Related papers: Log-periodic oscillations for diffusion on self-si…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
Dynamic heterogeneity, believed to be one of the hallmarks of the dynamics of supercooled liquids, is expected to affect the diffusion of the particles comprising the liquid. We have carried out extensive molecular dynamics simulations of…
Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
Spatio-temporally modulated impedance surfaces can be good candidates for generation of radiating waves with arbitrary eigenstates by breaking momentum and energy conservations. Here, we present a theoretical framework based on the…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
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…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
We study cumulative scattering effects on wave front propagation in time dependent randomly layered media. It is well known that the wave front has a deterministic characterization in time independent media, aside from a small random shift…
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
A 3D copepod trajectory is recorded in the laboratory, using 2 digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this…