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There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here, a novel method to elucidate the fluctuating diffusivity from trajectory data is developed. The time-averaged…

Statistical Mechanics · Physics 2017-10-25 Tomoshige Miyaguchi

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

A theoretical framework for analyzing stochastic data from single-particle tracking in complex or viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation we found…

Statistical Mechanics · Physics 2010-11-22 M. A. Despósito , A. D. Viñales

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…

Statistical Mechanics · Physics 2009-11-07 A. V. Chechkin , R. Gorenflo , I. M. Sokolov

For the first time, the diffusion phase diagram in highly confined colloidal systems, predicted by Continuous Time Random Walk (CTRW), is experimentally obtained. Temporal and spatial fractional exponents, $\alpha$ and $\mu$, introduced…

Disordered Systems and Neural Networks · Physics 2015-05-27 M. Palombo , A. Gabrielli , S. De Santis , C. Cametti , G. Ruocco , S. Capuani

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…

Statistical Mechanics · Physics 2021-11-16 Daniel Han , Dmitri V. Alexandrov , Anna Gavrilova , Sergei Fedotov

The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…

Data Analysis, Statistics and Probability · Physics 2017-01-04 Rafał Połoczański , Agnieszka Wyłomańska , Janusz Gajda , Monika Maciejewska , Andrzej Szczurek

The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…

Statistical Mechanics · Physics 2009-11-07 Eli Barkai

The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…

Chaotic Dynamics · Physics 2007-10-29 H. Isliker

In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…

Computational Physics · Physics 2018-08-20 Gurtek Gill , Peter Straka

Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to…

Probability · Mathematics 2010-05-14 Peter Straka , Bruce Ian Henry

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting random walks can be quite different however. The diffusion coefficient can be made responsible for the size of jumps or…

Probability · Mathematics 2022-03-10 Vassili N. Kolokoltsov

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow - their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these…

Statistical Mechanics · Physics 2017-01-04 Ludvig Lizana , Tobias Ambjörnsson , Michael A. Lomholt

We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly…

Statistical Mechanics · Physics 2017-03-08 L. Padilla , H. O. Mártin , J. L. Iguain

In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…

Probability · Mathematics 2016-11-29 Mark M. Meerschaert , Erkan Nane , Yimin Xiao

We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method…

Statistical Mechanics · Physics 2011-12-15 Shovan Dutta , Subhankar Ray , J. Shamanna

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

Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven L\'evy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move…

Statistical Mechanics · Physics 2015-06-22 Takuma Akimoto , Tomoshige Miyaguchi

The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…

Biological Physics · Physics 2025-10-09 Yann Lanoiselée , Gianni Pagnini , Agnieszka Wyłomańska

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here, one such mixed model, the quenched trap model (QTM) on fractal lattices, is investigated. It is…

Statistical Mechanics · Physics 2015-06-22 Tomoshige Miyaguchi , Takuma Akimoto