三维复合材料的磁电阻效应
Magneto-resistance in three-dimensional composites
摘要：
本文研究三维复合材料的磁阻效应，即低磁场扰动下电阻率的二阶项。推广[4]的二维周期框架，通过H收敛方法证明了有效磁阻引起的耗散能大于或等于复合材料各相磁阻引起的耗散能的平均值。这个不等式验证了复合材料的科勒定律，这是已知的均匀导体。等式的情况下，示出是非常敏感的磁场取向。我们用层状和柱状周期结构来说明结果。
英文摘要：
In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [4], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is shown to be very sensitive to the magnetic fi eld orientation. We illustrate the result with layered and columnar periodic structures.
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