Related papers: Discrete-to-continuum limits of particles with an …
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
We study a class of interacting particle systems in which $n$ signed particles move on the real line. At close range particles with the same sign repel and particles with opposite sign attract each other. The repulsion and attraction are…
We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…
Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
We consider a one-dimensional system with particles having either positive or negative velocity, which annihilate on contact. To the ballistic motion of the particle, a diffusion is superimposed. The annihilation may represent a reaction in…
In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a $\Gamma$-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we…
We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for…
We introduce detector-level entanglement, a unified entanglement concept for identical particles that takes into account the possible deletion of many-particle which-way information through the detection process. The concept implies a…
We apply a recently developed perturbative formalism which describes the evolution under their self-gravity of particles displaced from a perfect lattice to quantify precisely, up to shell crossing, the effects of discreteness in…
We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
This paper considers the equilibrium positions of $n$ particles in one dimension. Two forces act on the particles; a nonlocal repulsive particle-interaction force and an external force which pushes them to an impenetrable barrier. While the…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…
The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the…