Related papers: Normal and Anomalous Diffusion: A Tutorial
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix…
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement…
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the…
The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347…
We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We…
The characterization of particle diffusion is a classical problem in physics and probability theory. The field of microrheology is based on experiments in which microscopic tracer beads are placed into a non-Newtonian fluid and tracked…
Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…