Related papers: Systems of interacting diffusions with partial ann…

We examine a two-dimensional system of sterically repulsive interacting disks where each particle runs in a random direction. This system is equivalent to a run-and-tumble dynamics system in the limit where the run time is infinite. At low…

We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat…

For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…

In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach…

Thin films are gaining ground in photonics and optoelectronics, promising improvements in their efficiency and functionality as well as decreased material usage as compared to bulk technologies. However, proliferation of thin films would…

We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…

In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…

We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

We review the theory of interacting Fermi systems whose low-energy physics is governed by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids…

We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…

The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…

We consider a two species process which evolves in a finite or infinite domain in contact with particles reservoirs at different densities, according to the superposition of a generalised contact process and a rapid-stirring dynamics in the…

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…

We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…

We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that,…

In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…

We apply a recently proposed novel thermostating mechanism to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics. At the boundaries the system is thermalized by deterministic and…

Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…

In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…

We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…