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Related papers: Cluster approximation solution of a two species an…

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The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…

Statistical Mechanics · Physics 2009-10-31 Geza Odor

We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…

Probability · Mathematics 2021-09-29 Joaquín Fontbona , Felipe Muñoz-Hernández

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

Probability · Mathematics 2021-07-21 Watthanan Jatuviriyapornchai , Stefan Grosskinsky

We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…

Analysis of PDEs · Mathematics 2023-04-07 Alexander Mielke , Stefanie Schindler

Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…

Condensed Matter · Physics 2012-01-27 A. Aghamohammadi , A. H. Fatollahi , M. Khorrami , A. Shariati

Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…

Populations and Evolution · Quantitative Biology 2020-02-19 D. Bazeia , M. V. de Moraes , B. F. de Oliveira

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 diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is…

Statistical Mechanics · Physics 2009-11-07 Olivier Deloubriere , Henk Hilhorst , Uwe C. Tauber

In this article we review the problem of reaction annihilation $A+A \rightarrow \emptyset$ on a real lattice in one dimension, where $A$ particles move ballistically in one direction with a discrete set of possible velocities. We first…

Statistical Mechanics · Physics 2021-12-16 Soham Biswas , Francois Leyvraz

We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…

Statistical Mechanics · Physics 2009-11-07 S. Habib , K. Lindenberg , G. Lythe , C. Molina-Paris

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

Statistical Mechanics · Physics 2015-07-08 Ricardo Martínez-García , Clara Murgui , Emilio Hernández-García , Cristóbal López

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…

Condensed Matter · Physics 2009-11-07 M. Khorrami , A. Aghamohammadi , M. Alimohammadi

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

Statistical Mechanics · Physics 2009-10-31 K. Mussawisade , J. E. Santos , G. M. Schütz , ;

A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the…

Statistical Mechanics · Physics 2009-11-07 Farinaz Roshani , Mohammad Khorrami

The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in…

Statistical Mechanics · Physics 2008-11-26 Malte Henkel , Haye Hinrichsen

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is…

Statistical Mechanics · Physics 2007-05-23 Amir Aghamohammadi , Mohammad Khorrami

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…

Condensed Matter · Physics 2009-11-07 Amir Aghamohammadi , Masoud Alimohammadi , Mohammad Khorrami

In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…

Statistical Mechanics · Physics 2011-08-09 Amir Aghamohammadi , Mohammad Khorrami

Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for closedness of the evolution equations of the $n$-point functions are obtained. The average number of the particles…

Statistical Mechanics · Physics 2009-11-07 Ahmad Shariati , Amir Aghamohammadi , Mohammad Khorrami

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…

Condensed Matter · Physics 2010-10-12 V. Privman , C. R. Doering , H. L. Frisch