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The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By…

Pattern Formation and Solitons · Physics 2009-11-07 Hiroaki Takagi , Kunihiko Kaneko

Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…

Biological Physics · Physics 2026-02-13 Louis Brezin , Kyle J. Shaffer , Kirill S. Korolev

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

The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…

Mathematical Physics · Physics 2015-05-28 Jean-Guy Caputo , Benoit Sarels

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the…

Pattern Formation and Solitons · Physics 2016-01-20 John R. Mahoney , John Li , Carleen Boyer , Tom Solomon , Kevin A. Mitchell

The formation of regular precipitate stripes in the wake of moving chemical reaction-diffusion fronts is investigated. Experiments on the $NaOH+CuCl_2$ reaction in PVA hydrogel yield stripes parallel or slightly oblique to the front that…

Materials Science · Physics 2007-05-23 Peter Hantz , Istvan Biro

We investigate the effects of an electric current on the width of a stationary reaction zone in an irreversible A^- + B^+ -> C reaction-diffusion process. The ion dynamics of the electrolytes A = (A^+, A^-) and B = (B^+, B^-) is described…

Chemical Physics · Physics 2009-07-13 Kirsten Martens , Michel Droz , Zoltan Rácz

Resonantly-forced oscillatory reaction-diffusion systems can exhibit fronts with complicated interfacial structure separating phase-locked homogeneous states. For values of the forcing amplitude below a critical value the front "explodes"…

Pattern Formation and Solitons · Physics 2009-11-11 Jörn Davidsen , Alexander Mikhailov , Raymond Kapral

Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…

Statistical Mechanics · Physics 2018-10-09 C. Escudero , S. B. Yuste , E. Abad , F. Le Vot

We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed…

Analysis of PDEs · Mathematics 2015-02-03 Matthieu Alfaro , Thomas Giletti

We study front propagation in the reaction diffusion process $\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one dimensional (1d) lattice with hard core interaction between the particles. Using the leading particle…

Statistical Mechanics · Physics 2007-05-23 Niraj Kumar , Goutam Tripathy

Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to…

Statistical Mechanics · Physics 2017-04-05 Tadeusz Kosztołowicz

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…

Analysis of PDEs · Mathematics 2025-06-06 Henri Berestycki , Luca Rossi , Andrea Tellini

We analyze the long time behavior of initial value problems that model a process where particles of type A and B diffuse in some substratum and react according to $nA+nB\to C$. The case n=1 has been studied before; it presents nontrivial…

Mathematical Physics · Physics 2009-10-31 Guillaume van Baalen , Alain Schenkel , Peter Wittwer

A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…

Statistical Mechanics · Physics 2009-11-13 F H Jafarpour , B Ghavami

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…

Chemical Physics · Physics 2019-11-05 Denis S. Grebenkov , Diego Krapf

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions ${\cal R}_t \sim t n_A^\infty n_B^\infty$ is 2nd order in the far-field densities $n_A^\infty,n_B^\infty$. First order…

Soft Condensed Matter · Physics 2009-10-31 Ben O'Shaughnessy , Dimitrios Vavylonis

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the…

Statistical Mechanics · Physics 2008-12-01 E. Agliari , R. Burioni , D. Cassi , F. M. Neri

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…

Materials Science · Physics 2008-09-04 Lynda Amirouche , Mathis Plapp

We study a two-species reaction-diffusion model where A+A->0, A+B->0 and B+B->0, with annihilation rates lambda0, delta0 > lambda0 and lambda0, respectively. The initial particle configuration is taken to be randomly mixed with mean…

Statistical Mechanics · Physics 2009-10-31 Zoran Konkoli , Henrik Johannesson