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List of Contributors
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- By Harold P. Adams, Colum F. Amory, Anne Angelillo-Scherrer, Irena Anselm, Marcel Arnold, Robert W. Baloh, Ralf W. Baumgartner, José Biller, Valérie Biousse, Matthias Bischof, Julien Bogousslavsky, Natan M. Bornstein, Marie Germaine Bousser, Robin L. Brey, John C. M. Brust, Alan Bryer, Olivier Calvetti, Louis R. Caplan, José Castillo, Hugues Chabriat, Chin-Sang Chung, Charlotte Cordonnier, Steven C. Cramer, Luís Cunha, Rima M. Dafer, John F. Dashe, Cyrus K. Dastur, Antonio Dávalos, Larry E. Davis, Patricia Davis, Stephen M. Davis, Jan L. De Bleecker, Michael A. De Georgia, Amir R. Dehdashti, Oscar H. Del Brutto, Jacques L. De Reuck, Hans-Christoph Diener, Kathleen B. Digre, Vivian U. Fritz, Nancy Futrell, Bhuwan P. Garg, Philip B. Gorelick, Glenn D. Graham, Alexander Y. Gur, John J. Halperin, Michael Hennerici, Isabel Lestro Henriques, Roberto C. Heros, Daniel B. Hier, Lorenz Hirt, Joanna C. Jen, Taro Kaibara, Sumit Kapoor, Sarosh M. Katrak, Siddharth Kharkar, Walter J. Koroshetz, Monisha Kumar, Sandeep Kumar, Emre Kumral, Tobias Kurth, Rogelio Leira, Steven R. Levine, Didier Leys, Doris Lin, Jonathan Lipton, Alfredo M. Lopez-Yunez, Betsy B. Love, Ayrton Roberto Massaro, Heinrich P. Mattle, Manu Mehdiratta, John H. Menkes, Philippe Metellus, Reto Meuli, Patrik Michel, Panayiotis Mitsias, Jorge Moncayo-Gaete, Julien Morier, Krassen Nedeltchev, Bernhard Neundörfer, Olukemi A. Olugemo, Nikolaos I. H. Papamitsakis, Stephen D. Reck, Luca Regli, Marc D. Reichhart, Daniele Rigamonti, Michael J. Rivkin, E. Steve Roach, Jose F. Roldan, David Z. Rose, Daniel M. Rosenbaum, N. Paul Rosman, Elayna O. Rubens, Sean I. Savitz, Marc Schapira, Robert J. Schwartzman, Magdy Selim, Yukito Shinohara, Aneesh B. Singhal, Michael A. Sloan, Barney J. Stern, Mathias Sturzenegger, Oriana Thompson, A. Wesley Thevathasan, Jonathan D. Trobe, Michael Varner, Dana Védy, Jorge Vidaurre, Engin Y. Yilmaz, Khaled Zamel, Mathieu Zuber
- Edited by Louis R. Caplan, Julien Bogousslavsky
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- Book:
- Uncommon Causes of Stroke
- Published online:
- 06 January 2010
- Print publication:
- 09 October 2008, pp ix-xiv
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- Chapter
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Diffraction by slender bodies
- J. C. Engineer, J. R. King, R. H. Tew
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- Journal:
- European Journal of Applied Mathematics / Volume 9 / Issue 2 / April 1998
- Published online by Cambridge University Press:
- 01 April 1998, pp. 129-158
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- Article
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The scattering of high-frequency sound waves by two-dimensional curved boundaries has received much attention over the past few decades, with particular interest in the effects of tangential ray incidence. In the event that the radius of curvature is not small, an analysis near the point of tangency gives rise to the Fock–Leontovič equation for the local field amplitude which, in turn, matches the creeping field of Keller's geometrical theory of diffraction. If the radius of curvature is sufficiently small, however, then this analysis is not valid and it is necessary to solve the full Helmholtz equation in the presence of a parabolic boundary. Under these conditions, which are canonical for diffraction by a sufficiently slender body, results are presented for the case of a plane wave impinging upon an acoustically hard parabolic cylinder. This diffraction process engenders a creeping field at one tip of the slender body, which then propagates around the body to the other tip. Here its energy is partially reflected, partially transmitted and partially radiated out in a detached field. A full description of this is given, along with a discussion of the ‘blunt’ limit in which we show that not only do we get the traditional creeping field of Keller's geometrical theory of diffraction, but also an exponentially small backward-propagating creeping field not predicted by traditional ray methods.