The problem of survival of a Brownian particle diffusing on a disk with a reflective boundary that has two absorbing arcs is treated analytically. The framework of boundary homogenization is applied to calculate the effective trapping rate of the disk boundary, and this enables estimation of the mean first passage time. The method of conformal mapping is applied to transform the original system to a simpler geometrical configuration (a flat reflective boundary with a periodic configuration of identical absorbing strips) for which the analytical solution is known. The expression for the mean first passage time is simplified for some limiting cases (small arc or small gap). The derived analytical expressions compare favorably with the results of Brownian particle simulations and other analytical results from the literature.

中文翻译：

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粒子在圆盘上扩散的平均第一次通过时间，该圆盘在边界处有两个吸收阱。

分析地解决了布朗粒子在具有两个吸收弧的反射边界的磁盘上扩散的生存问题。边界均匀化的框架可用于计算磁盘边界的有效陷印率，从而可以估计平均第一次通过时间。共形映射方法用于将原始系统转换为已知解析解决方案的更简单的几何配置（具有相同吸收带的周期性配置的平坦反射边界）。平均首次通过时间的表达式在某些极限情况（小弧度或小间隙）下得到简化。派生的分析表达式与布朗粒子模拟的结果和文献中的其他分析结果相比具有优势。