波被小物体散射并产生具有所需折射系数的材料
Wave scattering by small bodies and creating materials with a desired refraction coefficient
摘要：
在多个小散射体的情况下，给出了多体波散射问题的渐近解。小散射体可以是其物理性质由边界阻抗描述的粒子，或者它们可以是其物理性质由其折射系数描述的小不均匀体。导出了极限介质中的有效场方程。该极限被认为是颗粒或不均匀性的尺寸$a$趋于零，而它们的数量$M(a)$趋于无穷大。这些结果适用于创建具有所需折射系数的材料的问题。例如，折射系数可以具有波聚焦特性，或者其可以具有负折射，即，群速度可以与相速度相反。本文是作者在MR 2442305（2009 g：78016）、MR 2354140（2008 g：82123）、MR 2317263（2008 a：35040）、MR 2362884（2008 j：78010）中提出的结果的综述，并包含新结果。
英文摘要：
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small inhomogeneities, whose physical properties are described by their refraction coefficients. Equations for the effective field in the limiting medium are derived. The limit is considered as the size $a$ of the particles or inhomogeneities tends to zero while their number $M(a)$ tends to infinity. These results are applied to the problem of creating materials with a desired refraction coefficient. For example, the refraction coefficient may have wave-focusing property, or it may have negative refraction, i.e., the group velocity may be directed opposite to the phase velocity. This paper is a review of the author's results presented in MR2442305 (2009g:78016), MR2354140 (2008g:82123), MR2317263 (2008a:35040), MR2362884 (2008j:78010), and contains new results.
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