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Numerical simulations and cluster mean-field approximations with coherent anomaly extrapolation show that the critical line of the 1d annihilation fission process is separated into two regions. In both the small and high diffusion cases the…

Statistical Mechanics · Physics 2009-10-31 Geza Odor

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of…

Statistical Mechanics · Physics 2009-11-07 Julien Kockelkoren , Hugues Chaté

We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an…

Condensed Matter · Physics 2009-10-28 Valeriy V. Ginzburg , Leo Radzihovsky , Noel A. Clark

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$)…

Statistical Mechanics · Physics 2009-11-07 G. Oshanin , S. F. Burlatsky

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…

Condensed Matter · Physics 2016-08-31 Pierre-Antoine Rey , Michel Droz

A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…

Chaotic Dynamics · Physics 2015-06-12 Giorgio Krstulovic , Massimo Cencini , Jeremie Bec

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

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

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

A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to…

Condensed Matter · Physics 2010-10-12 Vladimir Privman

We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…

Statistical Mechanics · Physics 2009-11-07 Alan J. Bray , Satya N. Majumdar , Richard A. Blythe

A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class…

Statistical Mechanics · Physics 2009-11-10 Dexin Zhong , Daniel ben-Avraham , Miguel A. Munoz

We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…

Statistical Mechanics · Physics 2015-05-13 P. L. Krapivsky , E. Ben-Naim

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 present an exact mapping between two simple spin models: the Fredrickson-Andersen (FA) model and a model of annihilating random walks with spontaneous creation from the vacuum, A+A <-> 0. We discuss the geometric structure of the mapping…

Statistical Mechanics · Physics 2007-05-23 Robert Jack , Peter Mayer , Peter Sollich

Phase transitions of the 2A-> 3A, 4A->0 reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations.The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the…

Statistical Mechanics · Physics 2009-11-10 Geza Odor

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

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…

Statistical Mechanics · Physics 2009-10-31 Enrico Carlon , Malte Henkel , Ulrich Schollwoeck

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 study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…

Condensed Matter · Physics 2016-08-31 Dexin Zhong , Daniel ben-Avraham