Related papers: Chemical Continuous Time Random Walks under Anomal…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population…
This paper proposes an effective phase diffusion method to analyze chemical exchange in nuclear magnetic resonance (NMR). The chemical exchange involves spin jumps around different sites where the spin angular frequencies vary, which leads…
Coagulation and fragmentation (CF) is a fundamental process by which particles attach to each other to form clusters while existing clusters break up into smaller ones. It is a ubiquitous process that plays a key role in many physical and…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their…
The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent…
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 present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of…
Using molecular simulations, we identify microscopic relaxation events of individual particles in ageing structural glasses, and determine the full distribution of relaxation times. We find that the memory of the waiting time $t_w$ elapsed…
We propose a general stochastic formalism for describing the evolution of chemical reactions involving a finite number of molecules. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and…
In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this…
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…
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
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…