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Exact Dynamics in a Model of the Bimolecular Reaction A+B→ 0

Published online by Cambridge University Press:  15 February 2011

Eric Clément ,
Patrick Leroux-Hugon  and
Leonard M. Sander
Eric Clément
Affiliation:
Laboratoire d'Optique de la Matière condensée, Universite Paris VI, 4 place Jussieu, 75005, Paris, FRANCE
Patrick Leroux-Hugon
Affiliation:
Groupe de Physique des Solides Universite Paris 7, 2 place Jussieu 75251 Paris cedex 05, FRANCE
Leonard M. Sander
Affiliation:
Dept. of Physics, The University of Michigan, Ann Arbor MI 48109-1120, USA.
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Abstract

We have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 345
Copyright
Copyright © Materials Research Society 1993

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References

1. Clement, E., Leroux-Hugon, P., and Sander, L. M., Phys. Rev. Lett, 67, 1661 (1991), and J. Stat. Phys. 65, 925 (1991)Google Scholar
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5. Clément, E., Sander, L., Kopelman, R., Phys.Rev.A 39, 6455 (1989); Phys.Rev.A 39, 6466 (1989).Google Scholar
6. Flament, C., Clément, E., Leroux-Hugon, P., Sander, L., J. Phys. A in press.Google Scholar