Related papers: Intermittency for branching walks with heavy tails
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We revisited the problem of heavy particles suspended in homogeneous box turbulence flow subjected to rotation along the vertical axis, which introduces anisotropy along the vertical and horizontal planes. We investigate the effect of the…
Results from Direct Numerical Simulations of particle relative dispersion in three dimensional homogeneous and isotropic turbulence at Reynolds number $Re_\lambda \sim 300$ are presented. We study point-like passive tracers and heavy…
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
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…
This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed L\'evy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations.…
By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of…
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state.…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
The mechanisms of information transmission are investigated in a lattice of coupled continuous maps, by analyzing the propagation of both finite and infinitesimal disturbances. Two distinct regimes are detected: in the former case, both…
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
We study the one-dimensional branching random walk in the case when the step size distribution has a stretched exponential tail, and, in particular, no finite exponential moments. The tail of the step size $X$ decays as $\mathbb{P}[X \geq…
The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number $Re_{\lambda} \sim 200$…
This paper is concerned with spreading properties of space-time heterogeneous Fisher--KPP equations in one space dimension. We focus on the case of everywhere favorable environment with three different zones, a left half-line with slow or…