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Diffusion-Limited Reactions and Mortal Random Walkers in Confined Geometries

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Abstract

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, Cologne, Germany

    Ingo Lohmar & Joachim Krug

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  1. Ingo Lohmar
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  2. Joachim Krug
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Correspondence to Joachim Krug.

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Lohmar, I., Krug, J. Diffusion-Limited Reactions and Mortal Random Walkers in Confined Geometries. J Stat Phys 134, 307–336 (2009). https://doi.org/10.1007/s10955-009-9680-x

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