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The influence of spatial fluctuations in simple reaction-diffusion systems

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
173
Issue
3
Identifiers
DOI: 10.1016/0378-4371(91)90379-q

Abstract

Abstract In this paper we study the kinetics of the irreversible diffusion-controlled reactions A+ A→ inert and A+ B→ inert, respectively. By means of van Kampen's “method of compounding moments” we derive a modified rate equation describing the time evolution of the average particle density, which includes the influence of spatial density fluctuations. We show that below an upper critical spatial dimension d 0=2( d 0=4) the particle density of the A+ A system ( A+ B system with equal initial densities of A- and B-particles) decays at t − α with α=2/(4− d) ( α= d/4), which is slower than the t −1 decay predicted by the usual rate equation.

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