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Elucidating the Role of Subdiffusion and Evanescence in theTarget Problem: Some Recent Results

Published online by Cambridge University Press:  24 April 2013

E. Abad ,
S. B. Yuste  and
K. Lindenberg
E. Abad*
Affiliation:
Departamento de Física Aplicada, Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain
S. B. Yuste
Affiliation:
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
K. Lindenberg
Affiliation:
Department of Chemistry and Biochemistry, and BioCircuits Institute, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0340, USA
*
⋆Corresponding author. E-mail: eabad@unex.es
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Abstract

We present an overview of recent results for the classic problem of the survivalprobability of an immobile target in the presence of a single mobile trap or of acollection of uncorrelated mobile traps. The diffusion exponent of the traps is taken tobe either γ = 1, associated with normal diffusive motion, or0 < γ < 1, corresponding to subdiffusive motion. We considertraps that can only die upon interaction with the target and, alternatively, traps thatmay die due to an additional evanescence process even before hitting the target. Theevanescence reaction is found to completely modify the survival probability of the target.Such evanescence processes are important in systems where the addition of scavengermolecules may result in the removal of the majority species, or ones where the mobiletraps have a finite intrinsic lifetime.

Keywords

diffusion limited reactionsanomalous diffusionfractional equations

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Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 100 - 113
Copyright
© EDP Sciences, 2013

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