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We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the…

Statistical Mechanics · Physics 2009-11-07 Zbigniew Koza

The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived,…

Condensed Matter · Physics 2009-10-22 Benjamin P. Lee , John Cardy

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 consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems,…

Statistical Mechanics · Physics 2009-11-07 S. B. Yuste , Katja Lindenberg

We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous…

Statistical Mechanics · Physics 2015-05-13 S. B. Yuste , J. J. Ruiz-Lorenzo , Katja Lindenberg

The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here, we consider the specific example of diffusion limited coalescence and annihilation reactions in one-dimensional…

Statistical Mechanics · Physics 2018-10-22 F. Le Vot , C. Escudero , E. Abad , S. B. Yuste

The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a…

Statistical Mechanics · Physics 2013-01-15 Xavier Durang , Jean-Yves Fortin , Diego Del Biondo , Malte Henkel , Jean Richert

The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…

Analysis of PDEs · Mathematics 2025-06-25 Elisabetta Brocchieri , Lucilla Corrias

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Analysis of PDEs · Mathematics 2026-04-01 Hideki Murakawa , Florian Salin

We study the steady state of diffusion-limited coalescence, A+A<-->A, in the presence of a trap and with a background drift. In one dimension this model can be analyzed exactly through the method of inter-particle distribution functions…

Statistical Mechanics · Physics 2009-10-31 Daniel ben-Avraham

We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous…

Statistical Mechanics · Physics 2007-05-23 S. B. Yuste , Katja Lindenberg

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…

Condensed Matter · Physics 2009-10-22 P. L. Krapivsky

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

Analysis of PDEs · Mathematics 2017-10-11 E. S. Daus , L. Desvillettes , A. Jüngel

The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…

Statistical Mechanics · Physics 2007-05-23 L. Turban

We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…

Analysis of PDEs · Mathematics 2008-08-05 R. Eymard , D. Hilhorst , M. Olech

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…

Populations and Evolution · Quantitative Biology 2023-10-09 Stuart T. Johnston , Matthew J. Simpson

A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…

Statistical Mechanics · Physics 2009-10-31 Mauro Mobilia , Pierre-Antoine Bares

We present a systematic analysis of diffusion-controlled evolution and collapse of two identical spatially separated $d$-dimensional $A$-particle islands in the $B$-particle sea at propagation of the sharp reaction front $A+B\to 0$ at equal…

Statistical Mechanics · Physics 2019-12-25 Boris M. Shipilevsky

We study diffusion-limited coalescence, A+A<-->A, in one dimension, in the presence of a diffusing trap. The system may be regarded as a generalization of von Smoluchowski's model for reaction rates, in that: (a) it includes reactions…

Statistical Mechanics · Physics 2015-06-25 Aleksandar Donev , Jeff Rockwell , Daniel ben-Avraham

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…

Condensed Matter · Physics 2009-10-28 Daniele Balboni , Pierre-Antoine Rey , Michel Droz