University of Illinois Urbana-Champaign

Anderson localization in time domain numerical studies of waves in two dimensional disordered media

Weaver, Richard L.

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https://hdl.handle.net/2142/112399

Description

Title
Anderson localization in time domain numerical studies of waves in two dimensional disordered media
Author(s)
Weaver, Richard L.
Issue Date
1993-04
Keyword(s)
  • Waves
  • Two-dimensional Disordered Media
Abstract
"A numerical model for the dynamics of a classical wave equation in a two dimensional Anderson disordered medium is integrated over times of the order of 27000 inverse band widths. Excitations by narrow band sources lead to wave energy densities whose ensemble averages behave diffusively at early times. The behavior at more general times and distances is, however, not diffusive. The observed transport profiles are shown to be inconsistent with predictions from the hydrodynamical continuum model of Anderson localization, and to the hypothesis of exponentially slow diffusion. The evolution of the energy density distribution in systems with varying disorders and microstructures, and over a range of length scales, is found to collapse to a single function of rescale space and time well approximated by e(x,t) ≈ exp{-x/ξ -(x2+n/4 β ξn t)p } with n≈ 0.46, p≈ .76, where x is the distance from the source, ξ is the localization length and the β is a ""residual diffusivity"" not equal to the bare diffusivity. Dissipation is shown to have no de-localizing effect."
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 711
  • 1993-6009
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112399
Sponsor(s)/Grant Number(s)
National Science Foundation 93/04
Copyright and License Information
Copyright 1993 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.