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Contributors
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- By Victoria M. Allen, Frederic Amant, Sarah Armstrong, Thomas F. Baskett, Michael A. Belfort, Meredith Birsner, Renee D. Boss, Leanne Bricker, Josaphat K. Byamugisha, Giorgio Capogna, Michael P. Casaer, Frank A. Chervenak, Vicki Clark, Filip Claus, Malachy O. Columb, Charles Cox, Jean T. Cox, Vegard Dahl, John Davison, Jan Deprest, Clifford S. Deutschman, Roland Devlieger, Karim Djekidel, Steven Dymarkowski, Roshan Fernando, Clare Fitzpatrick, Sreedhar Gaddipati, Thierry Girard, Emily Gordon, Ian A. Greer, David Grooms, Sina Haeri, Katy Harrison, Edward J. Hayes, Michelle Hladunewich, Andra H. James, Tracey Johnston, Bellal Joseph, Erin Keely, Ruth Landau, Stephen E. Lapinsky, Susanna I. Lee, Larry Leeman, Hennie Lombaard, Stephen Lu, Alison MacArthur, Laura A. Magee, Paul E. Marik, Laurence B. McCullough, Alexandre Mignon, Carlo Missant, Jack Moodley, Lisa E. Moore, Kate Morse, Warwick D. Ngan Kee, Catherine Nelson-Piercy, Clemens M. Ortner, Geraldine O’Sullivan, Luis D. Pacheco, Fathima Paruk, Melina Pectasides, Nigel Pereira, Patricia Peticca, Sharon T. Phelan, Felicity Plaat, Lauren A. Plante, Michael P. Plevyak, Dianne Plews, Wendy Pollock, Laura C. Price, Peter Rhee, Leiv Arne Rosseland, Kathryn M. Rowan, Helen Ryan, Helen Scholefield, Neil S. Seligman, Nadir Sharawi, Alex Sia, Bob Silver, Mieke Soens, Ulrich J. Spreng, Silvia Stirparo, Nova Szoka, Andrew Tang, Kha M. Tran, Els Troost, Lawrence C. Tsen, Derek Tuffnell, Kristel Van Calsteren, Marc Van de Velde, Marcel Vercauteren, Chris Verslype, Peter von Dadelszen, Carl Waldman, Michelle Walters, Linda Watkins, Paul Westhead, Cynthia A. Wong, Gerda G. Zeeman, Joost J. Zwart
- Edited by Marc van de Velde, Helen Scholefield, Lauren A. Plante
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- Book:
- Maternal Critical Care
- Published online:
- 05 July 2013
- Print publication:
- 04 July 2013, pp ix-xiv
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6 - Chaotic Wave Scattering
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- By Jonathan P. Keating, School of Mathematics, University of Bristol, Bristol, UK, Marcel Novaes, School of Mathematics, University of Bristol, Bristol, UK
- Edited by Matthew Wright, University of Southampton, Richard Weaver, University of Illinois, Urbana-Champaign
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- Book:
- New Directions in Linear Acoustics and Vibration
- Published online:
- 05 October 2010
- Print publication:
- 26 July 2010, pp 96-109
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Summary
We give an overview of wave scattering in complex geometries, where the corresponding rays are typically chaotic. In the high-frequency regime, a number of universal (geometry-independent) properties that are described by random matrix theory emerge. Asymptotic methods based on the underlaying rays explain this universality and are able to go beyond it to account for geometry-specific effects. We discuss in this context statistics of the scattering matrix, scattering states, the fractal Weyl law for resonances, and fractal resonance wavefunctions.
Introduction
Our purpose here is to give an introductory overview of wave scattering in complex geometries, where the corresponding rays are typically chaotic. For simplicity, we focus our discussion on domains with lossless walls, inside which the wave speed is constant. The rays then are straight, with specular reflections at the boundaries. This situation is often encountered in experiments (Stöckmann 1999, Kuhl et al. 2005, Tanner & Søndergaard 2007) and in acoustic applications. However, many of the features we shall identify occur much more generally. Indeed, most recent developments in the subject have taken place in the context of quantum wave scattering, where the underlying rays are the classical trajectories of Newtonian mechanics. Much of this review will be devoted to translating quantum results into the language of classical wave scattering.
One of the main observations we wish to make is that many of the essential mathematical features of wave scattering in complex geometries can be found in certain very simple discrete models, which we here call wave maps.