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Physical Review Letters, ISSN 0031-9007, 06/2008, Volume 100, Issue 25, p. 250602
Most statistical theories of anomalous diffusion rely on ensemble-averaged quantities such as the mean squared displacement. Single molecule tracking... 
ANOMALOUS DIFFUSION | CELLS | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | MEMBRANE | KINETICS | DYNAMICS | SYSTEMS | CTRW | MICROSCOPY | FOKKER-PLANCK EQUATIONS
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2018, Volume 491, pp. 995 - 1000
The space–time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics, geology and... 
Space–time coupled CTRW | Time averaged mean square displacement | Ergodicity breaking | ANOMALOUS DIFFUSION | MODELS | PHYSICS, MULTIDISCIPLINARY | DISPERSION | Space-time coupled CTRW
Journal Article
Water Resources Research, ISSN 0043-1397, 12/2011, Volume 47, Issue 12, pp. W12538 - n/a
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 08/2019, Volume 527, p. 121347
In this paper, we study the bimolecular chemical reaction system A+B⇌C under anomalous diffusion. The master equations for reaction-anomalous diffusion... 
CTRW | Fractional reaction-anomalous diffusion equation | Anomalous diffusion | Generalized Einstein’s relation | Generalized Einstein's relation
Journal Article
Physical Review Letters, ISSN 0031-9007, 2006, Volume 97, Issue 14, p. 140602
We discuss the response of continuous-time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the... 
ANOMALOUS DIFFUSION | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | DYNAMICS | SYSTEMS | CTRW | FOKKER-PLANCK EQUATIONS
Journal Article
Journal of Petroleum Science and Engineering, ISSN 0920-4105, 12/2011, Volume 80, Issue 1, pp. 7 - 13
Concepts of classical diffusion are generalized through fractional derivatives to explain features of anomalous diffusion that are sometimes evident on... 
CTRW | Pressure behavior | Fractional derivatives | Well tests | ANOMALOUS DIFFUSION | TRANSPORT | ENERGY & FUELS | FRACTAL GEOMETRY | EQUATION | ENGINEERING, PETROLEUM
Journal Article
Physical Review Letters, ISSN 0031-9007, 12/2011, Volume 107, Issue 26, p. 260601
It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the... 
DYNAMICS | SYSTEMS | CTRW | PHYSICS, MULTIDISCIPLINARY | FOKKER-PLANCK EQUATIONS | RANDOM-WALK
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2019, Volume 22, Issue 1, pp. 60 - 77
Journal Article
Water Resources Research, ISSN 0043-1397, 10/2012, Volume 48, Issue 10, p. n/a
Improved predictions of hyporheic exchange based on easily measured physical variables are needed to improve assessment of solute transport and reaction... 
CTRW | multi‐scale | OTIS | model | stream | hyporheic | RESIDENCE TIME DISTRIBUTION | MOUNTAIN STREAM | ORGANIC-MATTER | SEASONAL-VARIATION | WATER RESOURCES | MATLAB-TOOLBOX | SOLUTE TRANSPORT | ENVIRONMENTAL SCIENCES | SUBSURFACE WATER EXCHANGE | RANDOM-WALKS | TRANSIENT STORAGE | GROUNDWATER DISCHARGE | LIMNOLOGY | Groundwater discharge | Solute movement | Topography
Journal Article
SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2018, Volume 78, Issue 3, pp. 1330 - 1349
In this work, we develop a unified generalized master equation (GME) framework that extends the theory of continuous time random walks to include the cases... 
CTRW | Fractional dynamics | Generalized master equations | GME | DERIVATION | DISPERSAL | MATHEMATICS, APPLIED | MODELS | FINANCE | fractional dynamics | FRACTIONAL CALCULUS | ANOMALOUS TRANSPORT | DIFFUSION | generalized master equations
Journal Article
理论物理通讯:英文版, ISSN 0253-6102, 2014, Issue 10, pp. 514 - 520
We consider a broad class of Continuous Time Random Walks(CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping,... 
walks | L′evy | diffusion | CTRW | anomalous
Journal Article
PHYSICAL REVIEW LETTERS, ISSN 0031-9007, 09/2007, Volume 99, Issue 12, p. 120602
We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the... 
ANOMALOUS DIFFUSION | SYSTEMS | CTRW | LINEAR-RESPONSE | TRANSPORT | PHYSICS, MULTIDISCIPLINARY | Physics - Statistical Mechanics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 02/2008, Volume 77, Issue 2, p. 021122
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space... 
ANOMALOUS DIFFUSION | STABLE DENSITIES | LAWS | MODELS | APPROXIMATION | FINANCE | PHYSICS, FLUIDS & PLASMAS | LINNIK | CALCULUS | CTRW | PHYSICS, MATHEMATICAL | WAITING-TIMES | Physics - Statistical Mechanics
Journal Article
Water resources research, ISSN 0043-1397, 03/2018, Volume 54, Issue 3, p. 2183
Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play... 
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2013, Volume 392, Issue 4, pp. 612 - 617
A coupled continuous time random walk (CTRW) model is proposed, in which the jump length of a walker is correlated with waiting time. The power law... 
Competition | Gaussian-like distribution | Power law distribution | Coupled CTRW | ANOMALOUS DIFFUSION | TRANSPORT | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | RELAXATION | LATTICES | TURBULENCE
Journal Article
Water Resources Research, ISSN 0043-1397, 02/2014, Volume 50, Issue 2, pp. 871 - 884
Non‐Fickian transport ubiquitously occurs across all scales within fractured geological media. Detailed characterization of non‐Fickian transport through... 
CTRW | Fractures | Non‐Fickian transport | Navier‐Stokes | Navier-Stokes | Non-Fickian transport | TIME RANDOM-WALKS | DISPERSION | HETEROGENEOUS MEDIA | ANOMALOUS TRANSPORT | GEOLOGICAL FORMATIONS | WATER RESOURCES | CONTAMINANT TRANSPORT | SOLUTE TRANSPORT | ENVIRONMENTAL SCIENCES | POROUS-MEDIA | LIMNOLOGY | MULTIRATE MASS-TRANSFER | SINGLE FRACTURE | Groundwater | Solute movement
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 509, pp. 369 - 382
Anomalous diffusion is an ubiquitous phenomenon which have been studied by several approaches, including simulation, analytical methods and experiments.... 
CTRW | Fractional diffusion equation | Calibration | Anomalous diffusion | [formula omitted]-Gaussian | q-Gaussian | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | DYNAMICS | FRACTIONAL DIFFUSION | Models | Distribution (Probability theory) | Analysis | Differential equations
Journal Article