We describe and analyze an approach to the pure Neumann problem of three-dimensional linearized elasticity, whose novelty consists in considering the strain tensor field as the sole unknown, instead of the displacement vector field as is customary. This approach leads to a well-posed quadratic minimization problem of a new type, constrained by a weak form of the classical Saint Venant compatibi...

We present the Discrete Duality Finite Volume method (DDFV) for solving the linear elasticity problem on unstructured mesh applied to solids undergoing mechanical loads. The procedure is described in detail for three dimensional problems and some theoretical results are provided: the discrete problem is well-posed, stable and convergent. A number of numerical test problems demonstrates the abil...

A. The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectoria...

In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in twodimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered...

We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from experimental and theoretical Cu 3p holograms from Cu(001) demonstrate that this method suppresses strong forward-scattering effects so as to yield more accurate thre...

Mailing address: Marcelo Luiz Campos Vieira • Rua Cardoso de Melo, 463/21 04548-002 São Paulo, SP Brazil E-mail: [email protected] Manuscript received January 09, 2007; revised manuscript received January 01, 2007; accepted March 13, 2007. The use of three-dimensional echocardiography for the analysis of cardiac structures allows the viewing of planes that make the anatomic identification m...

The results of experiments in developing a method for extracting three-dimensional information from a scene by means of a polarimetric passive imaging sensor are summarized. This sensor provides a full Stokes vector at each sensor pixel location from which degree and angle of linear polarization are computed. The angle of linear polarization provides the azimuth angle of the surface normal vect...

This article addresses the current state of the art of technology in three-dimensional echocardiography as it applies to transducer design, beam forming, display, and quantification. Because three-dimensional echocardiography encompasses many technical and clinical areas, this article reviews its strengths and limitations and concludes with an analysis of what to use when.

The surface alignment of lyotropic chromonic liquid crystals can not only be planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is d...