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We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position $x$ of the test particle and the process time $t$. This process thus combines the features of…

Statistical Mechanics · Physics 2015-02-06 Andrey G. Cherstvy , Ralf Metzler

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…

Statistical Mechanics · Physics 2015-05-14 Vincent Tejedor , Ralf Metzler

The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…

Statistical Mechanics · Physics 2021-10-27 M. A. F. dos Santos , E. H. Colombo , C. Anteneodo

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…

Data Analysis, Statistics and Probability · Physics 2013-05-29 Serge F. Timashev , Yuriy S. Polyakov , Pavel I. Misurkin , Sergey G. Lakeev

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…

Statistical Mechanics · Physics 2023-10-27 Francisco J. Sevilla , Guillermo Chacón-Acosta , Trifce Sandev

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…

Statistical Mechanics · Physics 2023-09-11 Haroldo V. Ribeiro , Angel A. Tateishi , Ervin K. Lenzi , Richard L. Magin , Matjaz Perc

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement…

Populations and Evolution · Quantitative Biology 2025-08-14 Ohad Vilk , Motti Charter , Sivan Toledo , Eli Barkai , Ran Nathan

We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…

Soft Condensed Matter · Physics 2007-05-23 Joseph Snider , Clare C. Yu

We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…

Statistical Mechanics · Physics 2010-05-06 Zhifu Huang , Guozhen Su , Qiuping A Wang , Jincan Chen

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report ''anomalous diffusion'', where mean-squared displacements scale as a power law of time with exponent $\alpha< 1$ (subdiffusion). While…

Quantitative Methods · Quantitative Biology 2014-01-27 Hugues Berry , Hugues Chaté

Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…

Data Analysis, Statistics and Probability · Physics 2018-10-17 Grzegorz Sikora

We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…

Numerical Analysis · Mathematics 2020-11-13 Daxin Nie , Jing Sun , Weihua Deng

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient…

Statistical Mechanics · Physics 2015-03-20 R. M. S. Ferreira , M. V. S. Santos , C. C. Donato , J. S. Andrade , F. A. Oliveira

We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…

Statistical Mechanics · Physics 2015-06-15 Andrey G. Cherstvy , Aleksei V. Chechkin , Ralf Metzler

Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…

Statistical Mechanics · Physics 2018-09-13 Trifce Sandev , Weihua Deng , Pengbo Xu

Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map.…

chao-dyn · Physics 2008-02-03 P. Leboeuf

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

Statistical Mechanics · Physics 2025-11-14 Alvaro Lanza , Xiang Qu , Stefano Bo

We propose a method to measure the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_{\alpha}$ which are defined by means of the relation $<x^2> =\frac{2D_\alpha} {\Gamma(1+\alpha)} t^\alpha$ where $<x^2>$ denotes a mean…

Statistical Mechanics · Physics 2009-11-11 T. Kosztolowicz , K. Dworecki , St. Mrowczynski

The dynamics of heavy quarks within the hot QCD medium have been revisited, considering the influence of anomalous diffusion. This study has been conducted using the framework of the fractional Langevin equation involving the Caputo…

High Energy Physics - Phenomenology · Physics 2024-06-11 Jai Prakash

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…

Soft Condensed Matter · Physics 2014-09-19 M. Reza Shaebani , Zeinab Sadjadi , Igor M. Sokolov , Heiko Rieger , Ludger Santen