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The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour…

Statistical Mechanics · Physics 2007-05-23 Malte Henkel , Haye Hinrichsen

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…

Condensed Matter · Physics 2016-08-31 Horatiu Simon

We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of…

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

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…

Statistical Mechanics · Physics 2007-05-23 Laleh Farhang Matin , Amir Aghamohammadi , Mohammad Khorrami

We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…

Mathematical Physics · Physics 2016-01-20 C. -L. Ho , C. -C. Lee

We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…

Statistical Mechanics · Physics 2013-10-03 Somayeh Zeraati , Farhad H. Jafarpour , Haye Hinrichsen

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 an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles…

Statistical Mechanics · Physics 2009-11-10 G. Oshanin , O. Benichou , A. Blumen

We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$, as well as a minor generalisation thereof. In this case, it is possible to evaluate the scaling…

Statistical Mechanics · Physics 2021-02-17 Francois Leyvraz

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

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…

Condensed Matter · Physics 2016-08-31 P. L. Krapivsky

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…

Condensed Matter · Physics 2009-11-07 M. Khorrami , A. Aghamohammadi , M. Alimohammadi

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…

Statistical Mechanics · Physics 2007-05-23 Uwe C. Tauber

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 reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…

Statistical Mechanics · Physics 2013-05-30 P. L. Krapivsky

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…

Condensed Matter · Physics 2009-11-07 Amir Aghamohammadi , Masoud Alimohammadi , Mohammad Khorrami

A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…

Statistical Mechanics · Physics 2009-11-10 F. Tabatabaee , A. Aghamohammadi

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 phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated…

Statistical Mechanics · Physics 2009-11-10 Geza Odor

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a…

Statistical Mechanics · Physics 2007-05-23 L. Turban