Survival probability in a random velocity field
Survival probability in a random velocity field
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随机速度场中的生存概率
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
S. Redner
中科院分区：
文献类型：
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作者：
S. Redner
生存概率S(t)的时间依赖性是由二维扩散粒子确定的，这些粒子也由随机的单向零平均速度场v_x(y)驱动。对于具有无界y和x>0，粒子吸收在x=0处的半无限系统，给出了S(t)~t^{-1/4}的定性论证。这一预测得到了数值模拟的支持。本文还给出了一个启发式论证，表明幸存粒子的纵向概率分布具有标度形式为P(x,t)~ t^{-1}u^{1/3}g(u)。这里缩放变量u与x/t^{3/4}成正比，因此P（x,t）的整体时间依赖性与t^{-5/4}成正比，并且缩放函数g(u)的极限依赖性为g(u)接近常数u- >和g(u)~exp（-u^{4/3}）为u- >∞。这一论点还提出了一个有效的连续统运动方程，它再现了正确的渐近纵向概率分布。
The time dependence of the survival probability, S(t), is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field, v_x(y). For a semi-infinite system with unbounded y and x>0, and with particle absorption at x=0, a qualitative argument is presented which indicates that S(t)~t^{-1/4}. This prediction is supported by numerical simulations. A heuristic argument is also given which suggests that the longitudinal probability distribution of the surviving particles has the scaling form P(x,t)~ t^{-1}u^{1/3}g(u). Here the scaling variable u is proportional to x/t^{3/4}, so that the overall time dependence of P(x,t) is proportional to t^{-5/4}, and the scaling function g(u) has the limiting dependences g(u) approaching a constant as u--->0 and g(u)~exp(-u^{4/3}) as u--->infinity. This argument also suggests an effective continuum equation of motion for the infinite system which reproduces the correct asymptotic longitudinal probability distribution.