English
Related papers

Related papers: Transition from distributional to ergodic behavior…

200 papers

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments…

Statistical Mechanics · Physics 2016-12-14 Daniel Molina-García , Tuan Minh Pham , Paolo Paradisi , Carlo Manzo , Gianni Pagnini

Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…

Statistical Mechanics · Physics 2016-05-25 Diego Krapf , Grace Campagnola , Kanti Nepal , Olve B. Peersen

Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…

Statistical Mechanics · Physics 2022-01-19 Xudong Wang , Yao Chen

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…

Disordered Systems and Neural Networks · Physics 2015-06-11 Yasmine Meroz , Igor M. Sokolov , Joseph Klafter

We investigate non-equilibrium fluctuations of a solid surface governed by the stochastic Mullins-Herring equation with conserved noise. This equation describes surface diffusion of adatoms accompanied by their exchange between the surface…

Statistical Mechanics · Physics 2016-02-17 Baruch Meerson , Arkady Vilenkin

Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…

Numerical Analysis · Mathematics 2025-11-20 Qiyao Peng , Sander C. Hille

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

A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $\sigma^2 t^{\alpha}$ as a function of time $t$ for some constant $\sigma^2$, where the diffusion exponent satisfies $\alpha \neq 1$.…

Soft Condensed Matter · Physics 2018-10-17 Kui Zhang , Katelyn P. R. Crizer , Mark H. Schoenfisch , David B. Hill , Gustavo Didier

Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$…

Statistical Mechanics · Physics 2019-05-01 Xudong Wang , Weihua Deng , Yao Chen

An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…

Soft Condensed Matter · Physics 2011-12-14 Baisakhi Mal , Subhankar Ray , J. Shamanna

It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…

Probability · Mathematics 2011-05-25 Angelika Rohde , Claudia Strauch

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…

Statistical Mechanics · Physics 2013-03-27 Tomoshige Miyaguchi , Takuma Akimoto

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time.…

Statistical Mechanics · Physics 2017-10-18 Mpumelelo Matse , Mykyta V. Chubynsky , John Bechhoefer

In this Letter, we present results of an extensive Monte Carlo study of the O/W(110) system under non-equilibrium conditions. We study the mean square displacements and long wavelength density fluctuations of adatoms. From these quantities,…

Condensed Matter · Physics 2009-10-28 I. Vattulainen , J. Merikoski , T. Ala-Nissila , S. C. Ying

Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the…

Probability · Mathematics 2016-07-27 Gustavo Didier , Kui Zhang

Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…

Statistical Mechanics · Physics 2022-03-02 Viktor Stojkoski , Trifce Sandev , Ljupco Kocarev , Arnab Pal

We report a new accelerated diffusion phenomenon that is produced by a one-dimensional ran- dom walk in which the flight probability to one of the two directions (i.e., bias) oscillates dynam- ically in periodic, quasiperiodic, and chaotic…

Chaotic Dynamics · Physics 2016-01-15 Song-Ju Kim , Makoto Naruse , Masashi Aono , Hirokazu Hori , Takuma Akimoto

We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially-varying diffusivity $D(r)$, mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this…

Statistical Mechanics · Physics 2014-12-24 Andrey G. Cherstvy , Aleksei V. Chechkin , Ralf Metzler

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…

Soft Condensed Matter · Physics 2014-09-23 P. Massignan , C. Manzo , J. A. Torreno-Pina , M. F. García-Parajo , M. Lewenstein , G. J. Lapeyre

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