Diffuse elastic waves in a nearly axisymmetric body: Energy distribution, transport and dynamical localization

Richard L. Weaver, John Y. Yoritomo, J. Patrick Coleman
2017 The European Physical Journal Special Topics  
We report measurements and theory on the distribution and evolution of diffuse ultrasonic waves in elastic bodies with weakly broken axisymmetry. Aluminum cylinders with dimensions large compared to wavelength were excited by transient point sources at the center of one of the circular faces. The resulting power spectral density PSD was then examined as a function of time and frequency and position on that face. It was found that the PSD showed a marked concentration at the center at early
more » ... , a concentration that subsequently slowly diminished towards a state of uniformity across the face, over times long compared to ultrasonic transit time across the sample. The evolution is attributed to scattering by symmetry breaking heterogeneities. Relaxation did not proceed all the way to uniformity and equipartition, behavior shown to be consistent with Enhanced Backscatter and Dynamical Anderson Localization. Review/background There is a long literature on diffuse ultrasound in solids with potential applications in nondestructive evaluation [1-9] and seismology [10] [11] [12] [13] [14] [15] [16] . Diffuse field ultrasound is employed also for explorations of stochastic wave fields in general, including systems described by random matrix theory and systems that may be analogs for mesoscopic electronics and quantum chaos [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] . Weaver [31] provides an overview and tutorial. Diffuse field concepts have been applied to room acoustics and vibro-acoustics in structures [32] [33] [34] . Throughout this work attention has generally been confined to elastic or fluid structures with little or no geometric symmetry. Irregular shapes and/or the presence of random scatterers have been imagined as required for the diffuse field assumption in which we take the field subsequent to a transient excitation to have been scattered sufficiently that the resulting wave field is maximally garbled. It is preferred to study structures with no special symmetries, so that that the energy is well mixed across all modes and positions. Ideally one would wish for structures in which ray trajectories are chaotic [28] and ergodic. Should the sample have a good a
doi:10.1140/epjst/e2016-60186-7 fatcat:ianam55hw5br3npewlzycptoaq