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We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which…

Analysis of PDEs · Mathematics 2025-04-28 Alpár R. Mészáros , Guy Parker

The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed.…

Statistical Mechanics · Physics 2020-10-28 Shengfeng Deng , Wei Li , Uwe C. Täuber

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 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 a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…

Analysis of PDEs · Mathematics 2022-06-16 Apratim Bhattacharya , Markus Gahn , Maria Neuss-Radu

We investigate quantum reaction-diffusion systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ($A + A \to \emptyset$)…

Statistical Mechanics · Physics 2024-05-20 Shiphrah Rowlands , Igor Lesanovsky , Gabriele Perfetto

We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov and calculate for a single…

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

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an…

Statistical Mechanics · Physics 2009-11-07 S. J. O'Donoghue , A. J. Bray

In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the…

Statistical Mechanics · Physics 2009-10-31 Hans-Karl Janssen

A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and…

Condensed Matter · Physics 2010-10-12 Vladimir Privman

We study the coupled two-species non-equilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may…

Statistical Mechanics · Physics 2009-11-10 Beth A. Reid , Jason C. Brunson , Uwe C. Tauber

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

We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…

Analysis of PDEs · Mathematics 2023-01-19 Jeffrey Morgan , Samia Zermani

The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the…

Statistical Mechanics · Physics 2008-08-06 Galit Evron , David A. Kessler , Nadav M. Shnerb

The exact solution of a diffusion$-$reaction model for the trapping and annihilation of positrons in small extended spherical defects (clusters, voids, small precipitates) with competitive rate-limited trapping in vacancy-type point defects…

Materials Science · Physics 2019-04-24 Roland Würschum , Laura Resch , Gregor Klinser

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

A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…

Statistical Mechanics · Physics 2009-10-28 John Cardy , Uwe C. Täuber

We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…

Analysis of PDEs · Mathematics 2019-05-28 Brian P. Cupps , Jeff Morgan , Bao Quoc Tang

We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…

Probability · Mathematics 2022-08-05 Riti Bahl , Philip Barnet , Tobias Johnson , Matthew Junge

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…

Statistical Mechanics · Physics 2014-07-18 P. L. Krapivsky