The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity

We present an implicit a-posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications involving large strain plane stress incompressible neo-hookean hyperelasticity.Singapore-MIT Alliance (SMA

Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.Singapore-MIT Alliance (SMA

Computing bounds for linear functionals of exact weak solutions to Poisson's equation

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of piecewise-polynomial linear functional outputs of the exact weak solution of the infinite-dimensional continuum problem with piecewise-polynomial forcing. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element approximations to calculate a primal and an adjoint solution along with well known hybridization techniques to calculate interelement continuity multipliers. The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the energy norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The elemental contributions to the bound gap are always positive and hence lend themselves to be used as adaptive indicators, as we demonstrate with a numerical example

Bandgap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods

In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design

Influencia de la naturaleza de las partículas de proyección en el proceso de shot peening en la mejora de la osteointegración de implantes dentales.

El presente trabajo se ha centrado en valorar el efecto que tiene sobre las características superficiales, tratar la superficie de discos de Ti C. P., mediante un shot peening con distintos tipos de partículas de proyección: AL2O2, TiO2 y SiC. También se ha determinado la influencia que tiene pasivar los discos tratados con SiC, con HCl o con HF/HNO3; sobre todo desde el punto de vista de la limpieza superficial después del tratamiento, ya que se pretende aprovechar la reacción química que se produce entre el SiC y el HF, con la formación de SiF4. Para todo ello se han efectuado ensayos de la rugosidad superficial de los discos después del shot peening; tanto cuantitativos como cualitativos. Así mismo se ha determinado la capacidad de la partícula de soportar el shot peening sin perder su característica más importante dentro del proceso: su tamaño inicial. Finalmente, se ha propuesto un proceso de fabricación de partículas de TiO2 por sinterización. La fabricación en el laboratorio ha sido necesaria debido a la imposibilidad de encontrar en el mercado las partículas de esta naturaleza.Peer Reviewe

Reproducibility of lateral excursive tooth contact in a semi-adjustable articulator depending on the type of lateral guidance

The purposes of this study were (i) to compare the reproducibility of lateral tooth contacts of casts mounted in a semi-adjustable articulator when condylar guidance was set by different methods and (ii) to assess the margin of error of the variations of condylar guidance without changing lateral tooth contacts, depending on the type of lateral guidance. In subjects with different types of lateral guidance, intraoral lateral tooth contacts identified with occlusal registration strips were compared with those identified by use of a semi-adjustable articulator, setting the condylar guidance in four different ways: using protrusive wax wafers, by axiography and by adding and subtracting 5 degrees from the value of condylar guidance obtained by protrusive wax wafers. Tolerance to variations of condylar guidance without changing lateral tooth contacts was determined by increasing and decreasing the value of condylar guidance until lateral tooth contacts changed. Different ways of setting condylar guidance on a semi-adjustable articulator give rise to different values of condylar guidance in the same subject. The occlusal repercussions of these variations of condylar guidance values depend on the type of lateral guidance. Canine protection had the greatest tolerance to variations in the setting of condylar guidance without changing lateral occlusal contacts

Lipidomics Reveals Reduced Inflammatory Lipid Species and Storage Lipids after Switching from EFV/FTC/TDF to RPV/FTC/TDF: A Randomized Open-Label Trial

HIV and antiretroviral therapy affect lipid metabolism. Lipidomics quantifies several individual species that are overlooked using conventional biochemical analyses, outperforming traditional risk equations. We aimed to compare the plasma lipidomic profile of HIV patients taking efavirenz (EFV) or rilpivirine (RPV). Patients >/= 18 years old on EFV co-formulated with emtricitabine and tenofovir disoproxil fumarate (FTC/TDF) with HIV-RNA /=6 months were randomized to continue EFV/FTC/TDF (n = 14) or switch to RPV/FTC/TDF (n =15). Lipidomic analyses conducted by mass spectrometry (MS) were performed at baseline and after 12 and 24 weeks. OWLiver((R)) Care and OWLiver((R)) tests were performed to estimate the presence of fatty liver disease (NAFLD). No significant differences (83% male, median age 44 years, 6 years receiving EFV/FTC/TDF, CD4(+) count 740 cells/mm(3), TC 207 [57 HDL-C/133 LDL-C] mg/dL, TG 117 mg/dL) were observed between the groups at baseline. Significant reductions in plasma lipids and lipoproteins but increased circulating bilirubin concentrations were observed in patients who switched to RPV/FTC/TDF. Patients on RPV/FTC/TDF showed a decrease in the global amount of storage lipids (-0.137 log2 [fold-change] EFV vs. 0.059 log2 [fold-change] RPV) but an increase in lysophosphatidylcholines (LPCs) and total steroids. Compared with EFV, RPV increased metabolites with anti-inflammatory properties and reduced the repository of specific lipotoxic lipids

Hybridization and Postprocessing Techniques for Mixed Eigenfunctions

We introduce hybridization and postprocessing techniques for the Raviart–Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart–Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using a square and an L-shaped domain illustrate the theoretical results

High-Throughput Fabrication of Resonant Metamaterials with Ultrasmall Coaxial Apertures via Atomic Layer Lithography

We combine atomic layer lithography and glancing-angle ion polishing to create wafer-scale metamaterials composed of dense arrays of ultrasmall coaxial nanocavities in gold films. This new fabrication scheme makes it possible to shrink the diameter and increase the packing density of 2 nm-gap coaxial resonators, an extreme subwavelength structure first manufactured via atomic layer lithography, both by a factor of 100 with respect to previous studies. We demonstrate that the nonpropagating zeroth-order Fabry-Pérot mode, which possesses slow light-like properties at the cutoff resonance, traps infrared light inside 2 nm gaps (gap volume ∼ λ[superscript]3/10[superscript 6]). Notably, the annular gaps cover only 3% or less of the metal surface, while open-area normalized transmission is as high as 1700% at the epsilon-near-zero (ENZ) condition. The resulting energy accumulation alongside extraordinary optical transmission can benefit applications in nonlinear optics, optical trapping, and surface-enhanced spectroscopies. Furthermore, because the resonance wavelength is independent of the cavity length and dramatically red shifts as the gap size is reduced, large-area arrays can be constructed with λresonance ≫ period, making this fabrication method ideal for manufacturing resonant metamaterials.United States. Air Force Office of Scientific Research (Grants FA9550-12-1-0357 and FA9550-11-1-0141