Related papers: Random death process for the regularization of sub…
The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
This paper is devoted to the study of a fractional version of non-linear $\mathpzc{M}^\nu(t)$, $t>0$, linear $M^\nu (t)$, $t>0$ and sublinear $\mathfrak{M}^\nu (t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual…
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…
Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and…
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
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…
A detailed study is presented for a large class of uncoupled continuous-time random walks (CTRWs). The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…
Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…
We study the death and restoration of collective oscillations in networks of oscillators coupled through random-walk diffusion. Differently than the usual diffusion coupling used to model chemical reactions, here the equilibria of the…