Related papers: Nonlocal Dynamics of Passive Tracer Dispersion wit…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…
Propagating intrinsic localised modes (discrete breathers) exist in the dissipative driven sine-Gordon chain as attractors of the dynamics. Thermal fluctuations induce random transitions between attracting configurations corresponding to…
The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying…
Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances,…
A theoretical framework for analyzing stochastic data from single-particle tracking in complex or viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation we found…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is…
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…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
The general problem of tracer diffusion in non-equilibrium baths is important in a wide range of systems, from the cellular level to geographical lengthscales. In this paper, we revisit the archetypical example of such a system: a…
We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…
Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the…