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Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation

Abstract

We report exact results for one-dimensional reaction-diffusion modelsA+A→inert,A+A→A, andA+B→inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasizes anisotropy of hopping rates; no changes in universal properties are found, due to anisotropy, in all three reactions. The method of solution employs mapping onto a model of coagulating positive integer charges. The dynamical rules are synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities are consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.

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Privman, V., Cadilhe, A.M.R. & Glasser, M.L. Exact solutions of anisotropic diffusion-limited reactions with coagulation and annihilation. J Stat Phys 81, 881–899 (1995). https://doi.org/10.1007/BF02179297

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Key Words

  • Reactions
  • anisotropic diffusion
  • coagulation
  • synchronous dynamics