Inverse problems in elasticity

This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Surgical Management of Gynecomastia—a 10-year Analysis

Background: Gynecomastia is defined as the benign enlargement of the male breast. Most studies on surgical treatment of gynecomastia show only small series and lack histopathology results. The aim of this study was to analyze the surgical approach in the treatment of gynecomastia and the related outcome over a 10-year period. Patients and methods: All patients undergoing surgical gynecomastia corrections in our department between 1996 and 2006 were included for retrospective evaluation. The data were analyzed for etiology, stage of gynecomastia, surgical technique, complications, risk factors, and histological results. Results: A total of 100 patients with 160 operations were included. Techniques included subcutaneous mastectomy alone or with additional hand-assisted liposuction, isolated liposuction, and formal breast reduction. Atypical histological findings were found in 3% of the patients (spindle-cell hemangioendothelioma, papilloma). The surgical revision rate among all patients was 7%. Body mass index and a weight of the resected specimen higher than 40 g were identified as significant risk factors for complications (p < 0.05). Conclusions: The treatment of gynecomastia requires an individualized approach. Caution must be taken in performing large resections, which are associated with increased complication rates. Histological tissue analysis should be routinely performed in all true gynecomastia corrections, because histological results may reveal atypical cellular patholog

Optical alignment and spinning of laser-trapped microscopic particles

Light-induced rotation of absorbing microscopic particles by transfer of angular momentum from light to the material raises the possibility of optically driven micromachines. The phenomenon has been observed using elliptically polarized laser beams or beams with helical phase structure. But it is difficult to develop high power in such experiments because of overheating and unwanted axial forces, limiting the achievable rotation rates to a few hertz. This problem can in principle be overcome by using transparent particles, transferring angular momentum by a mechanism first observed by Beth in 1936, when he reported a tiny torque developed in a quartz waveplate due to the change in polarization of transmitted light. Here we show that an optical torque can be induced on microscopic birefringent particles of calcite held by optical tweezers. Depending on the polarization of the incident beam, the particles either become aligned with the plane of polarization (and thus can be rotated through specified angles) or spin with constant rotation frequency. Because these microscopic particles are transparent, they can be held in three-dimensional optical traps at very high power without heating. We have observed rotation rates in excess of 350 Hz.Comment: 4 pages, 4 figure