The reaction schemes A+B{→}inert and A+A{→}A, controlled by enhanced diffusion, are investigated. The participating particles are assumed to perform L\'evy walks with L\'evy exponents 1{≤}2. Both theoretical expressions and numerical results are presented. Reaction behaviors are observed which indicate mixing properties. When compared with reactions controlled by Brownian motion we obtain fast- er processes, new kinetic patterns, and, more importantly, lower, {γ}-dependent, critical dimensions for the mean-field behavior. The latter suggests erosion of the segregation phenomenon.
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Zumofen et al. (1994) studied this question.
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