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We consider the continuous time random walk model (CTRW) of tracer's motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported in Holzner et al. Phys. Rev. E 92, 013015…

Statistical Mechanics · Physics 2017-05-31 Itzhak Fouxon , Markus Holzner

The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…

Statistical Mechanics · Physics 2021-06-03 Miquel Montero

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

Numerical Analysis · Mathematics 2022-06-15 Yuzhe Qin , Huaxiong Huang , Yi Zhu , Chun Liu , Shixin Xu

In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…

Statistical Mechanics · Physics 2020-08-05 Jakub Ślęzak , Stanislav Burov

Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…

Probability · Mathematics 2014-07-25 Mark M. Meerschaert , Peter Straka

Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…

Statistical Mechanics · Physics 2020-06-23 Liubov Tupikina

A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…

Statistical Mechanics · Physics 2008-05-27 Rudolf Gorenflo , Francesco Mainardi

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…

Statistical Mechanics · Physics 2013-02-21 S. Fedotov , A. O. Ivanov , A. Y. Zubarev

We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Michel G. Gauthier , Gary W. Slater

This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…

Computational Physics · Physics 2019-02-26 Maximilian Schäfer , Wayan Wicke , Rudolf Rabenstein , Robert Schober

We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…

Biological Physics · Physics 2026-03-16 Yann Lanoiselée , Denis S. Grebenkov , Gianni Pagnini

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

Mesoscale and Nanoscale Physics · Physics 2025-04-02 Nilotpal Chakraborty , Markus Heyl , Roderich Moessner

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the…

Quantitative Methods · Quantitative Biology 2022-02-09 Sergei Fedotov , Daniel Han , Alexey O Ivanov , Marco A A da Silva

Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…

Analysis of PDEs · Mathematics 2019-08-08 Adam Bobrowski

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…

Machine Learning · Computer Science 2024-06-04 Anjian Li , Zihan Ding , Adji Bousso Dieng , Ryne Beeson

The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…

In this paper we develop a random walk model on lattice for coordinate dependent diffusion at constant temperature in contact with a heat bath. We employ here a coordinate dependent waiting time of the random walker to make the diffusivity…

Statistical Mechanics · Physics 2020-08-27 Rohan Maniar , A. Bhattacharyay

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…

Statistical Mechanics · Physics 2008-10-01 E. Agliari , M. Casartelli , A. Vezzani

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Statistical Mechanics · Physics 2026-01-16 Gabriel Barreiro , Vladimir Pérez-Veloz

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability…

Condensed Matter · Physics 2009-11-10 Jorge A. Revelli , Carlos. E. Budde , Domingo Prato , Horacio S. Wio