Random walk with persistence and external bias
Random walk with persistence and external bias
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DOI：
10.1007/bf02476407
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发表时间：
1953-01-01
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影响因子：
--
通讯作者：
PATLAK, CLIFFORD S.
中科院分区：
文献类型：
--
作者：
PATLAK, CLIFFORD S.
导出了具有方向持久性和外偏置的随机游动问题的偏微分方程。方向的持续性或内部偏置意味着粒子在给定方向上行进的概率不需要对所有方向都相同，而是仅取决于粒子先前的运动方向。外部偏压由介质的各向异性或粒子上的外力引起。这个问题是通过考虑一个粒子的净位移由两个因素引起的，即粒子在转向后沿任何方向移动的概率和粒子沿给定方向移动的距离都不需要对所有方向都相同。本文首先假定粒子有一个分布，得到一个修正的Fokker-Planck方程。旅行时间和速度的平均值。各圈之间的行进时间不必为零。最后的方程，将假设的持久性的方向和外部偏置，然后导出。然后应用扩散的研究和长链聚合物。|| 摘要认证：Auth. Summ
The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias is meant the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from 2 factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distr. of travel times and speeds and that the avg. time of travel between turns need not be zero. The final equation incorporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made. || ABSTRACT AUTHORS: Auth. summ