Ultrasonic wave propagation through a two-dimensional nonreciprocal phononic crystal with asymmetric aluminum rods in viscous water is studied for its application in Anderson localization and trapping of acoustic energy. A one-dimensional disorder in the otherwise 2D periodic crystal is introduced by disorienting the asymmetric rods along the rows and by keeping them equally oriented along the columns. An exponential decay of sound waves travelling along the direction of disorder is observed demonstrating Anderson localization whereas sound propagates as extended wave along the ordered direction. Localization length for the case of strong disorder with high randomness in the orientation of rods and weak disorder with weak fluctuations in the orientation of rods is evaluated. The degree of randomness in the orientation of the rods controls the localization length of the wave. Thouless's theoretical prediction for the scaling of Lyapunov exponent with disorder is experimentally observed for weak disorder at frequency in the transmission band and anomalous scaling is observed for band edge frequency. Transmission spectra of acoustic waves is also measured for opposite direction of propagation and nonreciprocity is observed for the exponentially weak transmission in the disordered direction as well as for extended states in the ordered direction. Breaking of …

This dissertation is a collection of papers on anomalous phenomena in physics, biology, and sociology. These phenomena are primarily analyzed in terms of their temporal and spatiotemporal statistical properties. The analysis is based on both numerical simulations and, in some cases, real-world physiological and sociological data. The primary methods of analysis are diffusion entropy analysis, power spectral analysis, multifractal analysis, and survival (or waiting-time) analysis.