相关论文: Fractional diffusion equation for aging and equili…
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time…
Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function…
This paper derives and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
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…
In this paper we study controlled continuous time random walks (CTRWs) and heuristically derive pay-off function dynamic programming (DP) equations which turn in the limit of standard scaling to fractional Hamilton Jacobi Bellman type…
In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At…
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…
Continuous time random walks have been developed as a straightforward generalisation of classical random walk processes. Some 10 years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin…
The continuous time random walk (CTRW) approach has been widely applied to model large-scale non-Fickian transport in the flow through disordered media. Often, the underlying microscopic transport mechanisms and disorder characteristics are…
We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The non-trivial incorporation of the reaction process into the CTRW is achieved by…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
In the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this ever-lasting non-equilibrium evolution. A simple instance of such a behaviour is…
Using molecular dynamics computer simulations we investigate the aging dynamics of a gel. We start from a fractal structure generated by the DLCA-DEF algorithm, onto which we then impose an interaction potential consisting of a short-range…
We derive diffusion constants and martingales for senile random walks with the help of a time-change. We provide direct computations of the diffusion constants for the time-changed walks. Alternatively, the values of these constants can be…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…