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We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…

Probability · Mathematics 2012-08-21 Alan Hammond , Fraydoun Rezakhanlou

We analyze the trajectory of suspended spherical particles moving through a square array of obstacles, in the deterministic limit and at zero Reynolds number. We show that, in the dilute approximation of widely separated obstacles, the…

Fluid Dynamics · Physics 2016-05-04 Sumedh R. Risbud , German Drazer

Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. For any $\lambda>0$ we consider the percolation…

Probability · Mathematics 2019-07-10 David Dereudre , Mathew D. Penrose

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…

Condensed Matter · Physics 2016-08-31 P. L. Krapivsky

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic…

Statistical Mechanics · Physics 2024-06-19 Swetamber Das , Jason R. Green

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the…

Statistical Mechanics · Physics 2009-11-07 Thomas M. Masser , Daniel ben-Avraham

We show that there are shape-independent upper bounds to the extinction cross section per unit volume of randomly oriented nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the…

In this article we prove a sprinkled decoupling inequality for the stationary Hammersley's interacting particle process. Inspired by the work of Baldasso and Texeira (2018), and Hil\'ario, Kious and Texeira (2020), we apply this inequality…

Probability · Mathematics 2025-06-25 Leandro P. R. Pimentel , Roberto Viveros

We consider a branching-selection system of particles on the real line that evolves according to the following rules: each particle moves according to a Brownian motion during an exponential lifetime and then splits into two new particles…

Probability · Mathematics 2016-04-07 Michel Pain

The problem of ballistic annihilation for a spatially homogeneous system is revisited within Boltzmann's kinetic theory in two and three dimensions. Exact analytical results are derived for the time evolution of the particle density for…

Statistical Mechanics · Physics 2009-11-07 Francois Coppex , Michel Droz , Jaroslaw Piasecki , Emmanuel Trizac , Peter Wittwer

Given a Poisson point process on R, assign either one or two marks to each point of this process, independently of the others. We study the motion of a particle that jumps deterministically from its current location to the nearest point of…

Probability · Mathematics 2018-06-13 Leonardo T. Rolla , Vladas Sidoravicius , Laurent Tournier

We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, and meetings of opposite-type particles result in…

Probability · Mathematics 2026-05-07 John Haslegrave , Peter Keevash

We consider the dynamics of particles undergoing the reaction $A+A \to \emptyset$ in one dimension with a dynamic bias. Here the particles move towards their nearest neighbour with probability $0.5+\epsilon$ where $-0.5 \leq \epsilon < 0$.…

Statistical Mechanics · Physics 2020-09-15 Reshmi Roy , Parongama Sen

We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…

Probability · Mathematics 2018-01-29 Łukasz Treszczotko

The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…

Soft Condensed Matter · Physics 2008-07-09 Michael Schindler , Peter Talkner , Marcin Kostur , Peter Hanggi

We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift $-\sqrt{2+2\varepsilon}$, undergo dyadic fission at rate $1$, and are killed when they reach the origin. We…

Probability · Mathematics 2022-01-25 Jiaqi Liu

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the…

Statistical Mechanics · Physics 2012-07-24 Federico Benitez , Nicolas Wschebor

We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is…

Condensed Matter · Physics 2015-06-25 Jarosław Piasecki , Pierre-Antoine Rey , Michel Droz

We consider the behavior of extremal particles in $K$-symmetric exclusion on $\mathbb{Z}$ when the process starts from certain infinite-particle step configurations where there are no particles to the right of a maximal one. In such a…

Probability · Mathematics 2025-06-17 Michael Conroy , Adrián González Casanova , Sunder Sethuraman

A particle in the H\'enon-Heiles potential can escape when its energy is above the threshold value $E_{th}={1/6}$. We report a theoretical study on the the escape rates near threshold. We derived an analytic formula for the escape rate as a…

Chaotic Dynamics · Physics 2007-05-23 H. J. Zhao , M. L. Du