Characteristics of the probability function for three random-walk models of reaction--diffusion processes

Journal Article · Mon Oct 01 04:00:00 EDT 1984 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.448031· OSTI ID:6766335

Musho, M K; Kozak, J J

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), Journal Name: J. Chem. Phys.; (United States) Vol. 81:7; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
CHEMICAL REACTIONS
DIFFUSION
DISTRIBUTION FUNCTIONS
FUNCTIONS
MARKOV PROCESS
MATHEMATICAL MODELS
PROBABILITY
STOCHASTIC PROCESSES