Multiresolution approach for homogenization and effective properties - propagation in complex ducts

A new formulation, called the effective formulation, governing the propagation of the smoothed component of the field in complex ducts is derived. Effective measures for the system heterogeneity are derived using multiresolution and wavelet expansion. It is shown that, while the mapping of heterogeneity to its effective measure is unique, the converse is not true. Furthermore, the effective measures introduce an effective anisotropy into the propagation problem, even if the generic complete formulation is isotropic. Also, a self-adjoint effective formulation, and hence a reciprocal effective Green's function, is obtained. An effective ray theory is discussed and its physical interpretations are explored.