A WAVE AUTOMATON FOR WAVE-PROPAGATION IN THE TIME-DOMAIN .2. RANDOM-SYSTEMS

Following our previous description of the << wave automaton >>,a new l attice model introduced for the dynamical propagation of waves in arbi trary heterogeneous media which is efficient for calculations on large systems (1 024 x 1 024) over long times (several 10(6) inverse band w idths), 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 analyticall y, which allows us to derive the elastic mean free time tau and mean f ree length l(e) as a function of the model parameters and the frequenc y f = omega/2 pi. We then expose the different results on wave packets in random media which have been obtained using extensive numerical si mulations on a parallel computer. We study the different regimes (ball istic, diffusive, localized) which appear as the wave packets spread o ver the random media and compare these numerical results with weak loc alization predictions.