Characteristics of the probability function for three random-walk models of reaction--diffusion processes
A method is presented for calculating exactly the relative width (sigma/sup 2/)/sup 1/2//, the skewness ..gamma../sub 1/, and the kurtosis ..gamma../sub 2/ characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere (P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)) is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes.
- Research Organization:
- Department of Chemistry and Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556
- OSTI ID:
- 6766335
- Journal Information:
- J. Chem. Phys.; (United States), Vol. 81:7
- Country of Publication:
- United States
- Language:
- English
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