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We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame…

Statistical Mechanics · Physics 2009-11-11 Niraj Kumar , Goutam Tripathy

A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…

Fluid Dynamics · Physics 2022-10-05 Ricardo H. Deucher , Louis J. Durlofsky

The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…

Analysis of PDEs · Mathematics 2014-04-17 Pavel Gurevich , Roman Shamin , Sergey Tikhomirov

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…

Statistical Mechanics · Physics 2016-02-23 Xavier Durang , Jean-Yves Fortin , Malte Henkel

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Optimization and Control · Mathematics 2017-12-27 Kun Yuan , Bicheng Ying , Xiaochuan Zhao , Ali H. Sayed

We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D_A of particles A and initial…

Statistical Mechanics · Physics 2015-06-25 Zbigniew Koza

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

The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…

Soft Condensed Matter · Physics 2015-05-13 Ramin Golestanian

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 study the reaction-diffusion process $A+B\to \emptyset$ with injection of each species at opposite boundaries of a one-dimensional lattice and bulk driving of each species in opposing directions with a hardcore interaction. The system…

Statistical Mechanics · Physics 2009-10-28 M. J. E. Richardson , M. R. Evans

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes,…

Statistical Mechanics · Physics 2013-01-15 Yaghoob Naimi , Frinaz Roshani

A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…

Exactly Solvable and Integrable Systems · Physics 2026-03-27 Philip Broadbridge , Roman Cherniha , Vasyl' Davydovych , Ian Marquette

The reversible reactions A+A<=>C and A+B<=>C are investigated. From the exact Langevin equations describing our model, we set up a systematic approximation scheme to compute the approach of the density of C particles to its equilibrium…

Statistical Mechanics · Physics 2009-10-31 Pierre-Antoine Rey , John Cardy

In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…

Disordered Systems and Neural Networks · Physics 2009-10-30 Felix Ritort

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic…

Other Condensed Matter · Physics 2009-11-11 Ioana Bena , Michel Droz , Kirsten Martens , Zoltan Racz

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

Functional Analysis · Mathematics 2019-02-14 L. Paunonen , D. Seifert

We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…

Statistical Mechanics · Physics 2018-08-22 E. Abad , T. Abil , A. Santos , J. J. Kozak

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

We study the steady state of a stochastic particle system on a two-dimensional lattice, with particle influx, diffusion and desorption, and the formation of a dimer when particles meet. Surface processes are thermally activated, with…

Statistical Mechanics · Physics 2015-05-30 A. Wolff , I. Lohmar , J. Krug , O. Biham

We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…

Analysis of PDEs · Mathematics 2021-06-30 Thierry Gallay , Sinisa Slijepcevic