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

(Received 22 December 1992, revised 9 February 1993, accepted 17 February 1993)

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 ( ) 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  . and mean free length as a function of the model parameters and the frequency . 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.