论文标题
增强薄层的均质化
Homogenization of Enhancing Thin Layers
论文作者
论文摘要
本文通过使用解决有效的细胞问题有效边界条件（EBC）的某些有效细胞问题的解决方案来得出有效扩散张量的明确公式。 H. Li和X. Wang最近提出了道路EBC的概念，在本文中，我们将封闭曲线上的有效条件扩展到模式的曲线，尤其是在随附的节点上。我们还证明，同质化过程随着道路EBC的推导而通勤。通过分析有效的扩散张量，我们获得了几个规则，可以在每个单元中使用给定的道路效率扩张/尺度和长度/比例最大化其痕迹，并定义平衡模式的概念。此外，随着道路有效的扩散率/量表为无穷大，我们对一般模式的有效扩散张量进行了估计。
This paper derives an explicit formula for the effective diffusion tensor by using the solutions to some effective cell problems after homogenizing Road effective boundary conditions (EBCs). The concept of Road EBCs was proposed recently by H. Li and X. Wang, and in this paper, we extend the effective conditions on closed curves to those on patterns, especially on the included nodes. We also prove that homogenization process commutes with the derivation of Road EBCs. By analyzing the effective diffusion tensor, we obtain several rules for maximizing its trace with given Road-effective-diffusivity/scale and length/scale in each cell and define a notion of balanced patterns. Moreover, we give an estimate of the trace of effective diffusion tensor of general patterns as Road-effective-diffusivity/scale goes to infinity.
