Related papers: L\'{e}vy walk dynamics in non-static media
L\'evy walks represent a class of stochastic models (space-time coupled continuous time random walks) with applications ranging from the laser cooling to the description of animal motion. The initial model was intended for the description…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the…
This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…
Molecular flow gas damping of mechanical motion in confined geometries, and its associated noise, is important in a variety of fields, including precision measurement, gravitational wave detection, and MEMS devices. We used two torsion…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric L\'evy noise, being a minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the L\'evy…
A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for…
The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…
We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed L\'evy…
We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as…
The time that waves spend inside 1D random media with the possibility of performing L\'evy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered…
Levy walk at the finite velocity is considered. To analyze the spatial and temporal characteristics of this process, the method of moments has been used. The asymptotic distributions of the moments (at $t\to\infty$) have been obtained for…
We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that…
The Levy-type distributions are derived using the principle of maximum Tsallis nonextensive entropy both in the full and half spaces. The rates of convergence to the exact Levy stable distributions are determined by taking the N-fold…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
The integro-differential wave equation for the probability density function for a classical one-dimensional L\'evy walk with continuous sample paths has been derived. This equation involves a classical wave operator together with memory…
Many active matter systems are known to perform L\'{e}vy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been observed for microswimmers such as…
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior…
Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly)…