跨越窄窗的流入与流出扩散之间纳米区域内浓度差的建模与渐近分析
Modeling and asymptotic analysis of the concentration difference in a nanoregion between an influx and outflux diffusion across narrow windows
AI总结：
本文研究了有界区域表面窄窗间 Brownian 粒子扩散的浓度分布，利用 Green 函数和二阶渐近分析求解 Laplace 方程，并通过数值模拟验证了展开的有效性，引入长度尺度估计扩散电流深度，应用于生物物理。
摘要：
当一股 Brownian 粒子流被注入到有界区域表面上的一个窄窗时，这些粒子会发生扩散，并最终可能通过一个窄窗簇逃逸。在稳态下，我们渐近计算了不同窗口之间的浓度分布。该解是通过使用 Green 函数技术和二阶渐近分析求解 Laplace 方程获得的，并且取决于流入幅度、扩散特性以及所有窗口的几何组织（例如它们的距离和平均曲率）。我们利用混合边值问题的数值模拟探讨了当前渐近展开的有效性范围。最后，我们引入了一个长度尺度，以估计局部扩散电流能在区域内部扩散多深。我们讨论了在生物物理学中的一些应用。
英文摘要：
When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady-state, we compute asymptotically the distribution of concentration between the different windows. The solution is obtained by solving Laplace's equation using Green's function techniques and second order asymptotic analysis, and depends on the influx amplitude, the diffusion properties as well as the geometrical organization of all the windows, such as their distances and the mean curvature. We explore the range of validity of the present asymptotic expansions using numerical simulations of the mixed boundary value problem. Finally, we introduce a length scale to estimate how deep inside a domain a local diffusion current can spread. We discuss some applications in biophysics.
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