Related papers: Subdiffusion, superdiffusion and chemotaxis
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…
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…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
In this paper we reconsider the Mass Action Law (MAL) for the anomalous reversible reaction $A\rightleftarrows B$ with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states $A$ and $B$ are…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction. In this work, we extend the investigation initiated by…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
We present a nonlinear and non-Markovian random walk model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…