Diffusive escape in a nonlinear shear flow: Life and death at the edge of a windy cliff
Diffusive escape in a nonlinear shear flow: Life and death at the edge of a windy cliff
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非线性剪切流中的扩散逃逸：多风悬崖边缘的生与死
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
P. Krapivsky
中科院分区：
文献类型：
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作者：
S. Redner;P. Krapivsky
本文研究了在x =0的“风崖”附近x>0的二维区域中扩散的粒子的生存概率。粒子在到达悬崖边缘时死亡。除了扩散，粒子还受到速度为v（x，y）=v sign（y）x的稳定“风切变”的影响，即，没有偏向或远离悬崖的平均偏差。对于这个半无限系统，粒子的存活概率随时间衰减ast-1/4，而在没有风的情况下，粒子的存活概率随时间衰减t-1/2。标度描述的发展，以阐明这种行为，以及生存概率内的半无限条的有限宽度|y| <w，在x =0时具有粒子吸收。带状几何中的行为可以用泰勒扩散来描述，这是一种解释当带状宽度发散时t−1/4衰减交叉的方法。支持我们的分析结果的数值模拟。
The survival probability of a particle diffusing in the two-dimensional domainx>0 near a “windy cliff” atx=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 velocityv(x, y)=v sign(y)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 ast−1/4, compared tot−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 atx=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.