A multiresolution approach for homogenization and effective properties-propagation in complex ducts

Summary form only given. Multiresolution techniques can be used to study the effective properties of propagation and scattering in complex (finely structured) environments. As a case study, a new formulation that governs the propagation of the smoothed (large scale) component of the field in complex ducts is derived and compared to the generic formulation governing the propagation of the complete field. The former and the latter are termed here the "effective formulation" and the "complete formulation", respectively. The relation between the small scale structure of the system heterogeneity (the structure defined over length scales much smaller than the wavelength) and the large scale field (the component of the field defined over length scales of the order of the wavelength) are investigated. In particular, we use multiresolution and wavelet expansion to derive effective measures for the system heterogeneity. These measures are heterogeneity functions that are simpler (smoother) than the heterogeneity associated with the complete propagation formulation, but can still reproduce the correct large scale behavior of the field, and influence the correct far field as well, when used in conjunction with the new formulation. Three fundamental issues are discussed: effective measure in boundary value propagation problems, boundary conditions and associated modes, ray theories efficacy.