Dispersion of waves in two and three-dimensional periodic media

[1905.12529] Dispersion of waves in two and three-dimensional periodic media Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:1905.12529 (math) [Submitted on 29 May 2019 ( v1 ), last revised 3 Jul 2019 (this version, v2)] Title: Dispersion of waves in two and three-dimensional periodic media Authors: Yuri A. Godin , Boris Vainberg View a PDF of the paper titled Dispersion of waves in two and three-dimensional periodic media, by Yuri A. Godin and Boris Vainberg View PDF HTML (experimental) Abstract: We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the radius $a$ of inclusions is small. A new approach is suggested to derive the complete asymptotic expansions of the dispersion relations in two and three-dimensional cases as $a \to 0$ and evaluate explicitly several first terms. Our method is based on the reduction of the original singularly perturbed (by inclusions) problem to the regular one. The Neumann, Dirichlet and transmission boundary conditions are considered. The effective wave speed is obtained as a function of the wave frequency, the filling fraction of the inclusions, and the physical properties of the constituents of the mixture. Dependence of asymptotic formulas obtained in the paper on geometric and material parameters is illustrated by graphs. Comments: 22 pages, 6 figures Subjects: Analysis of PDEs (math.AP) ; Materials Science (cond-mat.mtrl-sci); Applied Physics (physics.app-ph) MSC classes: 35B27, 78A48, 78M35, 78M40 Cite as: arXiv:1905.12529 [math.AP] (or arXiv:1905.12529v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.1905.12529 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Waves in Random and Complex Media, 2020, 1-24 Related DOI : https://doi.org/10.1080/17455030.2020.1810822 Focus to learn more DOI(s) linking to related resources Submission history From: Yuri Godin A [ view email ] [v1] Wed, 29 May 2019 15:26:38 UTC (19 KB) [v2] Wed, 3 Jul 2019 16:16:23 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Dispersion of waves in two and three-dimensional periodic media, by Yuri A. Godin and Boris Vainberg View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2019-05 Change to browse by: cond-mat cond-mat.mtrl-sci math physics physics.app-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Dispersion of waves in two and three-dimensional periodic media#611196
• Instantaneous modes in dispersive laser cavities#625503
• Instantaneous modes in dispersive laser cavities#623230
• Guiding properties of a planar waveguide based on a three-periodic magnetophotonic crystal#1090507
• Waveguiding in systems of high contrast resonators: Theory and fast computations#799110