Related papers: Random walks in correlated diffusivity landscapes
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an…
A correlated Gaussian random walk(CGRW) model is proposed as a simple model of animal dispersal. The general features of CGRW is described. We will discuss how from this single model a number of different kinds of correlated random walk can…
We study systems of interacting Brownian particles in one dimension constructed as the diffusion scaling limits of Fisher's vicious walk models. We define two types of nonintersecting Brownian motions, in which we impose no condition (resp.…
Expanding media are typical in many different fields, e.g. in Biology and Cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties. Here, we focus on such…
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…
Non-Gaussian diffusion has been intensively studied in recent years, which reflects the dynamic heterogeneity in the disordered media. The recent study on the non-Gaussian diffusion in a static disordered landscape suggests novel phenomena…
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
Last year in [Phys. Rev. E 102, 042121 (2020)] the authors studied an overdamped dynamics of nonequilibrium noise driven Brownian particle dwelling in a spatially periodic potential and discovered a novel class of Brownian, yet non-Gaussian…
Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly…
This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle's initial location is random and uniformly…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…