I have been talking about Fractal structure and fractal frequancies but there was one concept i haven't talked about:
FRACTAL RESONANCE: i found this:
Richard Weaver, New Directions in Linear Acoustics and Vibration: Quantum Chaos, Random Matrix Theory and Complexity
FRACTAL RESONANCE: i found this:
Richard Weaver, New Directions in Linear Acoustics and Vibration: Quantum Chaos, Random Matrix Theory and Complexity
Linear acoustics was thought to be fully encapsulated in physics texts of the 1950s, but this view has been changed by developments in physics during the last four decades. There is a significant new amount of theory that can be used to address problemsi n linear acoustics and vibration, but only a small amount of reported work does so. This book is an attempt to bridge the gap between theoreticians and practitioners, as well as the gap between quantum and acoustic. Tutorial chapters provide introductions to each of the major aspects of the physical theory and are written using the appropriate terminology of the acoustical community. The book will act as a quick-start guide to the new methods while providing a wide-ranging introduction to the physical concepts
...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.
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.
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