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The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of…

Statistical Mechanics · Physics 2016-08-31 M. J. E. Richardson

We consider a general class of birth-and-death processes with state space $\{0,1,2,3,\ldots\}$ which describes the size of a population going eventually to extinction with probability one. We obtain the complete spectrum of the generator of…

Probability · Mathematics 2022-04-25 J. -R. Chazottes , P. Collet , S. Méléard

In this paper we consider coalescing random walks on a general connected graph $G=(V,E)$. We set up a unified framework to study the leading order of the decay rate of $P_t$, the expectation of the fraction of occupied sites at time $t$,…

Probability · Mathematics 2022-09-13 Jonathan Hermon , Shuangping Li , Dong Yao , Lingfu Zhang

We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of…

Mathematical Physics · Physics 2023-01-25 James Mason , Robert L Jack , Maria Bruna

Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…

Statistical Mechanics · Physics 2009-10-31 Gyorgy Szabo , Maria Augusta Santos

Annihilation processes, where the reacting particles are influenced by some external advective field, are one of the simplest examples of nonlinear statistical systems. This type of processes can be observed in miscellaneous chemical,…

Chaotic Dynamics · Physics 2015-06-12 Michal Hnatič , Juha Honkonen , Tomáš Lučivjanský

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…

Statistical Mechanics · Physics 2009-10-31 S. Trimper , U. C. Taeuber , G. M. Schuetz

Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical…

Statistical Mechanics · Physics 2024-10-07 R. Juhász , I. A. Kovács

A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…

Mathematical Physics · Physics 2013-11-15 Rong Yang , Li Chen

The idea of a metapopulation has become canonical in ecology. Its original mean field form provides the important intuition that migration and extinction interact to determine the dynamics of a population composed of subpopulations. From…

Populations and Evolution · Quantitative Biology 2021-07-01 John Vandermeer , Zachary Hajian-Forooshani

The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric…

Statistical Mechanics · Physics 2018-06-25 Arvind Ayyer , Dipankar Roy

This article presents a variant of Fleming-Viot particle systems, which are a standard way to approximate the law of a Markov process with killing as well as related quantities. Classical Fleming-Viot particle systems proceed by simulating…

Probability · Mathematics 2019-11-14 Frédéric Cérou , Arnaud Guyader , Mathias Rousset

The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…

Chemical Physics · Physics 2009-10-31 Martin Z. Bazant , Howard A. Stone

Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants D_A and D_B. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/\tau). The…

Statistical Mechanics · Physics 2015-06-25 F. van Wijland , K. Oerding , H. J. Hilhorst

Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are…

Statistical Mechanics · Physics 2009-10-31 Haye Hinrichsen

We start by providing an explicit characterization and analytical properties, including the persistence phenomena, of the distribution of the extinction time $\mathbb{T}$ of a class of non-Markovian self-similar stochastic processes with…

Probability · Mathematics 2022-05-24 Ronnie Loeffen , Pierre Patie , Mladen Savov

In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve, reproduce and die independently and, with a probability that…

Probability · Mathematics 2025-01-31 A M G Cox , E Horton , D Villemonais

We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise the phase boundary by the existence of a metastable density,…

Probability · Mathematics 2025-05-29 Benedikt Jahnel , Lukas Lüchtrath , Christian Mönch

We consider the simple exclusion process with $k$ particles on a segment of length $N$ performing random walks with transition $p>1/2$ to the right and $q=1-p$ to the left. We focus on the case where the asymmetry in the jump rates…

Probability · Mathematics 2018-06-01 C. Labbé , H. Lacoin

We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…

Analysis of PDEs · Mathematics 2026-05-05 Nadia Khoury , P. -E. Jabin