Related papers: Probability distribution functions of sub- and sup…
In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinear partial differential equations.…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
Transport of spherical Brownian particles of finite size possessing radii through narrow channels with varying cross-section area is considered. Applying the so-called Fick-Jacobs approximation, i.e. assuming fast equilibration in…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
We analyze the diffusive transport of Brownian particles in narrow channels with periodically varying cross-section. The geometrical confinements lead to entropic barriers, the particle has to overcome in order to proceed in transport…
We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
Diffusion of tracer particles in the cytoplasm of mammalian cells is often anomalous with a marked heterogeneity even within individual particle trajectories. Despite considerable efforts, the mechanisms behind these observations have…