具有径向分段常数扩散系数的圆形区域中的窄逃逸问题
The narrow escape problem in a circular domain with radial piecewise constant diffusivity
摘要：
活细胞中粒子的随机运动通常在空间上是不均匀的，由于沿着肌动蛋白丝的主动运输，在靠近细胞边界的区域中具有更高的有效扩散率。作为第一步，了解的后果存在的两个隔间具有不同的扩散常数的随机搜索问题，我们在这里考虑一个布朗粒子在一个圆形的域中具有不同的扩散常数在内部和外部壳。我们专注于窄逃逸问题，并计算布朗粒子的平均首次通过时间（MFPT）开始在一些预定义的位置，找到一个小区域的外反射边界。对于环的几何形状，我们发现，MFPT可以最小化的外壳的宽度的特定值。相反，对于两壳几何形状，我们表明，MFPT单调依赖于所有的模型参数，特别是对外壳的宽度。此外，我们发现，起始点之间的距离和最大化的MFPT的窄逃逸区不连续地依赖于内外扩散率之间的比率。
英文摘要：
The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the consequence of the existence of two compartments with different diffusion constant for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusion constants in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary. For the annulus geometry we find that the MFPT can be minimized for a specific value of the width of the outer shell. In contrast for the two-shell geometry we show that the MFPT depends monotonously on all model parameters, in particular on the outer shell width. Moreover we find that the distance between the starting point and the narrow escape region which maximizes the MFPT depends discontinuously on the ratio between inner and outer diffusivity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
