On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond

Abstract

We study the behavior of the chemical reactions $A+A\to A+S$ and $A+A\to S+S$ (where the reactive species $A$ and the inert species $S$ are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number $z$ and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the $A$ species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice ($z=2$). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.

23 pages, 10 eps figures, uses revtex4 style files

References in corpus (3)

• Random Sequential Adsorption of Mixtures of Dimers and Monomers on a Pre-Treated Bethe Lattice
• Nonlinear reactive systems viewed as Boolean dynamical systems
• Reactive dynamics on fractal sets: anomalous fluctuations and memory effects

Cited by in corpus (4)

• Yard-Sale exchange on networks: Wealth sharing and wealth appropriation
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Exact correlation functions in particle-reaction models with immobile particles
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices