J. Phys. I France 3 (1993) 1259-1280
A "wave automaton" for wave propagation in the time domain: I. Periodic systemsPatrick 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, accepted 9 February 1993)
In Vanneste et al., Europhys. Lett. 17 (1992) 715, a new lattice model was 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). Instead of starting from a wave equation or a Hamiltonian which needs to be discretized for numerical implementation, the model is defined by the set of S-matrices, one for each node, describing the interaction of the wave field with the scatterers. Here, we expose in detail the general method of construction of the S-matrices and discuss the physical meaning of the dynamical S-matrix approach. We calculate the properties of this model for a class of parameters in the periodic case and exhibit the form of the Bloch modes, the dispersion relation and the mode density. In a companion paper, we study the transport of wave packets in arbitrary random media.
03.40K - 42.20
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