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The Encounter Probability for Random Walkers in a Confined Space

Published online by Cambridge University Press:  26 February 2011

James P. Lavine
James P. Lavine*
Affiliation:
james.p.lavine@kodak.com, Eastman Kodak Company, Image Sensor Solutions, 1999 Lake Avenue, Rochester, NY, 14650-2008, United States, 585-477-7536
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Abstract

Particles diffusing in a confined space should encounter one another with a probability that depends on the size and dimension of the space. The present work uses pairs of random walkers on a lattice to investigate the encounter probability in one, two, and three spatial dimensions. There is an initial rapid decay of the survival-time distribution that is followed by an exponential decay in time. The characteristic time for this latter decay is strongly dependent on the model space size and scales as a power law in the size. The exponent of the power law depends on the number of spatial dimensions. For a fixed L, the exponential tail of the survival-time distribution has a similar slope when the initial separation of the two walkers is varied. The spacing between the exponential decay curves scales with the initial separation in 1-D, but not in 2-D or 3-D. In addition, the mapping of two random walkers to an equivalent single walker is explored.

Keywords

diffusionsimulationchemical reaction
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 899: Symposium N – Dynamics in Small Confining Systems VIII , 2005 , 0899-N07-13
Copyright
Copyright © Materials Research Society 2006

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References

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