{"title":"绕弯:波导拐角和迷宫对长波的反射和传输","authors":"P. A. Martin","doi":"10.1098/rspa.2023.0635","DOIUrl":null,"url":null,"abstract":"Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission coefficients, correct to first order in the ratio of the waveguide width to the wavelength. Detailed results are given for sharp bends of arbitrary angle, including right-angled bends and hairpin bends. Applications to multiple scattering by labyrinthine structures are also made.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"14 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths\",\"authors\":\"P. A. Martin\",\"doi\":\"10.1098/rspa.2023.0635\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission coefficients, correct to first order in the ratio of the waveguide width to the wavelength. Detailed results are given for sharp bends of arbitrary angle, including right-angled bends and hairpin bends. Applications to multiple scattering by labyrinthine structures are also made.\",\"PeriodicalId\":20716,\"journal\":{\"name\":\"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2023-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.2023.0635\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1098/rspa.2023.0635","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths
Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission coefficients, correct to first order in the ratio of the waveguide width to the wavelength. Detailed results are given for sharp bends of arbitrary angle, including right-angled bends and hairpin bends. Applications to multiple scattering by labyrinthine structures are also made.
期刊介绍:
Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.