ISSN:
1572-9613
Keywords:
Diffusion
;
order statistics
;
mean first passage times
;
mean trapping times
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider the problem of the first passage times for absorption (trapping) of the firstj (j = 1,2, ....) ofk, j 〈k, identical and independent diffusing particles for the asymptotic case k≫〉1. Our results are a special case of the theory of order statistics. We show that in one dimension the mean time to absorption at a boundary for the first ofk diffusing particles, μ1,k , goes as (lnk)−1 for the set of initial conditions in which none of thek particles is located at a boundary and goes ask −2 for the set of initial conditions in which some of thek particles may be located at the boundary. We demonstrate that in one dimension our asymptotic results (k21) are independent of the potential field in which the diffusion takes place for a wide class of potentials. We conjecture that our results are independent of dimension and produce some evidence supporting this conjecture. We conclude with a discussion of the possible import of these results on diffusion-controlled rate processes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011582
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