齐次化系数在Bernoulli扰动和Clausius-Mossotti公式下的解析性
Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas
摘要：
本文研究了随机平稳遍历介质的均匀化系数在Bernoulli扰动下的行为。引入一个新的家庭的能量估计相结合的概率和物理空间，我们证明了扰动均匀化系数的伯努利参数的解析性。我们的方法下的平稳性和遍历性的最小假设，无论是在标量和矢量的情况下，并给出了每个衍生物的分析公式，基本上符合物理学家使用的所谓的集群扩展。特别是，首项产生著名的（电和弹性）各向同性参考介质中的各向同性球形随机夹杂物的Clausius-Mossotti公式。这项工作构成了第一个普遍的证明，这些公式的情况下，随机夹杂物。
英文摘要：
This paper is concerned with the behavior of the homogenized coefficients associated with some random stationary ergodic medium under a Bernoulli perturbation. Introducing a new family of energy estimates that combine probability and physical spaces, we prove the analyticity of the perturbed homogenized coefficients with respect to the Bernoulli parameter. Our approach holds under the minimal assumptions of stationarity and ergodicity, both in the scalar and vector cases, and gives analytical formulas for each derivative that essentially coincide with the so-called cluster expansion used by physicists. In particular, the first term yields the celebrated (electric and elastic) Clausius-Mossotti formulas for isotropic spherical random inclusions in an isotropic reference medium. This work constitutes the first general proof of these formulas in the case of random inclusions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
