论文标题
在各向同性复合材料和相关问题的有效复杂介电常数上的紧密界限
Tight Bounds on the Effective Complex Permittivity of Isotropic Composites and Related Problems
论文作者
论文摘要
大约四十年前，伯格曼（Bergman）和米尔顿（Milton）独立地表明，具有给定体积分数的两相复合材料的各向同性有效电介电常数被限制在复杂平面的镜头形区域内，该区域受两个圆形弧线的界定。特殊显着性的含义是一组限制，以给定频率以各向同性复合材料的最大和最小吸收。在这里，在简要介绍了基础理论之后，我们表明与圆形弧相对应的界限至少通过引入某种类别的层次层压板几乎是最佳的。关于第二弧，我们表明可以使用变分方法得出更严格的结合。这种更紧密的结合是最佳的，因为它对应于双层涂层球的组合，可以通过更现实的微观结构轻松近似。我们简要讨论对相关问题的含义，包括对复杂极化性的界限。
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the complex plane that are bounded by two circular arcs. An implication of particular significance is a set of limits to the maximum and minimum absorption of an isotropic composite material at a given frequency. Here, after giving a short summary of the underlying theory, we show that the bound corresponding to one of the circular arcs is at least almost optimal by introducing a certain class of hierarchical laminates. In regard to the second arc, we show that a tighter bound can be derived using variational methods. This tighter bound is optimal as it corresponds to assemblages of doubly coated spheres, which can be easily approximated by more realistic microstructures. We briefly discuss the implications for related problems, including bounds on the complex polarizability.
