Numerical and Laboratory Studies of Ultrasonic Anderson Localization

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical and Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Loewenherz, James Henry

Contributors dc:contributor

• Weaver, Richard L.

• Physics, Acoustics
• Applied Mechanics

Identifier

(UMI)AAI9305604

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72619