Related papers: Space-time fractional diffusion in cell movement m…

Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their…

Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…

A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump…

The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting random walks can be quite different however. The diffusion coefficient can be made responsible for the size of jumps or…

Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…

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,…

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…

A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…

We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of L\'evy walks, in which transport is driven by a convex combination of fractional material derivatives and a source…

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…

Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…

Investigating the behavior of noninteracting fermions subjected to local dephasing, we reveal that quasi-particle dephasing can induce superdiffusive transport. This superdiffusion arises from nodal points within the momentum distribution…

Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…

We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic…

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including…

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…