ar X iv : c on d - m at / 9 50 50 62 v 1 1 5 M ay 1 99 5 Life and Death at the Edge of a Windy Cliff

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 v(x, y) = v sign(y) ˆ x, i. e., 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| < w with particle absorption at x = 0. The behavior in the strip geometry can be described in terms of Taylor diffusion, an approach which accounts for the crossover to the t −1/4 decay when the width of the strip diverges. Supporting numerical simulations of our analytical results are presented.