Life and death in an expanding cage and at the edge of a receding cliff
作者:
P. L. Krapivsky,
S. Redner,
期刊:
American Journal of Physics
(AIP Available online 1996)
卷期:
Volume 64,
issue 5
页码: 546-552
ISSN:0002-9505
年代: 1996
DOI:10.1119/1.18152
出版商: American Association of Physics Teachers
关键词: DIFFUSION;SURVIVAL TIME;BOUNDARY CONDITIONS;PROBABILITY;DISTRIBUTION FUNCTIONS;BOUNDARY−VALUE PROBLEMS;05.40;05.60
数据来源: AIP
摘要:
The survival probabilities of a particle diffusing within an expanding ‘‘cage’’ and near the edge of a receding ‘‘cliff,’’ with death occurring when the diffuser reaches a boundary of the system, are investigated. Especially interesting behavior arises when the position of the boundary recedes from the diffuser as √At. In this case, the recession matches the rms displacement √Dtwith which diffusion tends to bring the diffuser to its demise. For both the cage and cliff problems, the survival probabilityS(t) exhibits a nonuniversal power‐law decay in time,S(t)∼t−β, in which the value of β is dependent on the detailed properties of the boundary motion. Heuristic approaches are applied for the cases of ‘‘slow’’ (A/D≪1) and ‘‘fast’’ (A/D≫1) boundary motion which yield approximate expressions for β. An asymptotic analysis of the survival probability for the cage and cliff problems is also performed. The approximate expressions for β are in good agreement with the exact results for nearly the entire range of possible boundary motions.
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