Life and Death in a Cage and at the Edge of a Cliff

Details Life and Death in a Cage and at the Edge of a Cliff Life and Death in a Cage and at the Edge of a Cliff

1995-02-10

arxiv.org/abs/cond-mat/9502041v1

Am. J. Phys. 64, 546 (1996)

Physics

Condensed Matter

11 pages, plain TeX, 1 figure (not included), submitted to J. Stat. Phys

Scientific paper

10.1119/1.18152

The survival probabilities of a ``prisoner'' diffusing in an expanding cage and a ``daredevil'' diffusing at the edge of a receding cliff are investigated. When the diffuser reaches the boundary, he dies. For ``marginal'' boundary motion, i.e., the cage length grows as $\sqrt{At}$ or the cliff location recedes as $x_0(t)=-\sqrt{At}$ and the daredevil diffuses within the domain $x>x_0$, the survival probability of the diffuser exhibits non-universal power-law behavior, $S(t)\sim t^{-\b}$, which depends on the relative rates of boundary and diffuser motion. Heuristic approaches are applied for the cases of ``slow'' and ``fast'' boundary motion which yield approximate expressions for $\b$. An asymptotically exact analysis of these two problems is also performed and the approximate expressions for $\b$ coincide with the exact results for nearly entire range of possible boundary motions.

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