论文标题
在三维伸长域中，平均第一次 - 吸收目标
Mean first-passage time to a small absorbing target in three-dimensional elongated domains
论文作者
论文摘要
我们将平均第一学期时间（MFPT）的近似公式推导到一个在缓慢变化的轴对称轮廓的延长域内的小吸收靶标。为此，在三个维度上的原始泊松方程在具有半渗透半渗透膜的间隔内降低了有效的一维问题。近似公式正确捕获了MFPT对目标距离的依赖性，域的径向轮廓以及目标的大小和形状。该近似是通过蒙特卡洛模拟验证的。
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.
