相关论文: Random walk on disordered networks
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…
We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions.…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We consider random walks in dynamic random environments given by Markovian dynamics on $\mathbb{Z}^d$. We assume that the environment has a stationary distribution $\mu$ and satisfies the Poincar\'e inequality w.r.t. $\mu$. The random walk…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
Cell crawling is critical to biological development, homeostasis and disease. In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat surfaces often described such quasi-random-walk cell trajectories as…
Transport in disordered media is a central theme in probability and statistical physics, where randomness in the underlying medium produces phenomena such as localization, anomalous scaling, and slow relaxation. A paradigmatic model for…
We study L\'evy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent…