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

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 times, 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.