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Related papers: Four-parameter coalescing ballistic annihilation

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We consider a one-dimensional system of particles, moving at constant velocities chosen independently according to a symmetric distribution on $\{-1,0,+1\}$, and annihilating upon collision -- with, in case of triple collision, a uniformly…

Probability · Mathematics 2022-01-05 John Haslegrave , Laurent Tournier

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic…

Statistical Mechanics · Physics 2009-10-31 R. A. Blythe , M. R. Evans , Y. Kafri

We study the kinetics of ballistic annihilation for a one-dimensional ideal gas with continuous velocity distribution. A dynamical scaling theory for the long time behavior of the system is derived. Its validity is supported by extensive…

Statistical Mechanics · Physics 2009-10-30 Pierre-Antoine Rey , Michel Droz , Jaroslaw Piasecki

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

When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…

Probability · Mathematics 2026-03-10 Piotr Śniady

Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a…

Probability · Mathematics 2022-11-29 Clayton Barnes , Leonid Mytnik , Zhenyao Sun

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…

Probability · Mathematics 2025-11-18 Daniel Ahlberg , Omer Angel , Brett Kolesnik

When particles on a line collide, they may annihilate - both are destroyed. Computing exact annihilation probabilities has been difficult because collisions reduce the particle count, while determinantal methods require a fixed count…

Probability · Mathematics 2026-03-10 Piotr Śniady

The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…

Condensed Matter · Physics 2009-10-28 E. Ben-Naim , S. Redner , P. L. Krapivsky

Place an $A$-particle at each site of a graph independently with probability $p$ and otherwise place a $B$-particle. $A$- and $B$-particles perform independent continuous time random walks at rates $\lambda_A$ and $\lambda_B$, respectively,…

Probability · Mathematics 2023-08-02 Tobias Johnson , Matthew Junge , Hanbaek Lyu , David Sivakoff

In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We…

Mathematical Physics · Physics 2020-03-18 Bertrand Lods , Alessia Nota , Federica Pezzotti

The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian…

Probability · Mathematics 2012-01-10 Roger Tribe , Oleg Zaboronski

Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare…

Probability · Mathematics 2021-06-04 Irina Cristali , Yufeng Jiang , Matthew Junge , Remy Kassem , David Sivakoff , Grayson York

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents $\xi$ and $\gamma$ that describe the long-time decay of the number of particles ($n(t)\sim t^{-\xi}$) and of their typical…

Statistical Mechanics · Physics 2009-11-11 Adam Lipowski , Dorota Lipowska , Antonio L. Ferreira

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…

Analysis of PDEs · Mathematics 2022-07-01 Patrick van Meurs , Mark A. Peletier , Norbert Pozar

When particles on a line collide, they may coalesce into one. Such systems arise in the voter model, where boundaries between opinion clusters perform coalescing random walks, and in reaction-diffusion theory, where diffusing particles…

Probability · Mathematics 2026-03-10 Piotr Śniady

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…

Statistical Mechanics · Physics 2007-12-05 P. Horvai , S. V. Nazarenko , T. H. M. Stein

We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…

Statistical Mechanics · Physics 2015-05-13 P. L. Krapivsky , E. Ben-Naim

We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…

Probability · Mathematics 2018-06-19 Manuel Cabezas , Leonardo T. Rolla , Vladas Sidoravicius

This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…

Probability · Mathematics 2012-10-09 Siva Athreya , Jan Swart