方形导电晶格的有效行为边界

Andrea Braides, G. Francfort
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引用次数: 29

摘要

考虑一组具有两种可能电阻率的电阻器。本文研究了当两种电阻器以固定比例共存时,这种电阻器的正方形二维晶格的整体或宏观行为。宏观行为是在连续体水平上的各向异性导体的行为,本文的目标是描述所有可能的这种导体的集合。因此,这是一个边界问题,跟随在连续体情况下关于该主题的大量文献的脚步。本文的独创性在于,研究的重点是均匀化和从离散网络到连续体的通道之间的相互作用。提出了一组边界,并证明了当每个电阻在离散晶格上的比例为1 / 2时,其最优性。我们推测推导出的界对所有比例都是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bounds on the effective behaviour of a square conducting lattice
A collection of resistors with two possible resistivities is considered. This paper investigates the overall or macroscopic behaviour of a square two–dimensional lattice of such resistors when both types coexist in fixed proportions in the lattice. The macroscopic behaviour is that of an anisotropic conductor at the continuum level and the goal of the paper is to describe the set of all possible such conductors. This is thus a problem of bounds, following in the footsteps of an abundant literature on the topic in the continuum case. The originality of the paper is that the investigation focuses on the interplay between homogenization and the passage from a discrete network to a continuum. A set of bounds is proposed and its optimality is shown when the proportion of each resistor on the discrete lattice is½. We conjecture that the derived bounds are optimal for all proportions.
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期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
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