Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

A geometric approach to cosmological boundary conditions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of nitrous oxide on IOP and pupillary diameter in dogs anesthetized with varying concentrations of desflurane

Objective The aim of the present study was to evaluate the effects of nitrous oxide on TOP and pupillary diameter (PD) of dogs anesthetized with varying desflurane concentrations.Animals studied Twenty adult Mongrel dogs were used.Methods They were anesthetized with propofol (10 mg/kg, IV) and maintained with varying concentrations of desflurane (1.6, 1.4, and 1.2 MAC diluted in 100% oxygen (G1) or in 70% nitrous oxide and 30% oxygen (G2) (30 mL/kg/min). TOP was measured by applanation tonometry and horizontal PD was taken with a caliper adjacent to the cornea. Mean arterial pressure (MAP), heart rate (HR), respiratory rate (RR), and end-tidal CO, (etCO(2)) were also measured. All parameters were measured at TO, T30, T45, and T60 time points. One-way repeated measures ANOVA and the t-test were used to assess statistical differences (P < 0.05).Results T30, T45, and T60 TOP measures were Within normal limits for both groups and TOP did not differ between groups at any time. There was a significant decrease in PD in G I between TO and T30, T45 and T60, and also between T30 and T60. PD did not differ between groups. All vital parameters were within normal limits throughout anesthesia.Conclusions Administration of nitrous oxide with desflurane results in maintenance of normal TOP and prevents a decrease in horizontal PD during anesthesia. Therefore, this may be a suitable protocol in dogs undergoing intraocular surgeries that require mydriasis and maintenance of normal TOP.

Synthesis and physical properties of lipid-based poly(ester-urethane)s, I: Effect of varying polyester segment length

Four aliphatic thermoplastic poly(ester-urethane)s (PEUs) with similar molecular weights but varying polyesters molecular weight (534-1488 g/mol) were prepared from polyester diols, obtained by melt condensation of Azelaic acid and 1,9-Nonanediol, and 1,7-heptamethylene di-isocyanate (HPMDI) all sourced from vegetable oil feedstock. The thermal, and mechanical properties, and crystal structure of PEUs were investigated using DSC, TGA, DMA, tensile analysis and WAXD. For sufficiently long polyester chain, WAXD data indicated no hydrogen bonds polyethylene (PE)-like crystalline packing and for short polyester chains, small crystal domains with significant H-bonded polyamide (PA)-like packing. Crystallinity decreased with decreasing polyester molecular weights. The polymorphism of PEUs and consequently their melting characteristics were found to be largely controlled by polyester segment length. TGA of the PEUs indicated improved thermal stability with decreasing polyester chain length, suggesting a stabilization effect by urethane groups. Mechanical properties investigated by DMA and tensile analysis were found to scale predictably with the overall crystallinity of PEUs. (C) 2012 Elsevier Ltd. All rights reserved.

Superconducting boundary conditions for mesoscopic circular samples

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of the thermal damages in inlet engine valves varying the grinding wheels and the cutting fluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of thermal annealing treatment in oxygen atmosphere on grain boundary chemistry and non-ohmic properties of SnO2 center dot MnO polycrystalline semiconductors

The present work studied the influence of thermal treatment in oxygen rich atmosphere on heterogenous junctions in Mn-doped SnO2 polycrystalline system presenting varistor behavior. The samples were prepared by conventional oxide mixture methodology, and were submitted to heat treatment in oxygen rich atmosphere at 900 degrees C for 2h. The samples were characterized by X-ray diffraction, scanning electron microscopy, dc and ac electrical measurements. The results showed that there is an evident relationship between the microstructure heterogeneity and non-ohmic electrical properties. It was found that for this SnO2 center dot MnO-based varistor system the heat treatment in oxygen rich atmosphere does not necessarily increase the varistors properties, which was related to the decrease in the grain boundary resistance. The results are compared with Co-doped SnO2 varistors and ZnO based varistors. (C) 2008 WILEY-VCH Verlay GmbH & Co. KGaA, Weinheim.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Regular and Platform Switching: Bone Stress Analysis Varying Implant Type

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta formulae is developed for the efficient numerical solution of nonlinear stiff two-point boundary value problems. An analysis of the stability properties of general deferred correction schemes which are based on implicit Runge-Kutta methods is given and results which are analogous to those obtained for initial value problems are derived. A revised definition of symmetry is presented and this ensures that each deferred correction produces an optimal increase in order. Finally, some numerical results are given to demonstrate the superior performance of Lobatto formulae compared with mono-implicit formulae on stiff two-point boundary value problems. (C) 1998 Elsevier B.V. Ltd. All rights reserved.