va lnLa. It is shown that these results account for the anomalous low pressure minima observed by several investigators who have measured the specific flow GΔp through long capillary tubes as a function of mean pressure ¯ p. The failure to observe such minima with porous media, for which effectively L{\textbackslash}approxa in each pore, is also explained by these results. The formulae obtained here represent a rigorous solution to the long capillary diffusion problem, valid at all pressures and subject only to the limitations of the mean free path type of treatment.},
	number = {7},
	journal = {Physical Review},
	author = {Pollard, W. G. and Present, R. D.},
	month = apr,
	year = {1948},
	note = {Publisher: American Physical Society},
	pages = {762--774},
}

@article{prahofer_universal_2000,
	title = {Universal {Distributions} for {Growth} {Processes} in 1+1 {Dimensions} and {Random} {Matrices}},
	volume = {84},
	doi = {10.1103/PhysRevLett.84.4882},
	abstract = {We develop a scaling theory for Kardar-Parisi-Zhang growth in one dimension by a detailed study of the polynuclear growth model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.},
	number = {21},
	journal = {Physical Review Letters},
	author = {Prähofer, Michael and Spohn, Herbert},
	month = may,
	year = {2000},
	note = {Publisher: American Physical Society},
	pages = {4882--4885},
}

@article{prolhac_height_2011,
	title = {The {Height} {Distribution} of the {KPZ} {Equation} with {Sharp} {Wedge} {Initial} {Condition}: {Numerical} {Evaluations}},
	volume = {84},
	issn = {1539-3755, 1550-2376},
	shorttitle = {The {Height} {Distribution} of the {KPZ} {Equation} with {Sharp} {Wedge} {Initial} {Condition}},
	doi = {10.1103/PhysRevE.84.011119},
	abstract = {The time-dependent probability distribution function of the height for the Kardar-Parisi-Zhang equation with sharp wedge initial conditions has been obtained recently as a convolution between the Gumbel distribution and a difference of two Fredholm determinants. We evaluate numerically this distribution over the whole time span. The crossover from the short time behavior, which is Gaussian, to the long time behavior, which is governed by the GUE Tracy-Widom distribution, is clearly visible.},
	number = {1},
	journal = {Physical Review E},
	author = {Prolhac, Sylvain and Spohn, Herbert},
	month = jul,
	year = {2011},
	note = {arXiv: 1105.0383},
	keywords = {Condensed Matter - Statistical Mechanics, Mathematical Physics},
	pages = {011119},
}

@article{quastel_one-dimensional_2015,
	title = {The {One}-{Dimensional} {KPZ} {Equation} and {Its} {Universality} {Class}},
	volume = {160},
	issn = {1572-9613},
	doi = {10.1007/s10955-015-1250-9},
	abstract = {Our understanding of the one-dimensional KPZ equation, alias noisy Burgers equation, has advanced substantially over the past 5 years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice type models approximating it.},
	number = {4},
	journal = {Journal of Statistical Physics},
	author = {Quastel, Jeremy and Spohn, Herbert},
	month = aug,
	year = {2015},
	pages = {965--984},
}

@article{r_brownian_1911,
	title = {Brownian {Movement} and {Molecular} {Reality}},
	volume = {86},
	doi = {10.1038/086105a0},
	abstract = {How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this "Brownian motion" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownian Movement and Molecular Reality, a work that explains his painstaking measurements of the displacements of particles of a resin suspended in water-experiments that yielded average displacements in excellent accord with Einstein's theoretical prediction.The studies of Einstein and Perrin provided some of the first concrete evidence for the existence of molecules. Perrin, whose name is familiar to all who employ his methods for calculations in molecular dynamics, received the 1926 Nobel Prize in physics. In this classic paper, he introduced the concept of Avogadro's number, along with other groundbreaking work. Originally published in the French journal Annates de chimie et de physique, it was translated into English by Frederick Soddy to enduring influence and acclaim.},
	number = {2160},
	journal = {Nature},
	author = {R., E.},
	month = mar,
	year = {1911},
	keywords = {Humanities and Social Sciences, multidisciplinary, Science},
	pages = {105--105},
}

@article{ramaswamy_mechanics_2010-1,
	title = {The {Mechanics} and {Statistics} of {Active} {Matter}},
	volume = {1},
	doi = {10.1146/annurev-conmatphys-070909-104101},
	abstract = {Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles– active matter– with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.},
	number = {1},
	journal = {Annual Review of Condensed Matter Physics},
	author = {Ramaswamy, Sriram},
	year = {2010},
	keywords = {granular matter, bacterial motility, cell rheology, cytoskeleton, self-propulsion},
	pages = {323--345},
}

@article{rassoul-agha_almost_2005,
	title = {An {Almost} {Sure} {Invariance} {Principle} for {Random} {Walks} in a {Space}-{Time} {Random} {Environment}},
	volume = {133},
	issn = {0178-8051, 1432-2064},
	doi = {10.1007/s00440-004-0424-1},
	abstract = {We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an annealed {\textbackslash}L{\textasciicircum}2{\textbackslash} drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.},
	number = {3},
	journal = {Probability Theory and Related Fields},
	author = {Rassoul-Agha, F. and Seppalainen, T.},
	month = nov,
	year = {2005},
	note = {arXiv: math/0411602},
	keywords = {Mathematics - Probability, Mathematical Physics},
	pages = {299--314},
}

@article{rassoul-agha_quenched_2013,
	title = {Quenched {Free} {Energy} and {Large} {Deviations} for {Random} {Walks} in {Random} {Potentials}},
	volume = {66},
	issn = {1097-0312},
	doi = {10.1002/cpa.21417},
	abstract = {We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected, and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the potential, in relation to the degree of mixing of the ergodic environment. We derive two variational formulas for the limiting quenched free energy and prove a process-level quenched large deviation principle (LDP) for the empirical measure. As a corollary we obtain LDPs for types of random walks in random environments not covered by earlier results. © 2012 Wiley Periodicals, Inc.},
	number = {2},
	journal = {Communications on Pure and Applied Mathematics},
	author = {Rassoul-Agha, Firas and Seppäläinen, Timo and Yilmaz, Atilla},
	year = {2013},
	pages = {202--244},
}

@article{rayleigh_xii_1880,
	title = {{XII}. {On} the {Resultant} of a {Large} {Number} of {Vibrations} of the {Same} {Pitch} and of {Arbitrary} {Phase}},
	volume = {10},
	doi = {10.1080/14786448008626893},
	abstract = {V ERDETTt , in an investigation upon this subject, has arri{\textbackslash}textasciitilde ed at the conclusion that the resultant of n vibra-tions of unit amplitude and arbitrary phase approaches the definite value a/n when n is very great. It can be shown:{\textbackslash}textasciitilde, however, that this conclusion is inaccurate, and that the result-ant tends to no definite value, however great the number of components may be. But there is a modified form of the question, which admits of a definite answer, and was perhaps vaguely before ¥ erdet's mind. If we inquire what is the average intensity in a great number of cases, or, in the language of the theory of probabi-lities, what is the expectation of intensity in a single case of composition, we shall find that the result is that assigned by Verdet{\textbackslash}textasciitilde namely n. A simple but instructive variation of the problem may be obtained by snpposing the possible phases limited to two oppo-site phases, in which case it is convenient to discard the idea of phase altogether, and to regard the amplitudes as at ran-dom positive or negative. If all the signs are the same, the resultant intensity is uP; if, on the other hand, there are as many positive as negative, the result is zero. But although the intensity may range from 0 to n 2, the smaller values are much more probable than the greater ; and to calculate the ex-* Communicated by the Author. t Zeqons ar Optique physique, t. i. p. 297.},
	number = {60},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Rayleigh, Lord},
	month = aug,
	year = {1880},
	pages = {73--78},
}

@incollection{resnick_domains_1987,
	address = {New York, NY},
	series = {Springer {Series} in {Operations} {Research} and {Financial} {Engineering}},
	title = {Domains of {Attraction} and {Norming} {Constants}},
	isbn = {978-0-387-75953-1},
	abstract = {As in Chapter 0 suppose \{X n , n {\textbackslash}geq 1\} is an iid sequence of random variables with common distribution F(x). If G is an extreme value distribution then according to Proposition 0.3, G is of the for.},
	booktitle = {Extreme {Values}, {Regular} {Variation} and {Point} {Processes}},
	publisher = {Springer},
	author = {Resnick, Sidney I.},
	editor = {Resnick, Sidney I.},
	year = {1987},
	doi = {10.1007/978-0-387-75953-1_2},
	keywords = {Auxiliary Function, Equivalence Class, Moment Generate Function, Norming Constant, Regular Variation},
	pages = {38--75},
}

@article{richardson_atmospheric_1926,
	title = {Atmospheric {Diffusion} {Shown} on a {Distance}-{Neighbour} {Graph}},
	volume = {110},
	doi = {10.1098/rspa.1926.0043},
	abstract = {If the diffusivity K of a substance whose mass per volume of atmosphere is χ be defined by an equation of Fick's type ū {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialx + v- {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialy + w- {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialz + {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialt = {\textbackslash}partial/{\textbackslash}partialx (K {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialx) + {\textbackslash}partial/{\textbackslash}partialy (K {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialy) {\textbackslash}partial/{\textbackslash}partialz (K {\textbackslash}partial{\textbackslash}chi/{\textbackslash}partialz), (1) x, y, z, t being Cartesian co-ordinates and time, ū, v-, w- being the components of mean velocity, then the measured values of K have been found to be 0{\textbackslash}cdot2 cm.2 sec.-1 in capillary tubes (Kaye and Laby's Tables), 105 cm.2 sec.-1 when gusts are smoothed out of the mean wind (Akerblom, G. I. Taylor, Hesselberg, etc.), 108 cm.2 sec.-1 when the means extend over a time comparable with 4 hours (L. F. Richardson and D. Proctor), 1011 cm.2 sec.-1 when the mean wind is taken to be the general circulation characteristic of the latitude (Defant). Thus the so-called constant K varies in a ratio of 2 to a billion. The present paper records an attempt to comprehend all this range of diffusivity in one coherent scheme. Lest the method which I shall adopt should strike the reader as queer and roundabout, I wish to justify it by showing first why some known methods are in difficulties.},
	number = {756},
	journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
	author = {Richardson, Lewis Fry and Walker, Gilbert Thomas},
	month = apr,
	year = {1926},
	note = {Publisher: Royal Society},
	pages = {709--737},
}

@article{sabot_random_2017,
	title = {Random {Walks} in {Dirichlet} {Environment}: {An} {Overview}},
	volume = {26},
	issn = {2258-7519},
	shorttitle = {Random {Walks} in {Dirichlet} {Environment}},
	doi = {10.5802/afst.1542},
	number = {2},
	journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
	author = {Sabot, Christophe and Tournier, Laurent},
	year = {2017},
	pages = {463--509},
}

@article{sasamoto_one-dimensional_2010,
	title = {One-{Dimensional} {Kardar}-{Parisi}-{Zhang} {Equation}: {An} {Exact} {Solution} and {Its} {Universality}},
	volume = {104},
	shorttitle = {One-{Dimensional} {Kardar}-{Parisi}-{Zhang} {Equation}},
	doi = {10.1103/PhysRevLett.104.230602},
	abstract = {We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for the probability distribution function of the height h(x,t) for all t{\textgreater}0. In particular, we show that for large t, on the scale t1/3, the statistics is given by the Tracy-Widom distribution, known already from the Gaussian unitary ensemble of random matrix theory. Our solution confirms that the KPZ equation describes the interface motion in the regime of weak driving force. Within this regime the KPZ equation details how the long time asymptotics is approached.},
	number = {23},
	journal = {Physical Review Letters},
	author = {Sasamoto, Tomohiro and Spohn, Herbert},
	month = jun,
	year = {2010},
	note = {Publisher: American Physical Society},
	pages = {230602},
}

@article{saxton_single-particle_1997,
	title = {Single-{Particle} {Tracking}: {Applications} to {Membrane} {Dynamics}},
	volume = {26},
	doi = {10.1146/annurev.biophys.26.1.373},
	abstract = {Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.},
	journal = {Annual Review of Biophysics and Biomolecular Structure},
	author = {Saxton, Michael J. and Jacobson, Ken},
	year = {1997},
	keywords = {Cell membrane, Fluorescence recovery after photobleaching, Lateral diffusion, Membrane dynamics, Single-particle tracking},
	pages = {373--399},
}

@misc{noauthor_see_nodate,
	title = {See {Supplemental} {Material} at {XXXX}.},
}

@article{shen_single_2017,
	title = {Single {Particle} {Tracking}: {From} {Theory} to {Biophysical} {Applications}},
	volume = {117},
	doi = {10.1021/acs.chemrev.6b00815},
	abstract = {After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.},
	number = {11},
	journal = {Chemical Reviews},
	author = {Shen, Hao and Tauzin, Lawrence J. and Baiyasi, Rashad and Wang, Wenxiao and Moringo, Nicholas and Shuang, Bo and Landes, Christy F.},
	month = jun,
	year = {2017},
	pages = {7331--7376},
}

@article{sinai_limiting_1983,
	title = {The {Limiting} {Behavior} of a {One}-{Dimensional} {Random} {Walk} in a {Random} {Medium}},
	volume = {27},
	issn = {0040-585X},
	doi = {10.1137/1127028},
	abstract = {The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit surprisingly space efficient algorithms.The main result of this paper is a space efficient single pass random order streaming algorithm for simulating nearly independent random walks that start at uniformly random vertices. We show that the distribution of k-step walks from b vertices chosen uniformly at random can be approximated up to error {\textbackslash}smallin per walk using words of space with a single pass over a randomly ordered stream of edges, solving an open problem of Peng and Sohler [SODA '18]. Applications of our result include the estimation of the average return probability of the k-step walk (the trace of the kth power of the random walk matrix) as well as the estimation of PageRank. We complement our algorithm with a strong impossibility result for directed graphs.},
	number = {2},
	journal = {Theory of Probability \& Its Applications},
	author = {Sinai, Ya. G.},
	month = jan,
	year = {1983},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {256--268},
}

@article{stewart_diffusion_2003,
	title = {Diffusion in {Biofilms}},
	volume = {185},
	doi = {10.1128/JB.185.5.1485-1491.2003},
	abstract = {Diffusion in biofilms can be summarized by the following four points. (i) Diffusion is the predominant solute transport process within cell clusters. (ii) The time scale for diffusive equilibration of a nonreacting solute will range from a fraction of a second to tens of minutes in most biofilm systems. (iii) Diffusion limitation readily leads to gradients in the concentration of reacting solutes and hence to gradients in physiology. (iv) Water channels can carry solutes into or out of the depths of a biofilm, but they do not guarantee access to the interior of cell clusters.},
	number = {5},
	journal = {Journal of Bacteriology},
	author = {Stewart, Philip S.},
	month = mar,
	year = {2003},
	pages = {1485--1491},
}

@article{sutherland_lii_1893,
	title = {{LII}. {The} {Viscosity} of {Gases} and {Molecular} {Force}},
	volume = {36},
	issn = {1941-5982},
	doi = {10.1080/14786449308620508},
	number = {223},
	journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
	author = {Sutherland, William},
	month = dec,
	year = {1893},
	note = {Publisher: Taylor \& Francis},
	pages = {507--531},
}

@article{sykova_diffusion_2008,
	title = {Diffusion in {Brain} {Extracellular} {Space}},
	volume = {88},
	issn = {0031-9333, 1522-1210},
	doi = {10.1152/physrev.00027.2007},
	abstract = {Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is {\textbackslash}sim20\% and the tortuosity is {\textbackslash}sim1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.},
	number = {4},
	journal = {Physiological Reviews},
	author = {Syková, Eva and Nicholson, Charles},
	month = oct,
	year = {2008},
	pages = {1277--1340},
}

@techreport{sznitman_topics_2004,
	address = {International Atomic Energy Agency (IAEA)},
	title = {Topics in {Random} {Walks} in {Random} {Environment}},
	abstract = {Over the last twenty-five years random motions in random media have been intensively investigated and some new general methods and paradigms have by now emerged Random walks in random environment constitute one of the canonical models of the field However in dimension bigger than one they are still poorly understood and many of the basic issues remain to this day unresolved The present series of lectures attempt to give an account of the progresses which have been made over the last few years, especially in the study of multi-dimensional random walks in random environment with ballistic behavior (author)},
	number = {92-95003-25-X},
	author = {Sznitman, A.-S.},
	year = {2004},
	pages = {203--266},
}

@article{temkin_one-dimensional_1972,
	title = {One-{Dimensional} {Random} {Walks} in a {Two}-{Component} {Chain}},
	volume = {13},
	journal = {Soviet Math. Docl.},
	author = {Temkin, D. E.},
	year = {1972},
	pages = {1172--1176},
}

@article{thiery_integrable_2015,
	title = {On {Integrable} {Directed} {Polymer} {Models} on the {Square} {Lattice}},
	volume = {48},
	doi = {10.1088/1751-8113/48/46/465001},
	abstract = {In a recent work Povolotsky (2013 J. Phys. A: Math. Theor. 46 465205) provided a three-parameter family of stochastic particle systems with zero-range interactions in one-dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding condition for integrability of a class of directed polymer models with random weights on the square lattice. Analyzing the solutions we find, besides known cases, a new two-parameter family of integrable DP model, which we call the Inverse-Beta polymer, and provide its Bethe ansatz solution.},
	number = {46},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Thiery, Thimothï¿{\textbackslash}frac12e and Le Doussal, Pierre},
	month = oct,
	year = {2015},
	keywords = {Bethe ansatz, directed polymer, KPZ},
	pages = {465001--465001},
}

@article{tracy_level-spacing_1993,
	title = {Level-{Spacing} {Distributions} and the {Airy} {Kernel}},
	volume = {305},
	issn = {0370-2693},
	doi = {10.1016/0370-2693(93)91114-3},
	abstract = {Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models of N × N hermitian matrices and then going to the limit N → ınfty, leads to the Fredholm determinant of the sine kernel sin π (x - y)/π(x - y). Similarly a double scaling limit at the “edge of the spectrum” leads to the Airy kernel [Ai(x)Ai'(y) - Ai'(x)Ai(y)]/(x-y). We announce analogies for this Airy kernel of the following properties of the sine kernel: the completely integrable system of PDE's found by Jimbo, Miwa, Môri and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painlevé transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for general n, of the probability that an interval contains precisely n eigenvalues.},
	number = {1},
	journal = {Physics Letters B},
	author = {Tracy, Craig A. and Widom, Harold},
	month = may,
	year = {1993},
	pages = {115--118},
}

@book{truskey_transport_2009,
	edition = {Second},
	title = {Transport {Phenomena} in {Biological} {Systems}},
	publisher = {Pearson},
	author = {Truskey, Yuan and Katz, T},
	year = {2009},
}

@article{uhlenbeck_theory_1930,
	title = {On the {Theory} of the {Brownian} {Motion}},
	volume = {36},
	doi = {10.1103/PhysRev.36.823},
	abstract = {With a method first indicated by Ornstein the mean values of all the powers of the velocity u and the displacement s of a free particle in Brownian motion are calculated. It is shown that u-u0exp(-βt) and s-u0β[1-exp(-βt)] where u0 is the initial velocity and β the friction coefficient divided by the mass of the particle, follow the normal Gaussian distribution law. For s this gives the exact frequency distribution corresponding to the exact formula for s2 of Ornstein and Fürth. Discussion is given of the connection with the Fokker-Planck partial differential equation. By the same method exact expressions are obtained for the square of the deviation of a harmonically bound particle in Brownian motion as a function of the time and the initial deviation. Here the periodic, aperiodic and overdamped cases have to be treated separately. In the last case, when β is much larger than the frequency and for values of t{\textbackslash}gg{\textbackslash}beta-1, the formula takes the form of that previously given by Smoluchowski.},
	number = {5},
	journal = {Physical Review},
	author = {Uhlenbeck, G. E. and Ornstein, L. S.},
	month = sep,
	year = {1930},
	note = {Publisher: American Physical Society},
	pages = {823--841},
}

@article{von_smoluchowski_notiz_1915,
	title = {Notiz {Uiber} {Die} {Berechnung} {Der} {Brownschen} {Molekularbewegung} {Bei} {Der} {Ehrenhaft}-{Millikanschen} {Versuchsanordning}},
	volume = {16},
	journal = {Phys. Z},
	author = {Von Smoluchowski, M.},
	year = {1915},
	pages = {318--321},
}

@article{von_smoluchowski_zur_1906-1,
	title = {Zur {Kinetischen} {Theorie} {Der} {Brownschen} {Molekularbewegung} {Und} {Der} {Suspensionen}},
	volume = {326},
	doi = {10.1002/andp.19063261405},
	number = {14},
	journal = {Annalen der Physik},
	author = {von Smoluchowski, M.},
	year = {1906},
	pages = {756--780},
}

@article{waxman_diffusion_2017,
	title = {The {Diffusion} {Equation} of {Random} {Genetic} {Drift}– {Biology}'s {Analogue} of the {Schrödinger} {Equation}?},
	volume = {58},
	doi = {10.1080/00107514.2017.1349370},
	abstract = {This work is a self-contained introduction to some basic aspects of the dynamics that occurs in biological populations. It focusses on the proportion (or frequency) of a population that carries a particular gene. We make use of the notion of a force, in the context of genetics and evolution, to describe the dynamics of the frequency in an effectively infinite population. We then show how randomness enters into the dynamics of populations with a finite size, a randomness known as random genetic drift. We derive an equation, involving random numbers, which describes how the frequency behaves in a population of finite size. It is shown that in some situations this equation exhibits irreversible absorption phenomena. These phenomena are associated with the extinction (or loss) of the gene, or the complete takeover by the gene (termed fixation), where 100\% of the population carries the gene. Taking the theory further, we show how an approximation leads to a stochastic differential equation for the frequency, where random genetic drift takes the form of an additional contribution to the force, that randomly fluctuates. The stochastic differential equation is, in turn, related to a diffusion equation, which encompasses many fundamental phenomena. Because of this, the diffusion equation plausibly has a similar status in biology to the Schrödinger equation in physics. It is notable that both the Schrödinger equation and the diffusion equation have a somewhat similar mathematical structure: they both involve first order derivatives of time and second order derivatives of space (or the analogue of space). There are, however, some significant mathematical differences. In contrast to the Schrödinger equation, the diffusion equation can routinely have solutions which are singular, in that the solutions contain Dirac delta functions. The delta functions are not, however, problematic, and have an explicit biological significance. We illustrate results with some basic calculations and computer simulations.},
	number = {3},
	journal = {Contemporary Physics},
	author = {Waxman, David},
	month = jul,
	year = {2017},
	keywords = {evolution, Diffusion analysis, population genetics, stochastic process},
	pages = {253--261},
}

@article{zangi_frequency-dependent_2007,
	title = {Frequency-{Dependent} {Stokes}-{Einstein} {Relation} in {Supercooled} {Liquids}},
	volume = {75},
	doi = {10.1103/PhysRevE.75.051501},
	abstract = {We investigate by molecular dynamics simulations the validity of the frequency-dependent Stokes-Einstein (SE) relation in supercooled liquids at different temperatures. The results indicate that the SE relation holds at intermediate frequencies that correspond to the β-relaxation and the onset of the α-relaxation regimes. Large deviations, which increase as the temperature decreases, are observed at frequencies well below the frequency at which the non-Gaussian parameter α2 is maximum. We argue that the breakdown of the SE relation in supercooled liquids arises from underestimation of the diffusion coefficient due to neglect of correlated motions.},
	number = {5},
	journal = {Physical Review E},
	author = {Zangi, Ronen and Kaufman, Laura J.},
	month = may,
	year = {2007},
	note = {Publisher: American Physical Society},
	pages = {051501},
}

@article{zezyulin_related_2018,
	title = {Related {Content} {Solitons} in a {Hamiltonian} {Solitons} in a {Hamiltonian} {PT} -{Symmetric} {Coupler}},
	doi = {10.1088/1751-8121},
	abstract = {The position x(t) of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray x = v 0 t, where v 0 is the average drift. However, it has been found that it exhibits at large time sample to sample fluctuations characteristic of the Kardar-Parisi-Zhang (KPZ) universality class when observed in an atypical direction, i.e. along the ray x = vt with v = v 0. Here we show, from exact solutions, that in the moderate deviation regime x - v 0 t {\textbackslash}propto t 3/4 these fluctuations are precisely described by the finite time KPZ equation, which thus describes the crossover between the Gaussian typical regime and the KPZ fixed point regime for the large deviations. This confirms heuristic arguments given in [2]. These exact results include the discrete model known as the Beta random walk in a time dependent random environment, and a continuum diffusion. They predict the behavior of the maximum of a large number of independent walkers , which should be easier to observe (e.g. in experiments) in this moderate deviations regime. Keywords: random walk in random environment, Kardar-Parisi-Zhang uni-versality, random matrices, large deviations, extreme value theory, Langevin equation},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	author = {Zezyulin, Dmitry A and Konotop, Vladimir V},
	year = {2018},
}

@article{wakeley_limits_2005,
	title = {The {Limits} of {Theoretical} {Population} {Genetics}},
	volume = {169},
	issn = {1943-2631},
	url = {https://doi.org/10.1093/genetics/169.1.1},
	doi = {10.1093/genetics/169.1.1},
	number = {1},
	urldate = {2025-03-21},
	journal = {Genetics},
	author = {Wakeley, John},
	month = jan,
	year = {2005},
	pages = {1--7},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\SGFNTK8E\\Wakeley - 2005 - The Limits of Theoretical Population Genetics.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\8C4FSSEV\\6060370.html:text/html},
}

@article{stokes_effect_1851,
	title = {On the {Effect} of the {Internal} {Friction} of {Fluids} on the {Motion} of {Pendulums}},
	volume = {9},
	url = {https://ui.adsabs.harvard.edu/abs/1851TCaPS...9....8S},
	urldate = {2025-03-21},
	journal = {Transactions of the Cambridge Philosophical Society},
	author = {Stokes, G. G.},
	month = jan,
	year = {1851},
	note = {ADS Bibcode: 1851TCaPS...9....8S},
	pages = {8},
}

@article{navier_memoire_1827,
	title = {Mémoire sur les lois du {Mouvement} des {Fluides}},
	volume = {6},
	copyright = {domaine public},
	url = {https://gallica.bnf.fr/ark:/12148/bpt6k3221x},
	abstract = {Mémoires de l'Académie des sciences de l'Institut de France -- 1823 -- fascicules},
	language = {EN},
	urldate = {2025-03-21},
	journal = {Mémoires de l’Académie Royale des Sciences de l’Institut de France},
	author = {Navier, Claude-Louis},
	year = {1827},
	pages = {389--440},
	file = {Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\2V9AJIE9\\f577.item.html:text/html},
}

@article{cruickshank_miller_stokes-einstein_1924,
	series = {A},
	title = {The {Stokes}-{Einstein} {Law} for {Diffusion} in {Solution} on {JSTOR}},
	volume = {106},
	url = {https://www.jstor.org/stable/94335?seq=1},
	number = {740},
	urldate = {2025-03-21},
	journal = {Proceedings of the Royal Society of London},
	author = {Cruickshank Miller, Christina},
	year = {1924},
	pages = {724--749},
	file = {The Stokes-Einstein Law for Diffusion in Solution on JSTOR:C\:\\Users\\centrifuge\\Zotero\\storage\\4GLKIYC4\\94335.html:text/html},
}

@misc{carroll-godfrey_measurements_2025,
	title = {Measurements of extreme first passage times in photon transport},
	url = {http://arxiv.org/abs/2502.19359},
	doi = {10.48550/arXiv.2502.19359},
	abstract = {Photon transport through turbid media has typically been modeled through diffusion or telegraph equations. These models describe behavior of the average, or typical, photon with remarkable accuracy, however, we show here that they fail to capture the Extreme First Passage Times (EFPTs) of photon transport. By sending ultra-fast bursts of photons through a scattering medium and timing the arrival of the first passage photon, we measure the distribution of these EFPTs of photons in a random environment. Our measured EFPTs differ from those predicted by both the diffusion approximation and telegraph equation. Instead, we observe the EFPT as the time expected for light to travel through an index-averaged medium. These results reveal flaws in both models and invite a re-examining of their underlying assumptions.},
	urldate = {2025-03-21},
	publisher = {arXiv},
	author = {Carroll-Godfrey, Aileen N. and Corwin, Eric I.},
	month = feb,
	year = {2025},
	note = {arXiv:2502.19359 [physics]},
	keywords = {Condensed Matter - Statistical Mechanics, Physics - Optics},
	file = {Preprint PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\S56KPZKN\\Carroll-Godfrey and Corwin - 2025 - Measurements of extreme first passage times in photon transport.pdf:application/pdf;Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\PM9YBZX5\\2502.html:text/html},
}

@book{regnault_calcul_1863,
	title = {Calcul des chances et philosophie de la bourse},
	url = {http://archive.org/details/calculdeschances00regn},
	abstract = {32},
	language = {fre},
	urldate = {2025-03-21},
	publisher = {Paris : Mallet-Bachelier [et] Castel},
	author = {Regnault, Jules},
	collaborator = {{Fisher - University of Toronto}},
	year = {1863},
	keywords = {Chance},
}

@article{hass_extreme_2024,
	title = {Extreme {Diffusion} {Measures} {Statistical} {Fluctuations} of the {Environment}},
	volume = {133},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.133.267102},
	doi = {10.1103/PhysRevLett.133.267102},
	abstract = {We consider many-particle diffusion in one spatial dimension modeled as “random walks in a random environment.” A shared short-range space-time random environment determines the jump distributions that drive the motion of the particles. We determine universal power laws for the environment’s contribution to the variance of the extreme first passage time and extreme location. We show that the prefactors rely upon a single extreme diffusion coefficient that is equal to the ensemble variance of the local drift imposed on particles by the random environment. This coefficient should be contrasted with the Einstein diffusion coefficient, which determines the prefactor in the power law describing the variance of a single diffusing particle and is equal to the jump variance in the ensemble averaged random environment. Thus a measurement of the behavior of extremes in many-particle diffusion yields an otherwise difficult to measure statistical property of the fluctuations of the generally hidden environment in which that diffusion occurs. We verify our theory and the universal behavior numerically over many random walk in a random environment models and system sizes.},
	number = {26},
	urldate = {2025-04-01},
	journal = {Physical Review Letters},
	author = {Hass, Jacob B. and Drillick, Hindy and Corwin, Ivan and Corwin, Eric I.},
	month = dec,
	year = {2024},
	note = {Publisher: American Physical Society},
	pages = {267102},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\URJZWFJA\\PhysRevLett.133.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\TEWW64UH\\Hass et al. - 2024 - Extreme Diffusion Measures Statistical Fluctuations of the Environment.pdf:application/pdf},
}

@article{hammond_direct_2017,
	title = {Direct measurement of the ballistic motion of a freely floating colloid in {Newtonian} and viscoelastic fluids},
	volume = {96},
	url = {https://link.aps.org/doi/10.1103/PhysRevE.96.042606},
	doi = {10.1103/PhysRevE.96.042606},
	abstract = {A thermal colloid suspended in a liquid will transition from a short-time ballistic motion to a long-time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long-time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx–Schram model for motion in a dense fluid. Measurements of the functional form of the ballistic-to-diffusive transition provide direct measurements of the temperature, viscosity, and tracer radius. We likewise measure the motion in a viscoelastic Maxwell fluid and find a significant disagreement between the theoretical asymptotic behavior and our measured values of the microscopic properties of the fluid. We observe a greatly increased effective mass for a freely moving particle and a decreased plateau modulus.},
	number = {4},
	urldate = {2025-04-03},
	journal = {Physical Review E},
	author = {Hammond, Andrew P. and Corwin, Eric I.},
	month = oct,
	year = {2017},
	note = {Publisher: American Physical Society},
	pages = {042606},
	file = {APS Snapshot:C\:\\Users\\centrifuge\\Zotero\\storage\\RQCZDY4I\\PhysRevE.96.html:text/html;Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\GMUUCA87\\Hammond and Corwin - 2017 - Direct measurement of the ballistic motion of a freely floating colloid in Newtonian and viscoelasti.pdf:application/pdf},
}

@article{parthasarathy_rapid_2012,
	title = {Rapid, accurate particle tracking by calculation of radial symmetry centers},
	volume = {9},
	copyright = {2012 Springer Nature America, Inc.},
	issn = {1548-7105},
	url = {https://www.nature.com/articles/nmeth.2071},
	doi = {10.1038/nmeth.2071},
	abstract = {An analytically exact approach that determines the radial symmetry center of the image of any radially symmetric particle allows faster localization than iterative methods while also giving localization accuracies approaching theoretical limits.},
	language = {en},
	number = {7},
	urldate = {2025-04-03},
	journal = {Nature Methods},
	author = {Parthasarathy, Raghuveer},
	month = jul,
	year = {2012},
	note = {Publisher: Nature Publishing Group},
	keywords = {Biophysics, Imaging, Microscopy},
	pages = {724--726},
	file = {Full Text PDF:C\:\\Users\\centrifuge\\Zotero\\storage\\Y7J38IAI\\Parthasarathy - 2012 - Rapid, accurate particle tracking by calculation of radial symmetry centers.pdf:application/pdf},
}

@book{carus_nature_2010,
	title = {On the {Nature} of {Things}},
	isbn = {978-1-935238-76-8},
	language = {en},
	publisher = {Richer Resources Publications},
	author = {Carus, Titus Lucretius},
	translator = {Johnston, Ian},
	year = {2010},
}