相关论文: Ballistic Coalescence Model
Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…
In coalescing ballistic annihilation, infinitely many particles move with fixed velocities across the real line and, upon colliding, either mutually annihilate or generate a new particle. We compute the critical density in symmetric…
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…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each…
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…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
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 study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial…
Three-velocity ballistic annihilation is an interacting system in which stationary, left-, and right-moving particles are placed at random throughout the real line and mutually annihilate upon colliding. We introduce a coalescing variant in…
We study several fundamental properties of a class of stochastic processes called spatial Lambda-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the…
We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the…
We consider a fully asymmetric one-dimensional model with mass-conserving coalescence. Particles of unit mass enter at one edge of the chain and coalescence while performing a biased random walk towards the other edge where they exit. The…
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…
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous…
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…
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…
We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like…