磁场扰动下高对比度两相电导率的均匀化。二维与三维的比较
Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three
摘要：
均匀化的法律序列的高对比度的两相非对称电导率由一个参数$h$扰动推导出在二维和三维。参数$h$表征了存在磁场时导体理想化模型的电导率的反对称部分。在二维的扩展的Dykhne变换的非周期性的高电导率允许证明，均匀化的电导率取决于$h$通过一些均匀化的矩阵值函数在磁场的情况下获得。由于另一种方法，这一结果在周期性框架中得到了改善，并通过十字形薄结构来说明。使用其他工具，三维的纤维增强介质提供了完全不同的均匀导电性。
英文摘要：
Homogenized laws for sequences of high-contrast two-phase non-symmetric conductivities perturbed by a parameter $h$ are derived in two and three dimensions. The parameter $h$ characterizes the antisymmetric part of the conductivity for an idealized model of a conductor in the presence of a magnetic field. In dimension two an extension of the Dykhne transformation to non-periodic high conductivities permits to prove that the homogenized conductivity depends on $h$ through some homogenized matrix-valued function obtained in the absence of a magnetic field. This result is improved in the periodic framework thanks to an alternative approach, and illustrated by a cross-like thin structure. Using other tools, a fiber-reinforced medium in dimension three provides a quite different homogenized conductivity.
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