Life and Death at the Edge of a Windy Cliff

Details Life and Death at the Edge of a Windy Cliff Life and Death at the Edge of a Windy Cliff

1995-05-15

arxiv.org/abs/cond-mat/9505062v1

J. Stat. Phys. 82, 999 (1996).

Physics

Condensed Matter

13 pages, plain TeX, 5 figures available upon request to SR (submitted to J. Stat. Phys.)

Scientific paper

The survival probability of a particle diffusing in the two dimensional domain $x>0$ near a ``windy cliff'' at $x=0$ is investigated. The particle dies upon reaching the edge of the cliff. In addition to diffusion, the particle is influenced by a steady ``wind shear'' with velocity $\vec v(x,y)=v\,{\rm sign}(y)\,\hat x$, \ie, no average bias either toward or away from the cliff. For this semi-infinite system, the particle survival probability decays with time as $t^{-1/4}$, compared to $t^{-1/2}$ in the absence of wind. Scaling descriptions are developed to elucidate this behavior, as well as the survival probability within a semi-infinite strip of finite width $|y|

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