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Diffusion and reaction among traps: some theoretical and simulation results

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Abstract

Diffusion and reaction in heterogeneous media arise in a host of phenomena in the physical and biological sciences. The determination of the mean survival timeτ (i.e., inverse trapping rate) and relaxation timesT n, n=1,2,3,... (i.e., inverse eigenvalues), associated with diffusion among partially absorbing, static traps with surface rate constantk are problems of long-standing interest. The limitsk=∞ andk=0 correspond to the diffusion-controlled case (i.e., perfect absorbers) and reaction-controlled case (i.e., perfect reflectors), respectively. This paper reviews progress we have made on several basic aspects of this problem: (i) the formulation of rigorous bonding techniques and computational methodologies that enable one to estimate the mean survival time τ and principal relaxation timeT 1 (ii) the quantitative characterization of the microstructure of nontrivial continuum (i.e., off-lattice) models of heterogeneous media; and (iii) evaluation of τ and T1 for the same models. We also describe a rigorous link between the mean survival time t and a different effective parameter of the system, namely the fluid permeability tensork associated with Stokes flow through the same porous medium.

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Author notes

  1. S. Torquato

    Present address: Department of Mechanical and Aerospace Engineering, North Carolina State University, 27695-7910, Raleigh, North Carolina

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 10012, New York, New York

    S. Torquato

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  1. S. Torquato
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Torquato, S. Diffusion and reaction among traps: some theoretical and simulation results. J Stat Phys 65, 1173–1206 (1991). https://doi.org/10.1007/BF01049606

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