J. Phys. I France
Volume 3, Numéro 6, June 1993
Page(s) 1281 - 1302
DOI: 10.1051/jp1:1993155
J. Phys. I France 3 (1993) 1281-1302

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

Patrick Sebbah, Didier Sornette and Christian Vanneste

Laboratoire de Physique de la Matière Condensée CNRS URA 190, Université de Nice-Sophia Antipolis, Parc Valrose, B.P. 71, 06108 Nice Cedex 2, France

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

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 ( $1\,024 \times 1\,024$) 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  $\tau$. and mean free length $\ell_{\rm e}$ as a function of the model parameters and the frequency $f = \omega/2 \pi$. 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.

71.55J - 03.40K - 42.20

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