三维细长区域中小吸收靶的平均首次通过时间
Mean first-passage time to a small absorbing target in three-dimensional elongated domains
摘要：
本文推导了一个计算任意形状吸收小目标在慢变轴对称截面细长区域内的平均首次穿越时间（MFPT）的近似公式。为此目的，原来的泊松方程在三维简化为一个有效的一维问题的区间上的半渗透半吸收膜。近似公式正确地捕捉到的MFPT上的距离的目标，域的径向轮廓，和目标的大小和形状的依赖性。通过蒙特卡罗模拟验证了这种近似。
英文摘要：
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in three dimensions is reduced an effective one-dimensional problem on an interval with a semi-permeable semi-absorbing membrane. The approximate formula captures correctly the dependence of the MFPT on the distance to the target, the radial profile of the domain, and the size and the shape of the target. This approximation is validated by Monte Carlo simulations.
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