Some exact results for the trapping of subdiffusive particles in one dimension

Abstract

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is made

15 pages, 2 figures

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• Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents
• The target problem with evanescent subdiffusive traps
• First-encounter time of two diffusing particles in confinement
• Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains
• Number of distinct sites visited by a subdiffusive random walker
• Simulations for trapping reactions with subdiffusive traps and subdiffusive particles
• Random walk approach to the analytic solution of random systems with multiplicative noise - the Anderson localization problem
• Spatial fluctuations of a surviving particle in the trapping reaction
• Effective numerical treatment of sub-diffusion equation with non-smooth solution