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We consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems,…

Statistical Mechanics · Physics 2009-11-07 S. B. Yuste , Katja Lindenberg

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

We study the two-species diffusion-annihilation process, $A+B\rightarrow$ \O, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master…

Statistical Mechanics · Physics 2018-07-03 Loïc Turban

We study the pairwise annihilation process $A+A\to$ inert of a number of random walkers, which originally are localized in a small region in space. The size of the colony and the typical distance between particles increases with time and,…

Statistical Mechanics · Physics 2007-05-23 Georg Foltin , Karin A. Dahmen , Nadav M. Shnerb

The kinetics of the q-state Potts model in the zero temperature limit in one dimension is analyzed exactly through a generalization of the method of empty intervals, previously used for the analysis of diffusion-limited coalescence, A+A->A.…

Statistical Mechanics · Physics 2009-10-31 Thomas Masser , Daniel ben Avraham

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

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

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…

Condensed Matter · Physics 2009-10-28 Malte Henkel , Enzo Orlandini , Gunter M. Schütz

When particles on a line collide, they may annihilate - both are destroyed. Computing exact annihilation probabilities has been difficult because collisions reduce the particle count, while determinantal methods require a fixed count…

Probability · Mathematics 2026-03-10 Piotr Śniady

We consider a one-dimensional system with particles having either positive or negative velocity, which annihilate on contact. To the ballistic motion of the particle, a diffusion is superimposed. The annihilation may represent a reaction in…

Statistical Mechanics · Physics 2016-03-02 Soham Biswas , Hernán Larralde , Francois Leyvraz

We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous…

Statistical Mechanics · Physics 2015-05-13 S. B. Yuste , J. J. Ruiz-Lorenzo , Katja Lindenberg

The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian…

Probability · Mathematics 2012-01-10 Roger Tribe , Oleg Zaboronski

Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…

Probability · Mathematics 2022-09-21 Darío Cruzado Padró , Matthew Junge , Lily Reeves

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 study diffusion-limited coalescence, A+A<-->A$, in one dimension, and derive an exact solution for the steady state in the presence of a trap. Without the trap, the system arrives at an equilibrium state which satisfies detailed balance,…

Statistical Mechanics · Physics 2009-10-31 Daniel ben-Avraham

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

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

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…

Condensed Matter · Physics 2009-10-28 Daniele Balboni , Pierre-Antoine Rey , Michel Droz

We study diffusion-limited coalescence, A+A<-->A, in one dimension, in the presence of a diffusing trap. The system may be regarded as a generalization of von Smoluchowski's model for reaction rates, in that: (a) it includes reactions…

Statistical Mechanics · Physics 2015-06-25 Aleksandar Donev , Jeff Rockwell , Daniel ben-Avraham

When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…

Probability · Mathematics 2026-03-10 Piotr Śniady