Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

The CATH Hierarchy Revisited-Structural Divergence in Domain Superfamilies and the Continuity of Fold Space

This paper explores the structural continuum in CATH and the extent to which superfamilies adopt distinct folds. Although most superfamilies are structurally conserved, in some of the most highly populated superfamilies (4% of all superfamilies) there is considerable structural divergence. While relatives share a similar fold in the evolutionary conserved core, diverse elaborations to this core can result in significant differences in the global structures. Applying similar protocols to examine the extent to which structural overlaps occur between different fold groups, it appears this effect is confined to just a few architectures and is largely due to small, recurring super-secondary motifs (e.g., alpha beta-motifs, alpha-hairpins). Although 24% of superfamilies overlap with superfamilies having different folds, only 14% of nonredundant structures in CATH are involved in overlaps. Nevertheless, the existence of these overlaps suggests that, in some regions of structure space, the fold universe should be seen as more continuous.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

Preparation and characterization of Ti-15Mo alloy used as biomaterial

With the increase in life expectancy, biomaterials have become an increasingly important focus of research because they are used to replace parts and functions of the human body, thus contributing to improved quality of life. In the development of new biomaterials, the Ti-15Mo alloy is particularly significant. In this study, the Ti-15Mo alloy was produced using an arc-melting furnace and then characterized by density, X-ray diffraction, optical microscopy, hardness and dynamic elasticity modulus measurements, and cytotoxicity tests. The microstructure was obtained with β predominance. Microhardness, elasticity modulus, and cytotoxicity testing results showed that this material has great potential for use as biomaterial, mainly in orthopedic applications.

Mechanical properties and porosity of dental glass-ceramics hot-pressed at different temperatures

The objective of this work was to evaluate biaxial-flexural-strength (σf), Vickers hardness (HV), fracture toughness (K Ic), Young's modulus (E), Poisson's ratio (ν) and porosity (P) of two commercial glass-ceramics, Empress (E1) and Empress 2 (E2), as a function of the hot-pressing temperature. Ten disks were hot-pressed at 1065, 1070, 1075 and 1080 °C for E1; and at 910, 915, 920 and 925 °C for E2. The porosity was measured by an image analyzer software and s f was determined using the piston-on-three-balls method. K Ic and HV were determined by an indentation method. Elastic constants were determined by the pulse-echo method. For E1 samples treated at different temperatures, there were no statistical differences among the values of all evaluated properties. For E2 samples treated at different temperatures, there were no statistical differences among the values of σf, E, and ν, however HV and K Ic were significantly higher for 910 and 915 °C, respectively. Regarding P, the mean value obtained for E2 for 925 °C was significantly higher compared to other temperatures.

Morpho-Anatomical Analysis of the Rhizome in Species of Scleria Berg. (Cyperaceae) from Serra do Cipó (MG)

Aspects related to the nature of stem thickening in monocotyledons have been the subject of many studies. Primary thickening has been attributed to the Primary Thickening Meristem (PTM). According to most authors, it gives rise, besides the adventitious roots, to the vascular tissues and part of the cortex. In other words, it has centripetal and centrifugal activity. For some authors, however, it gives rise only to the vascular system, and for others, only to part of the cortex. However, this work demonstrated that PTM corresponds to the pericycle in the meristematic phase or to the pericycle associated with the endodermis, also with meristematic activity. It was observed that the pericycle was responsible for the formation of the vascular system of the rhizome and of the adventitious roots; the endodermis gave rise to cell layers with radial disposition which comprised the inner portion of the stem cortex, and which corresponded to the region known as the derivatives of the meristematic endodermis (DME). A continuity was also demonstrated between the tissues of the stem and root in species of Scleria Berg. (Cyperaceae).

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

Ablation Rate and Morphology of Superficial and Deep Dentin Irradiated with Different Er:YAG Laser Energy Levels

Objective: In this study we evaluated the ablation rate of superficial and deep dentin irradiated with different Er:YAG laser energy levels, and observed the micromorphological aspects of the lased substrates with a scanning electron microscope (SEM). Background Data: Little is known about the effect of Er: YAG laser irradiation on different dentin depths. Materials and Methods: Sixty molar crowns were bisected, providing 120 specimens, which were randomly assigned into two groups ( superficial or deep dentin), and later into five subgroups (160, 200, 260, 300, or 360 mJ). Initial masses of the specimens were obtained. After laser irradiation, the final masses were obtained and mass losses were calculated followed by the preparation of specimens for SEM examination. Mass-loss values were subjected to two-way ANOVA and Fisher's least significant difference multiple-comparison tests (p < 0.05). Results: There was no difference between superficial and deep dentin. A significant and gradual increase in the mass-loss values was reached when energies were raised, regardless of the dentin depth. The energy level of 360 mJ showed the highest values and was statistically significantly different from the other energy levels. The SEM images showed that deep dentin was more selectively ablated, especially intertubular dentin, promoting tubule protrusion. At 360 mJ the micromorphological features were similar for both dentin depths. Conclusion: The ablation rate did not depend on the depth of the dentin, and an energy level lower than 360 mJ is recommended to ablate both superficial and deep dentin effectively without causing tissue damage.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

Recovery of the star formation history of the LMC from the VISTA survey of the Magellanic system

The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJK(s) photometry reaching stars in the oldest turn-off point throughout the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy in the star formation history (SFH) that can be expected from VMC data, in particular for the Large Magellanic Cloud (LMC). To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground Milky Way (MW) stars and background galaxies. The simulations cover the whole range of density of LMC field stars. We then perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimisation of a chi-squared-like statistics. We verify that the foreground MW stars are accurately recovered by the minimisation algorithms, whereas the background galaxies can be largely eliminated from the CMD analysis due to their particular colours and morphologies. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known age-metallicity relation (AMR). It turns out that, for a given sky area, the random errors for ages older than similar to 0.4 Gyr seem to be independent of the crowding. This can be explained by a counterbalancing effect between the loss of stars from a decrease in the completeness and the gain of stars from an increase in the stellar density. For a spatial resolution of similar to 0.1 deg(2), the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the lower stellar statistics for stars younger than similar to 0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR( t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that these parameters can be determined with (relative) accuracies of Delta(m-M)(0) similar to 0.02 mag and Delta E(B-V) similar to 0.01 mag, for each individual field over the LMC. The propagation of these errors in the SFR(t) implies systematic errors below 30%. This level of accuracy in the SFR(t) can reveal significant imprints in the dynamical evolution of this unique and nearby stellar system, as well as possible signatures of the past interaction between the MCs and the MW.

Direct measurement of spin correlations using magnetostriction

We demonstrate that the short-range spin correlator < S(i)center dot S(j)>, a fundamental measure of the interaction between adjacent spins, can be directly measured in certain insulating magnets. We present magnetostriction data for the insulating organic compound NiCl(2)-4SC(NH(2))(2), and show that the magnetostriction as a function of field is proportional to the dominant short-range spin correlator. Furthermore, the constant of proportionality between the magnetostriction and the spin correlator gives information about the spin-lattice interaction. Combining these results with the measured Young's modulus, we are able to extract dJ/dz, the dependence of the superexchange constant J on the Ni interionic distance z.