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We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…

Condensed Matter · Physics 2016-08-31 Jaime E. Santos , Gunter M. Schutz , Robin B. Stinchcombe

We consider two species of particles performing random walks in a domain in $\mathbb{R}^d$ with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law so that the total number of particles of…

Probability · Mathematics 2007-05-23 Krzysztof Burdzy , Jeremy Quastel

Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their…

Statistical Mechanics · Physics 2015-06-24 Uwe C. Tauber

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…

Statistical Mechanics · Physics 2018-03-13 L. Turban , J. -Y. Fortin

We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be…

Statistical Mechanics · Physics 2007-05-23 Steffen Trimper , Knud Zabrocki , Michael Schulz

We propose the general scaling model for the diffusio n-annihilation reaction $A_{+} + A_{-} \longrightarrow \emptyset$ with long-range power-law i nteractions. The presented scaling arguments lead to the finding of three different regimes,…

Condensed Matter · Physics 2009-10-28 Sergei F. Burlatsky , Valeriy V. Ginzburg , Noel A. Clark

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same…

Condensed Matter · Physics 2009-10-22 P. L. Krapivsky , E. Ben-Naim , S. Redner

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density…

Statistical Mechanics · Physics 2009-11-10 H. J. Hilhorst , O. Deloubriere , M. J. Washenberger , U. C. Tauber

The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in…

Statistical Mechanics · Physics 2008-11-26 Malte Henkel , Haye Hinrichsen

A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…

Mathematical Physics · Physics 2014-03-17 Mohammad Khorrami , Amir Aghamohammadi

Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of…

Statistical Mechanics · Physics 2007-05-23 E. Ben-Naim , P. L. Krapivsky

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…

Statistical Mechanics · Physics 2009-10-31 S. Trimper , U. C. Taeuber , G. M. Schuetz

In this article we review the problem of reaction annihilation $A+A \rightarrow \emptyset$ on a real lattice in one dimension, where $A$ particles move ballistically in one direction with a discrete set of possible velocities. We first…

Statistical Mechanics · Physics 2021-12-16 Soham Biswas , Francois Leyvraz

We present the growth dynamics of an island of particles $A$ injected from a localized $A$-source into the sea of particles $B$ and dying in the course of diffusion-controlled annihilation $A+B\to 0$. We show that in the 1d case the island…

Statistical Mechanics · Physics 2009-11-10 Boris M. Shipilevsky

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for…

Condensed Matter · Physics 2010-10-12 Daniel ben-Avraham , Vladimir Privman , Dexin Zhong

We study diffusion-limited (on-site) pair annihilation $A+A\to 0$ and (on-site) fusion $A+A\to A$ which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour…

Statistical Mechanics · Physics 2009-10-30 G. M. Schütz

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

An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…

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

We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…

Statistical Mechanics · Physics 2024-10-22 H. Bendekgey , G. Huber , D. Yllanes

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…

Condensed Matter · Physics 2009-10-22 Daniel ben-Avraham , Francois Leyvraz , Sid Redner