{"title":"许多小阻抗粒子的波散射及其应用","authors":"Alexander G. Ramm","doi":"10.1016/S0034-4877(22)00065-9","DOIUrl":null,"url":null,"abstract":"<div><p>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 <em>a</em> of small particles tends to zero while their number tends to infinity at a suitable rate. The basic physical assumption is <em>a << d << λ</em>, where <em>d</em> is the minimal distance between neighboring particles, <em>λ</em> is the wavelength, and the particles can be impedance balls <em>B</em>(<em>x<sub>m</sub>, a</em>) with centers <em>x<sub>m</sub></em> 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 <em>a</em> 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.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wave scattering by many small impedance particles and applications\",\"authors\":\"Alexander G. Ramm\",\"doi\":\"10.1016/S0034-4877(22)00065-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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 <em>a</em> of small particles tends to zero while their number tends to infinity at a suitable rate. The basic physical assumption is <em>a << d << λ</em>, where <em>d</em> is the minimal distance between neighboring particles, <em>λ</em> is the wavelength, and the particles can be impedance balls <em>B</em>(<em>x<sub>m</sub>, a</em>) with centers <em>x<sub>m</sub></em> 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 <em>a</em> 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.</p></div>\",\"PeriodicalId\":49630,\"journal\":{\"name\":\"Reports on Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0034487722000659\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487722000659","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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.
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.