论文标题
在细长的平面域中的小吸收靶标的平均第一次填充时间
Mean first-passage time to a small absorbing target in an elongated planar domain
论文作者
论文摘要
我们将平均第一学期时间（MFPT）的近似但完全显式公式得出，以在平面中的一般细长域中的任意形状吸收靶标。我们的近似值结合了共形映射，边界均匀化和Fick-Jacobs方程，以在扩散率和几何参数方面表达MFPT。当起点不太接近目标时，与原始问题的数值解决方案进行系统的比较验证了其准确性。这是用于快速估算MFPT化学物理和生物学应用的实用工具。
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary homogenisation, and Fick-Jacobs equation to express the MFPT in terms of diffusivity and geometric parameters. A systematic comparison with a numerical solution of the original problem validates its accuracy when the starting point is not too close to the target. This is a practical tool for a rapid estimation of the MFPT for various applications in chemical physics and biology.
