| EPSRC Reference: |
GR/R03396/01 |
| Title: |
Application of Quantum Chaos Methods To Eigenfrequency Spectra of Vibrating Plates |
| Principal Investigator: |
Tanner, Professor G |
| Other Investigators: |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
University of Nottingham |
| Scheme: |
Fast Stream |
| Starts: |
01 January 2001 |
Ends: |
31 August 2002 |
Value (£): |
62,361
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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An analysis of linear wave equations in terms of semiclassical methods or large wavelength asymptotics is an important tool to study wave problems in terms of their underlying classical (or ray) dynamics. Research along this line became very popular especially in quantum theory over the last 15 years when it became apparent that the type of classical mechanics (i.e. chaos or regular dynamics) has an important influence on quantum wave phenomenon. A variety of increasingly sophisticated methods have been developed to get information about eigenvalues, wavefunctions or other quantum properties from the underlying classical mechanics. In addition important conjectures about the statistical properties of quantum spectra were formulated stating that the energy levels of classically chaotic systems are correlated in the same way as the eigenvalues of random matrices.None of these findings are restricted to Schroedinger's equation and can, with modifications, be applied to other linear wave equations. Wave equations in electromagnetism or elastodynamics are, however, vector wave equations. This fact causes a significant changes in our perception of a classical ray dynamics corresponding to a multi-mode wave equations. We will apply semiclassical methods to problems of in-plane modes in plates where mode conversion between sheer and pressuremodes occurs at the boundaries. The classical ray-dynamics for plates will be studied in detail ( using modern chaos theory ) and estimates for eigenfrequencies using semiclassical techniques will be developed. An analysis of the statistical properties of plate spectra will be attempted with the help of classical and semiclassical sum rules.
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.nottingham.ac.uk |