许多小阻抗粒子的波散射及其应用

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Alexander G. Ramm
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引用次数: 0

摘要

导出了均匀介质中小阻抗粒子对多体波散射问题的求解公式。考虑了小粒子的大小a以适当的速率趋近于零而粒子数趋近于无穷大的极限情况。基本的物理假设是<<d & lt; & lt;λ,其中d为相邻粒子之间的最小距离,λ为波长,粒子可以是位于网格上的以xm为中心的阻抗球B(xm, a)。导出了介质中极限有效场(自洽场)的方程。证明了通过在自由空间中嵌入许多半径为a的具有规定边界阻抗的小球,可以得到具有期望折射系数的材料。小球可以以网格上的点为中心。提出了一种制造具有期望折射系数的材料的配方。实验证明,可以制造出具有理想辐射模式的材料,例如波聚焦材料。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Wave scattering by many small impedance particles and applications

Formulas are derived for solutions of many-body wave scattering problem by small impedance particles embedded in a homogeneous medium. The limiting case is considered, when the size a of small particles tends to zero while their number tends to infinity at a suitable rate. The basic physical assumption is a << d << λ, where d is the minimal distance between neighboring particles, λ is the wavelength, and the particles can be impedance balls B(xm, a) with centers xm located on a grid. Equations for the limiting effective (self-consistent) field in the medium are derived. It is proved that one can create material with a desired refraction coefficient by embedding in a free space many small balls of radius a with prescribed boundary impedances. The small balls can be centered at the points located on a grid. A recipe for creating materials with a desired refraction coefficient is formulated. It is proved that materials with a desired radiation pattern, for example, wave-focusing materials, can be created.

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来源期刊
Reports on Mathematical Physics
Reports on Mathematical Physics 物理-物理:数学物理
CiteScore
1.80
自引率
0.00%
发文量
40
审稿时长
6 months
期刊介绍: Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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