B. Z. Steinberg
Univ. of Tel Aviv, Tel Aviv 69978, Israel
J. J. McCoy
Catholic Univ. of America, Washington, DC 20064
Complexity in the context of radiation and scattering of waves can be intuitively perceived as the analytical and computational difficulties encountered when a radiating system interacts with a medium or a scatterer that are described on a wide range of length scales. The wavelength (lambda) constitutes a physically motivated discriminator of the various length scales pertaining to a time harmonic scattering problem. It is convenient to refer to the length scales of the order of (lambda) and above as the macroscales, and to the length scales much smaller than (lambda) as the microscales. A complexity frequently encountered in scattering problems is the one characterized by a microscale heterogeneity that occupies domains in space measured on the macroscale. A new formulation, tuned to govern the macroscale response component, has been presented in several recent papers. This formulation is sufficient for estimating the radiation of a sound field into the far-field of a surrounding fluid. In this presentation we concentrate on the formulation's implications. The questions addressed are: What type of microscale heterogeneity has no footprint in macroscale response measures? What classes of microscale heterogeneity have an identical footprint in macroscale response measures?