A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. (C) 2011 Elsevier Ltd. All rights reserved.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Evaluation of Mid-upper Arm Circumference in Pre-school Children: Comparison Between NCHS/CDC-2000 and WHO-2006 References

We aimed to evaluate the classification of arm circumference (AC) in pre-school children by using National Center for Health Statistics (NCHS/CDC-2000) and World Health Organization (WHO-2006) references. We evaluated 205 children: weight, height and AC were assessed and the body mass index (BMI) was calculated. The BMI values were classified into Z-scores by the WHO referential. The AC was classified into Z-cores by two references, comparing the whole-sample value and among groups (tercis) of BMI Z-score. The correlation was also evaluated between differences of AC with BMI Z-score. The WHO referential classified the AC in Z-scores greater than the NCHS/CDC, which is more specific and less sensitive than the NCHS/CDC for lean children and at the same time more sensitive and less specific for children with overweight. In conclusion, a significant difference in the AC classification occurs according to the referential used.

Upper-mantle seismic structure beneath SE and Central Brazil from P- and S-wave regional traveltime tomography

We present models for the upper-mantle velocity structure beneath SE and Central Brazil using independent tomographic inversions of P- and S-wave relative arrival-time residuals (including core phases) from teleseismic earthquakes. The events were recorded by a total of 92 stations deployed through different projects, institutions and time periods during the years 1992-2004. Our results show correlations with the main tectonic structures and reveal new anomalies not yet observed in previous works. All interpretations are based on robust anomalies, which appear in the different inversions for P-and S-waves. The resolution is variable through our study volume and has been analyzed through different theoretical test inversions. High-velocity anomalies are observed in the western portion of the Sao Francisco Craton, supporting the hypothesis that this Craton was part of a major Neoproterozoic plate (San Franciscan Plate). Low-velocity anomalies beneath the Tocantins Province (mainly fold belts between the Amazon and Sao Francisco Cratons) are interpreted as due to lithospheric thinning, which is consistent with the good correlation between intraplate seismicity and low-velocity anomalies in this region. Our results show that the basement of the Parana Basin is formed by several blocks, separated by suture zones, according to model of Milani & Ramos. The slab of the Nazca Plate can be observed as a high-velocity anomaly beneath the Parana Basin, between the depths of 700 and 1200 km. Further, we confirm the low-velocity anomaly in the NE area of the Parana Basin which has been interpreted by VanDecar et al. as a fossil conduct of the Tristan da Cunha Plume related to the Parana flood basalt eruptions during the opening of the South Atlantic.

Upper-mantle seismic anisotropy from SKS splitting in the South American stable platform: A test of asthenospheric flow models beneath the lithosphere

Upper-mantle seismic anisotropy has been extensively used to infer both present and past deformation processes at lithospheric and asthenospheric depths. Analysis of shear-wave splitting (mainly from core-refracted SKS phases) provides information regarding upper-mantle anisotropy. We present average measurements of fast-polarization directions at 21 new sites in poorly sampled regions of intra-plate South America, such as northern and northeastern Brazil. Despite sparse data coverage for the South American stable platform, consistent orientations are observed over hundreds of kilometers. Over most of the continent, the fast-polarization direction tends to be close to the absolute plate motion direction given by the hotspot reference model HS3-NUVEL-1A. A previous global comparison of the SKS fast-polarization directions with flow models of the upper mantle showed relatively poor correlation on the continents, which was interpreted as evidence for a large contribution of ""frozen"" anisotropy in the lithosphere. For the South American plate, our data indicate that one of the reasons for the poor correlation may have been the relatively coarse model of lithospheric thicknesses. We suggest that improved models of upper-mantle flow that are based on more detailed lithospheric thicknesses in South America may help to explain most of the observed anisotropy patterns.

Potamotrygon tigrina, a new species of freshwater stingray from the upper Amazon basin, closely related to Potamotrygon schroederi Fernandez-Yepez, 1958 (Chondrichthyes: Potamotrygonidae)

A new species of Neotropical freshwater stingray, family Potamotrygonidae, is described from the Rio Nanay in the upper Rio Amazonas basin of Peru. Potamotrygon tigrina, n. sp., is easily distinguished from all congeners by its conspicuous dorsal disc coloration, composed of bright yellow to orange vermiculations strongly interwoven with a dark-brown to deep-black background. Additional features that in combination diagnose P. tigrina, n. sp., include the presence of a single angular cartilage, low and not closely grouped dorsal tail spines, and coloration of tail composed of relatively wide and alternating bands of creamy white and dark brown to black. Potamotrygon tigrina is closely related to Potamotrygon schroederi Fernandez-Yepez, 1958, which occurs in the Rio Negro (Brazil) and Rio Orinoco (Venezuela, Colombia). Both species are very similar in proportions and counts, and share features hypothesized to be derived within Potamotrygonidae, related to their specific angular cartilage morphology, distal tail color, dorsal tail-spine pattern, and ventral lateral-line system. To further substantiate the description of P. tigrina, n. sp., we provide a redescription of P. schroederi based on material from the Rio Negro (Brazil) and Rio Orinoco (Venezuela). Specimens from the two basins differ in number of vertebral centra and slightly in size and frequency of rosettes on dorsal disc, distinctions that presently do not warrant their specific separation. Potamotrygon tigrina is frequently commercialized in the international aquarium trade but virtually nothing is known of its biology or conservation status.

Two new species of Loricariidae (Teleostei: Siluriformes) from main channels of the upper and middle Amazon Basin, with discussion of deep water specialization in loricariids

Hemiancistrus pankimpuju, new species, and Panaque bathyphilus, new species, are described from the main channel of the upper (Maranon) and middle (Solimoes)Amazon River, respectively. Both species are diagnosed by having a nearly white body, long filamentous extensions of both simple caudal-fin rays, small eyes, absence of an iris operculum and unique combinations of morphometrics. The coloration and morphology of these species, unique within Loricariidae, are hypothesized to be apomorphies associated with life in the dark, turbid depths of the Amazon mainstem. Extreme elongation of the caudal filaments in these and a variety of other main channel catfishes is hypothesized to have a mechanosensory function associated with predator detection.

Stigma/style cell cycle inhibitor 1 (SCI1), a tissue-specific cell cycle regulator that controls upper pistil development

P>A cDNA encoding a small lysine-rich protein of unknown function was identified in a tobacco (Nicotiana tabacum) stigma/style suppression subtractive hybridization cDNA library. After its characterization, the corresponding gene was designated stigma/style cell cycle inhibitor 1 (SCI1). Fluorescence microscopy with an SCI1-GFP protein fusion demonstrated its nuclear localization, which was confined to the interchromatic region. Real-time RT-PCR and in situ hybridization experiments showed that SCI1 is stigma/style-specific and developmentally regulated. SCI1 RNAi knockdown and overexpression plants had stigmas/styles with remarkably enlarged and reduced areas, respectively, which was attributable to differences in cell numbers. These results indicate that SCI1 is a tissue-specific negative cell cycle regulator. The differences in cell division had an effect on the timing of the differentiation of the stigmatic papillar cells, suggesting that their differentiation is coupled to stigma cell divisions. This is consistent with a role for SCI1 in triggering differentiation through cell proliferation control. Our results revealed that SCI1 is a novel tissue-specific gene that controls cell proliferation/differentiation, probably as a component of a developmental signal transduction pathway.

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

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.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Upper limit on the cosmic-ray photon flux above 10(19) eV using the surface detector of the Pierre Auger Observatory

A method is developed to search for air showers initiated by photons using data recorded by the surface detector of the Auger Observatory. The approach is based on observables sensitive to the longitudinal shower development, the signal risetime and the curvature of the shower front. Applying this method to the data, tipper limits on the flux of photons of 3.8 x 10(-3), 2.5 x 10(-3), and 2.2 x 10(-3) km(-2) sr(-1) yr(-1) above 10(19) eV, 2 x 10(19) eV, and 4 x 10(19) eV are derived, with corresponding limits on the fraction of photons being 2.0%, 5.1%, and 31% (all limits at 95% c.l.). These photon limits disfavor certain exotic models of sources of cosmic rays. The results also show that the approach adopted by the Auger Observatory to calibrate the shower energy is not strongly biased by a contamination from photons. (C) 2008 Elsevier B.V. All rights reserved.