Acoustic Analog Experimental Studies of Effects of Anderson Localization in One Dimension and Physical Properties of TwoDimensional Quasiperiodic Systems
Abstract
In this thesis, experimental studies of the effects of Anderson localization in a onedimensional random system and of physical properties of a twodimensional quasiperiodic system by using acoustic analog techniques are reported. The acoustic simulation of Anderson localization involves a string/mass system. The wave field consists of transverse waves in the the string generated with an electromechanical actuator. The Blochwave behavior is verified with the masses spaced periodically. In the study of localization effects, the positions of the masses are varied. Several sets of measurements are made with the positions randomly varied within maximum displacements from lattice sites of 1%, 2%, and 5% of the lattice constant. Inelastic scattering effects in the localization problem are studied with 2% spacing disorder. In this investigation, a measured hopping probability of inelastic scattering as a function of the longitudinal drive amplitude is obtained. Some phasecorrelation effects are evident. The acoustic simulation experiment used to investigate the physical properties of quasicrystals involved coupled oscillators in a twodimensional Penrose lattice. By analogy with a tightbinding model, the tuning forks mounted at the centers of the rhombuses of the Penrose tile as local oscillators are nearestneighborcoupled together with arcs of steel wire connecting the tines of neighboring tuning forks. The oscillations of the system is driven by an electromagnet. The responses of the system are monitored by electrodynamic transducers. The eigenvalue spectrum shows a feature resulting from the quasiperiodic symmetry: the spectrum has gaps and bands whose widths are in the ratio of the Golden Mean (surd{5 + 1 })/2. The eigenfunctions of the system are obtained.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT.......189H
 Keywords:

 QUASIPERIODIC SYSTEMS;
 Physics: Acoustics