Related papers: Fluctuations of the front in a one dimensional mod…
In this work, we investigate an off-lattice version of the diffusion-reaction model, $A + A \leftrightarrow A$. We consider extensive numerical simulation of the radial system obtained from a single seed. Observed fluctuations in such an…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
We study a one-dimensional gas of $n$ charged particles confined by a potential and interacting through the Riesz potential or a more general potential. In equilibrium, and for symmetric potential the particles arrange themselves…
Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
We consider the asymptotic behavior of the (one dimensional) two-species annihilation reaction A + B --> 0, where both species have a uniform drift in the same direction and like species have a hard core exclusion. Extensive numerical…
Based on the fluctuation-electromagnetic theory, we have calculated the retarded force of attraction, frictional moment and heating rate of a neutral particle rotating near a polarizable surface. The particle and surface are characterized…
The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
In this note we discuss a paradigmatic example of interacting particles subject to non conservative external forces and to the action of thermostats consisting of external (finite) reservoirs of particles. We then consider a model of…
We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type $1$ can enter any…
The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
Consider the model where particles are initially distributed on $\mathbb{Z}^d, \, d\geq 2$, according to a Poisson point process of intensity $\lambda>0$, and are moving in continuous time as independent simple symmetric random walks. We…
We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already…
The configurational and melting properties of large two-dimensional clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
We study front propagation in the irreversible epidemic model $A+B\to 2A$ in one dimension. Here, we allow the particles $A$ and $B$ to diffuse with rates $D_A$ and $D_B$, which, in general, may be different. We find analytic estimates for…