Waves in Highly Heterogeneous Media

Recent time-domain ultrasonic and numerical experiments on classical waves in two-dimensional Anderson localizing random media are reviewed. It is shown that the transport, albeit weak, occurs on a time scale comparable to a diffusive time scale, and is not exponentially slow. The time scales of the transport over distances of several localization lengths are found to scale with the ≈2.46 power of source/receiver distance. It is also shown that absorption has no effect on the localization of the eigenmodes, though it can make the observation of that localization more difficult, especially if those observations are by means of measurements of steady state transmission.