Related papers: Stability of a cross-diffusion system and approxim…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This…
We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic…
We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under…
We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every…
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…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
We propose two nonlinear random walk models which are suitable for the analysis of both chemotaxis and anomalous transport. We derive the balance equations for the population density for the case when the transition rate for a random walk…
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…