35 research outputs found
Finite-time scaling at the Anderson transition for vibrations in solids
A model in which a three-dimensional elastic medium is represented by a
network of identical masses connected by springs of random strengths and
allowed to vibrate only along a selected axis of the reference frame, exhibits
an Anderson localization transition. To study this transition, we assume that
the dynamical matrix of the network is given by a product of a sparse random
matrix with real, independent, Gaussian-distributed non-zero entries and its
transpose. A finite-time scaling analysis of system's response to an initial
excitation allows us to estimate the critical parameters of the localization
transition. The critical exponent is found to be in
agreement with previous studies of Anderson transition belonging to the
three-dimensional orthogonal universality class.Comment: Revised manuscript. 8 pages, 5 figure
Anderson transition for elastic waves in three dimensions
We use two different fully vectorial microscopic models featuring nonresonant
and resonant scattering, respectively, to demonstrate the Anderson localization
transition for elastic waves in three-dimensional (3D) disordered solids.
Critical parameters of the transition determined by finite-time and finite-size
scaling analyses suggest that the transition belongs to the 3D orthogonal
universality class. Similarities and differences between the elastic-wave and
light scattering in strongly disordered media are discussed.Comment: A misprint in Eq. (21) was corrected. No other change