A “wave automaton” for wave propagation in the time domain: II. Random systems

Abstract

Following our previous description of the wave automaton, a new lattice model introduced for the dynamical propagation of waves in arbitrary heterogeneous media which is efficient for calculations on large systems (1 024×1 024) over long times (several 10 6 inverse band widths), we present a detailed study of the time-dependent transport of wave packets in 2D-random systems. The scattering of a Bloch wave in a periodic system by a single impurity is first calculated analytically, which allows us to derive the elastic mean free time τ and mean free length l e as a function of the model parameters and the frequency f=ω/2 π. We then expose the different results on wave packets in random media which have been obtained using extensive numerical simulations on a parallel computer. We study the different regimes (ballistic, diffusive, localized) which appear as the wave packets spread over the random media and compare these numerical results with weak localization predictions