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首页> 外文期刊>Journal of Statistical Physics >Exit Time Distribution in Spherically Symmetric Two-Dimensional Domains
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Exit Time Distribution in Spherically Symmetric Two-Dimensional Domains

机译：球对称二维域中的退出时间分布

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摘要

The distribution of exit times is computed for a Brownian particle in spherically symmetric two-dimensional domains (disks, angular sectors, annuli) and in rectangles that contain an exit on their boundary. The governing partial differential equation of Helmholtz type with mixed Dirichlet-Neumann boundary conditions is solved analytically. We propose both an exact solution relying on a matrix inversion, and an approximate explicit solution. The approximate solution is shown to be exact for an exit of vanishing size and to be accurate even for large exits. For angular sectors, we also derive exact explicit formulas for the moments of the exit time. For annuli and rectangles, the approximate expression of the mean exit time is shown to be very accurate even for large exits. The analysis is also extended to biased diffusion. Since the Helmholtz equation with mixed boundary conditions is encountered in microfluidics, heat propagation, quantum billiards, and acoutics, the developed method can find numerous applications beyond exit processes.
机译：计算布朗对称粒子在球对称二维域（圆盘，角扇区，环形区域）中以及边界上包含出口的矩形中的出口时间分布。通过解析求解了混合Dirichlet-Neumann边界条件的Helmholtz型控制偏微分方程。我们提出依赖矩阵求逆的精确解和近似显式解。事实证明，近似解对于尺寸消失的出口是准确的，甚至对于较大的出口也是精确的。对于角扇区，我们还导出了出口时刻的精确显式公式。对于环形空间和矩形区域，平均出口时间的近似表达式显示出即使对于较大出口也非常精确。该分析还扩展到偏向扩散。由于在微流体，热传播，量子台球和声波中会遇到具有混合边界条件的亥姆霍兹方程，因此开发的方法可以找到除出口过程之外的许多应用。

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