Related papers: Ageing in Mortal Superdiffusive L\'evy Walkers
L\'evy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of…
We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…
We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers composed of coupled DNAzyme legs known as molecular spiders. The mechanism of the…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
We study a two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is the same as in our previous work [J. Chem. Phys. 140, 044706 (2014)] in which standard, gaussian…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior…
We consider the advection-diffusion transport of tracers in a one-parameter family of plane periodic flows where the patterns of streamlines feature regions of confined circulation in the shape of "cat's eyes", separated by meandering jets…
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,…
We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…
We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at…
This work addresses the superdiffusive motion of a discrete time random walker on ordered discrete substrates and complex networks with the presence of long-range interactions (LRIs). In ordered regular lattices, where LRIs have a clear…
A spreading process can be observed when a particular behavior, substance, or disease spreads through a population over time in social and biological systems. It is widely believed that contact interactions among individual entities play an…
We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a…