Density of nearest-neighbor distances in diffusion-controlled reactions at a single trap.
Density of nearest-neighbor distances in diffusion-controlled reactions at a single trap.
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单个陷阱的扩散控制反应中最近邻距离的密度。
DOI：
10.1103/physreva.39.466
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
Havlin
中科院分区：
文献类型：
--
作者：
Weiss;Kopelman;Havlin
导出了一维和三维布朗粒子到孤立陷阱的近邻距离的概率密度函数。一维最近邻距离的渐近(时间)密度是一个含时的斜高斯函数，其平均值以t1~4渐近增加。该函数的大距离形式是一个简单指数。在三维空间中，在存在吸收球的情况下，类似的结果在很远的距离上与赫兹密度非常相似。渐近反应速率在三维上表现为c(密度)，在一维上表现为ct−1 2。实验结果与激子融合和反应动力学有关。
We derive the probability density function for the nearest-neighbor distance of the closest Brownian particle to an isolated trap in one and three dimensions. The asymptotic (in time) density of the nearest-neighbor distance in one dimension is a time-dependent skewed Gaussian function and the mean value of this distance increases asymptotically as t 1 4. The large-distance form of this function is a simple exponential. In three dimensions the analogous result in the presence of an absorbing sphere is shown to resemble the Hertz density closely at large distances. The asymptotic reaction rate goes as c (density) in three dimensions but as c t− 1 2 in one dimension. The results are related to exciton fusion and reaction kinetics.