Mathematical Studies of Wavelet Inverse Reconstructions for NondestructiveEvaluation, Novel Dielectrics, and the Dispersion from Chaotic Motions in Water

摘要

Wavelet inverse methods for non-destructive evaluation of high technologymaterials using transient pulses of ultrasound have been developed using the Kullback-Liehler information. This selects scales with small energy wavelet coefficients which have large information content. Wavelet aliasing by all compactly supported orthonormal wavelet families has been proven, and pathological multiresolutions were ruled out by choosing the correct group for the films; SU(2). The PBGS, photonic band gap structures, have been studied for electromagnetic and elastic waves. These periodic, two-component dielectrics have been studied with loss-tangent (dissipation) dispersion and lattice-disorder. Localized defects have been studied. An elastic wave filter and a gap opened by the high contrast of waver at microwave frequencies were found.