Exact algorithm for d-dimensional walks on finite and infinite lattices with traps. II. General formulation and application to diffusion-controlled reactions
A method for calculating exactly the expected walk length for random walks on d-dimensional lattices with traps, reported recently by the authors (Phys. Rev. Lett. 47, 1500 (1981)), is elaborated in some detail in order to exhibit the underlying structure of the theory and to demonstrate the generality of the approach. Formulated as a problem in matrix transformation theory, the properties of a certain linear operator A and its inverse A/sup -1/ are explored in d = 1,2,3. In d = 1, the analytic result = N(N+1)/6 derived by Montroll for trapping on a (periodic) chain with a single, deep trap is recovered. In the higher dimensions d = 2,3, extensive new data are reported on the results of exact calculations of for two types of reaction-diffusion processes. The first is that of a reactant migrating toward a target molecule in a volume of d dimensions, and reacting there irreversibly upon first encounter. Then, it is assumed that the N-1 sites surrounding the target molecule are not passive (nonabsorbing, neutral) but may react with the diffusing molecule to form an excited-state complex which may, with nonzero probability s, result in the irreversible removal of reactant from the system. In both models, the efficiency of reaction is studied as a function of the spatial extent of the reaction volume and of the boundary conditions imposed on the underlying lattice.
- Research Organization:
- Department of Chemistry and Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556
- OSTI ID:
- 6520242
- Journal Information:
- Phys. Rev. B: Condens. Matter; (United States), Vol. 26:8
- Country of Publication:
- United States
- Language:
- English
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