Diffraction by a plane sector

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Budaev Bair V. and Bogy David B. 2004Diffraction by a plane sectorProc. R. Soc. Lond. A.4603529–3546http://doi.org/10.1098/rspa.2004.1322SectionRestricted accessDiffraction by a plane sector Bair V. Budaev Bair V. Budaev Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author and David B. Bogy David B. Bogy Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author Bair V. Budaev Bair V. Budaev Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author and David B. Bogy David B. Bogy Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author Published:08 December 2004https://doi.org/10.1098/rspa.2004.1322AbstractThe problem of diffraction by a perfectly reflecting screen occupying an infinite sector of the equatorial plane is addressed by the random–walk method. The solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen. The diffracted field is explicitly represented as the mathematical expectation of a specified functional on trajectories of the random motion, the radial component of which runs in a complex space while the two–dimensional angular component remains real valued. The numerical results confirm the efficiency of the random–walk approach to the analysis of diffraction by wedge–shaped screens of arbitrary angles. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Castro L and Kapanadze D (2008) Exterior Wedge Diffraction Problems with Dirichlet, Neumann and Impedance Boundary Conditions, Acta Applicandae Mathematicae, 10.1007/s10440-008-9408-y, 110:1, (289-311), Online publication date: 1-Apr-2010. Castro L and Kapanadze D (2008) Wave diffraction by a 45 degree wedge sector with Dirichlet and Neumann boundary conditions, Mathematical and Computer Modelling, 10.1016/j.mcm.2007.09.004, 48:1-2, (114-121), Online publication date: 1-Jul-2008. Budaev B and Bogy D (2008) Diffraction by a Nonconvex Polygon, SIAM Journal on Applied Mathematics, 10.1137/070699548, 69:2, (398-418), Online publication date: 1-Jan-2008. Budaev B and Bogy D (2007) Diffraction by a wedge with a face of variable impedance, Radio Science, 10.1029/2006RS003597, 42:6, Online publication date: 1-Dec-2007. Budaev B and Bogy D (2007) Novel solutions of the Helmholtz equation and their application to diffraction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463:2080, (1005-1027), Online publication date: 8-Apr-2007. Budaev B and Bogy D (2006) Diffraction by a convex polygon with side-wise constant impedance, Wave Motion, 10.1016/j.wavemoti.2006.05.007, 43:8, (631-645), Online publication date: 1-Oct-2006. Budaev B and Bogy D (2006) Diffraction of a Plane Skew Electromagnetic Wave by a Wedge With General Anisotropic Impedance Boundary Conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2006.874317, 54:5, (1559-1567), Online publication date: 1-May-2006. Budaev B and Bogy D (2005) A probabilistic approach to wave propagation and scattering, Radio Science, 10.1029/2004RS003176, 40:6, (n/a-n/a), Online publication date: 1-Dec-2005. Budaev B and Bogy D Two-dimensional diffraction by a wedge with impedance boundary conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2005.848512, 53:6, (2073-2080) Budaev B and Bogy D Diffraction of a plane wave by a sector with Dirichlet or Neumann boundary conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2004.841303, 53:2, (711-718) Budaev B and Bogy D Probabilistic representation of waves scattered by inhomogeneities of the medium 2005 IEEE Antennas and Propagation Society International Symposium, 10.1109/APS.2005.1551671, 0-7803-8883-6, (751-753) Budaev B and Bogy D (2004) Wave scattering by surface-breaking cracks and cavities, Wave Motion, 10.1016/j.wavemoti.2004.02.003, 40:2, (163-172), Online publication date: 1-Aug-2004. This Issue08 December 2004Volume 460Issue 2052 Article InformationDOI:https://doi.org/10.1098/rspa.2004.1322Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/12/2004Published in print08/12/2004 License: Citations and impact Keywordsdiffractionwave propagationray methodBrownian motion