BOUNDARY HOMOGENIZATION AND CAPTURE TIME DISTRIBUTIONS OF SEMIPERMEABLE MEMBRANES WITH PERIODIC PATTERNS OF REACTIVE SITES
BOUNDARY HOMOGENIZATION AND CAPTURE TIME DISTRIBUTIONS OF SEMIPERMEABLE MEMBRANES WITH PERIODIC PATTERNS OF REACTIVE SITES
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DOI：
10.1137/17m1162512
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发表时间：
2018-01-01
影响因子：
1.6
通讯作者：
Schmidt, Daniel D.
中科院分区：
文献类型：
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作者：
Bernoff, Andrew J.;Lindsay, Alan E.;Schmidt, Daniel D.
我们考虑粒子在半空间中随机游动的捕获动力学，该半空间由具有周期性吸收孔图案的平面所包围。特别是，我们对捕获时间的分布进行了数值测量和渐近表征。在数值上，我们开发了一种动力学蒙特卡罗（KMC）方法，该方法利用精确的解来创建一个有效的基于粒子的捕获时间模拟，该模拟精确地处理无限半空间，并且其运行时间与孔开始的距离无关。过去的研究人员提出了均匀化表面边界条件，用混合边界条件（Robin）代替反射（Neumann）和吸收（Dirichlet）边界条件。我们扩展了以前的工作，渐近地确定了稀分数极限下任意周期孔隙构型混合边界条件下的泄漏参数。在此渐近极限下，我们提出并求解了使吸收孔捕获率最大化的Bravais晶格的优化问题，发现六边形晶格是全局最大值。
We consider the capture dynamics of a particle undergoing a random walk in a half-space bounded by a plane with a periodic pattern of absorbing pores. In particular, we numerically measure and asymptotically characterize the distribution of capture times. Numerically we develop a kinetic Monte Carlo (KMC) method that exploits exact solutions to create an efficient particle-based simulation of the capture time that deals with the infinite half-space exactly and has a run time that is independent of how far from the pores one begins. Past researchers have proposed homogenizing the surface boundary conditions, replacing the reflecting (Neumann) and absorbing (Dirichlet) boundary conditions with a mixed (Robin) boundary condition. We extend previous work to asymptotically determine the leakage parameter for the mixed boundary condition for arbitrary periodic pore configurations in the dilute fraction limit. In this asymptotic limit, we pose and solve an optimization problem for the Bravais lattice which maximizes the capture rate of the absorbing pores, finding the hexagonal lattice to be the global maximum.