Title:

S-matrices, Localization and Mesoscopics in Structures and Rooms

Speaker:

Dr. Richard Weaver

Affiliation:

University of Illinois

When:

Thursday, September 24, 2009 at 11:00:00 AM   Add to Calendar

Where:

Love Building, Room 210

Host:

Karim Sabra
karim.sabra@me.gatech.edu
404-385-6193

Abstract

Diffuse field methods such as reverberation room acoustics and statistical energy analysis purport to predict average acoustic energy flows in complex structures. They are predicated on (incorrect) assumptions of incoherence. The consequent failures of otherwise successful theories are occasionally striking. This talk reviews several mesoscopic consequences of residual coherence that are not predicted by classical diffuse wave theory. These include weak Anderson localization, modal echoes, Anderson localization, Thouless localization, power law dissipation, natural-frequency correlations, and Greens function retrieval. While it is sometimes possible to augment diffuse field theories with quantitatively valid afterthoughts, it would be preferable to replace these theories with more a fundamental approach that has general applicability. A new theory is proposed which may do this. It is based on an initial modeling of system S-matrices as incoherent - as conventional diffuse field theories would have it - but then corrected to assure exact energy conservation. It is found that the coherent responses (Greens functions) that are constructed from S then exhibit a legion of mesoscopic phenomena including power law dissipation, natural frequency correlations, weak localization and modal echoes. Anderson and Thouless localization emerge naturally from competition between rates of transport and rates of eigen-mode resolution. Examples are presented corresponding to coupled rooms and to diffusion in a multiply scattering medium. Future generalizations are discussed and the mathematical challenges are outlined.

Biography

Professor Richard Weaver received an A.B. degree in physics from Washington University in St Louis in 1971 and a Ph.D in astrophysics from Cornell University in 1977. He came to Illinois University in 1981 after a research associateship in theoretical elastic wave propagation and ultrasonics at Cornell. He was elected a fellow of the Acoustical Society of America in 1996 and received the Hetényi Award from the Society for Experimental Mechanics in 2004. He is associate editor of the Journal of the Acoustical Society of America. Formerly a professor in the Department of Theoretical and Applied Mechanics at Illinois, he joined the Department of Physics in 2006.