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Title:Numerical and Laboratory Studies of Ultrasonic Anderson Localization
Author(s):Loewenherz, James Henry
Doctoral Committee Chair(s):Weaver, Richard L.
Department / Program:Theoretical and Applied Mechanics
Discipline:Theoretical and Applied Mechanics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Applied Mechanics
Physics, Acoustics
Abstract:A numerical study of Anderson localization in two dimensions and a laboratory study of weak localization in three dimensions are presented. The two-dimensional study was performed by mathematically modelling a system of masses connected to a rigid base by springs of random stiffness. The masses were connected together by inextensible, massless strings. The resulting system of equations was then solved on a digital computer by stepping forward in time and solving explicitly for the displacements at each time step. Plots of the second moment of energy vs. time were made for different amounts of disorder, with values for the ratio of randomness to coupling strength (W/V) ranging from 6.0 to 9.0. No mobility edge was found, indicating that all modes were exponentially localized regardless of the degree of disorder. The three-dimensional study was performed by scattering a beam of 7 MHz ultrasound at a cell containing a slurry of glass or PMMA spherical beads and water, and measuring the backscattered energy as a function of angle. In accord with theoretical predictions, an enhanced backscatter peak with a width of 12 degrees and a magnitude twice that of the large-angle scattered energy was observed with the glass beads in a water slurry. An ultrasonic beam splitter was designed and successfully implemented to observe the small-angle scattered energy.
Issue Date:1992
Type:Text
Description:88 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992.
URI:http://hdl.handle.net/2142/72619
Other Identifier(s):(UMI)AAI9305604
Date Available in IDEALS:2014-12-17
Date Deposited:1992


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