On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Characterization of a dissolved oxygen sensor made of plastic optical fiber coated with ruthenium-incorporated solgel

A dissolved oxygen sensor made of plastic optical fiber as the substrate and dichlorotris (1, 10-phenanthroline) ruthenium as a fluorescence indicator is studied. Oxygen quenching characteristics of both intensity and phase were measured; the obtained characteristics showed deviation from the linear relation described by the Stern-Volmer equation. A two-layer model is proposed to explain the deviation, and main parameters can be deduced with the model. (C) 2009 Optical Society of America

Computational Microscopy: Breaking the Limit of Conventional Optics

Computational imaging is flourishing thanks to the recent advancement in array photodetectors and image processing algorithms. This thesis presents Fourier ptychography, which is a computational imaging technique implemented in microscopy to break the limit of conventional optics. With the implementation of Fourier ptychography, the resolution of the imaging system can surpass the diffraction limit of the objective lens's numerical aperture; the quantitative phase information of a sample can be reconstructed from intensity-only measurements; and the aberration of a microscope system can be characterized and computationally corrected. This computational microscopy technique enhances the performance of conventional optical systems and expands the scope of their applications.