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A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…

Dynamical Systems · Mathematics 2022-01-05 Anton S. Zadorin

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

The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…

Mathematical Physics · Physics 2015-05-13 Daniel Lenz , Robert V. Moody

The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…

Other Condensed Matter · Physics 2007-05-23 Serge Shpyrko , Vladimir M. Sysoev

We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…

Biomolecules · Quantitative Biology 2015-03-20 Aleksandr Kivenson , Michael F. Hagan

We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…

Statistical Mechanics · Physics 2020-01-29 Eial Teomy , Ralf Metzler

We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…

Probability · Mathematics 2007-05-23 Alexey M. Kulik

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

We briefly review some common diffusion-limited reactions with emphasis on results for two-species reactions with anisotropic hopping. Our review also covers single-species reactions. The scope is that of providing reference and general…

Condensed Matter · Physics 2010-10-12 Antonio M. R. Cadilhe , M. Lawrence Glasser , Vladimir Privman

We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…

Statistical Mechanics · Physics 2009-11-07 Vahid Karimipour

We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two…

Statistical Mechanics · Physics 2009-11-10 F. H. Jafarpour , S. R. Masharian

We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…

Statistical Mechanics · Physics 2009-11-07 Alan J. Bray , Satya N. Majumdar , Richard A. Blythe

In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special…

Statistical Mechanics · Physics 2009-11-13 W. G. Dantas , M. J. de Oliveira , J. F. Stilck

We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and…

Mathematical Physics · Physics 2015-07-22 Michael Baake , Holger Kösters , Robert V. Moody

The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…

Statistical Mechanics · Physics 2008-10-22 M. Sinder , V. Sokolovsky , J. Pelleg

A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…

Analysis of PDEs · Mathematics 2023-09-27 Nibedita Ghosh , Hari Shankar Mahato

The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact…

Statistical Mechanics · Physics 2009-10-31 Boaz Kol , Amnon Aharony

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…

Condensed Matter · Physics 2016-08-31 Pierre-Antoine Rey , Michel Droz

We consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre…

Condensed Matter · Physics 2009-10-22 Stephen Cornell , Zbigniew Koza , Michel Droz

In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that the nonlocal evolution equations reproduce similar patterns to…

Analysis of PDEs · Mathematics 2025-11-07 Hiroshi Ishii , Yoshitaro Tanaka