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.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. 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.

Immunological parameters related to the adjuvant effect of the ordered mesoporous silica SBA-15

In 2006, the first report of a nanostructured material as adjuvant was described establishing the effectiveness of the ordered mesoporous SBA-15 silica as an immune adjuvant. The present study evaluated the SBA-15 capacity to modulate the immune responsiveness of High and Low responder mice immunized with BSA encapsulated/adsorbed in SBA-15 by the intramuscular or oral route and the adjuvant effect was compared with the responsiveness induced by BSA in aluminum hydroxide salts or emulsified in Incomplete Freund adjuvant. These results demonstrate the ability of the non-toxic SBA-15 nanoparticles to increase the immunogenicity and repair the responsiveness of the constitutively low responder individuals inducing both the IgG2a and the IgG1 isotypes, independently of the immune cell committed and conditioning the low phenotype. This new adjuvant may reveal novel therapeutic targets for immune modulation and vaccine design. (C) 2010 Elsevier Ltd. All rights reserved.

Factorial design to optimize microwave-assisted synthesis of FDU-1 silica with a new triblock copolymer

The synthesis of FDU-1 silica with large cage-like mesopores prepared with a new triblock copolymer Vorasurf 504 (R) (Eo)(38)(BO)(46)(EO)(38) was developed. The hydrothermal treatment temperature, the dissolution of the copolymer in ethanol, the HCl concentration, the solution stirring time and the hydrothermal treatment time in a microwave oven were evaluated with factorial design procedures. The dissolution in ethanol is important to produce a material with better porous morphology. Increases in the hydrothermal temperature (100 degrees C) and HCl concentration (2 M) improved structural, textural and chemical properties of the cubic ordered mesoporous silica. Also, longer times induced better physical and chemical property characteristics. (C) 2010 Elsevier Inc. All rights reserved.

Immobilization of glucose oxidase enzyme (GOD) in large pore ordered mesoporous cage-like FDU-1 silica

Large pore ordered mesoporous silica FDU-1 with three-dimensional (3D) face-centered cubic, Fm3m arrangement of rnesopores, was synthesized under strong acid media using B-50-6600 poly(ethylene oxide)-poly(butylene oxide)-poly(ethylene oxide) triblock copolymer (EO(39)BO(47)EO(39)), tetraethyl orthosilicate (TEOS) and trimethyl-benzene (TMB). Large pore FDU-1 silica was obtained by using the following gel composition 1TEOS:0.00735B50-6600:0.00735TMB:6HCl:155H(2)O. The pristine material exhibited a BET specific surface area of 684 m(2) g(-1), total pore volume of 0.89 cm(3) g(-1), external surface area of 49 m(2) g(-1) and microporous volume of 0.09 cm(3) g(-1). The enzyme activity was determined by the Flow Injection Analysis-Chemiluminescence (FIA-CL) method. For GOD immobilized on the FDU-1 silica, GOD supernatant and GOD solution, the FIA-CL results were 9.0, 18.6 and 34.0 U, respectively. The value obtained for the activity of the GOD solution with FIA-CL method is in agreement with the 35 U, obtained by spectrophotometry. (C) 2011 Elsevier B.V. All rights reserved.

Adsorption of Pb(2+), Cu(2+) and Cd(2+) in FDU-1 silica and FDU-1 silica modified with humic acid

Ordered mesoporous silica with cubic structure, type FDU-1, was synthesized under strong acid media using B-50-6600 poly(ethylene oxide)-poly(butilene oxide)-poly(ethylene oxide) triblock copolymer (EO(39)BO(47)EO(39)) and tetraethyl orthosilicate (TEOS). Humic acid (HA) was modified to the synthesis process at a concentration of 1.5 mmol per gram of SiO(2). Thermogravimetry, small angle X-ray diffraction, nitrogen adsorption and high resolution transmission electron microscopy were used to characterize the samples. The pristine FDU-1 and FDU-1 with incorporated 1.5 mmol of HA were tested for adsorption of Pb(2+), Cu(2+) and Cd(2+) in aqueous solution. Incorporation of humic acid into the FDU-1 silica afforded an adsorbent with strong affinity for Cd(2+), Cu(2+) and Pb(2+) from single ion solutions. Adsorption of Cu(2+) was significantly enhanced after incorporation of humic acid, a fact that can be explained by the formation of complexes with carboxylic and phenolic groups at low concentrations of the metal cation. The results demonstrated the potential applicability of FDU-1 with incorporated HA in the removal of low concentrations of heavy metal cations from aqueous solution, such as wastewaters, after usual precipitation of metal hydroxides in alkaline medium and proper pH conditioning in the range between 6 and 7. (C) 2007 Elsevier Inc. All rights reserved.

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.

Synthesis and structure of cage-like mesoporous silica using different precursors

In this work the synthesis of cubic, FDU-1 type, ordered mesoporous silica (OMS) was developed from two types of silicon source, tetraethyl orthosilicate (TEOS) and a less expensive compound, sodium silicate (Na(2)Si(3)O(7)), in the presence of a new triblock copolymer template Vorasurf 504 (EO(38)BO(46)EO(38)). For both silicon precursors the synthesis temperature was evaluated. For TEOS the effect of polymer dissolution in methanol and the acid solution (HCl and HBr) on the material structure was analyzed. For Na(2)Si(3)O(7) the influence of the polymer mass and the hydrothermal treatment time were the explored experimental parameters. The samples were examined by Small Angle X-ray Scattering (SAXS) and Nitrogen Sorption. For both precursors the decrease on the synthesis temperature from ambient, -25 degrees C, to -15 degrees C improved the ordered porous structure. For TEOS, the SAXS results showed that there is an optimum amount of hydrophobic methanol that contributed to dissolve the polymer but did not provoke structural disorder. The less electronegative Br-ions, when compared to Cl-, induced a more ordered porous structure, higher surface areas and larger lattice parameters. For Na(2)Si(3)O(7) the increase on the hydrothermal treatment time as well as the use of an optimized amount of polymer promoted a better ordered porous structure. (C) 2011 Elsevier B.V. All rights reserved.

Thermal wave scattering by two overlapping and parallel cylinders

In this paper an analytical solution of the temperature of an opaque material containing two overlapping and parallel subsurface cylinders, illuminated by a modulated light beam, is presented. The method is based on the expansion of plane and cylindrical thermal waves in series of Bessel and Hankel functions. This model is addressed to the study of heat propagation in composite materials with interconnection between inclusions, as is the case of inverse opals and fiber reinforced composites. Measurements on calibrated samples using lock-in infrared thermography confirm the validity of the model.

Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time. (C) 2008 Elsevier GmbH. All rights reserved.

On the Stabilization of Gold Nanoparticles over Silica-Based Magnetic Supports Modified with Organosilanes

The immobilization of gold nanoparticles (Au NPs) on silica is made possible by the functionalization of the silica surfaces with organosilanes. Au NPs could only be stabilized and firmly attached to silica-support surfaces that were previously modified with amino groups. Au NPs could not be stabilized on bare silica surfaces and most of the NPs were then found in the solution. The metal-support interactions before and after the Au NP formation, observed by X-ray absorption fine structure spectroscopy (XAFS), indicate a stronger interaction of gold-(III) ions with amino-modified silica surfaces than with the silanol groups in bare silica. An amino-modified, silica-based, magnetic support was used to prepare an active Au NP catalyst for the chemoselective oxidation of alcohols, a reaction of great interest for the fine chemical industry.

The Schenberg spherical gravitational wave detector: the first commissioning runs

Here we present a status report of the first spherical antenna project equipped with a set of parametric transducers for gravitational detection. The Mario Schenberg, as it is called, started its commissioning phase at the Physics Institute of the University of Sao Paulo, in September 2006, under the full support of FAPESP. We have been testing the three preliminary parametric transducer systems in order to prepare the detector for the next cryogenic run, when it will be calibrated. We are also developing sapphire oscillators that will replace the current ones thereby providing better performance. We also plan to install eight transducers in the near future, six of which are of the two-mode type and arranged according to the truncated icosahedron configuration. The other two, which will be placed close to the sphere equator, will be mechanically non-resonant. In doing so, we want to verify that if the Schenberg antenna can become a wideband gravitational wave detector through the use of an ultra-high sensitivity non-resonant transducer constructed using the recent achievements of nanotechnology.

Dispersion and uncertainty in multislit matter wave diffraction

We show that single and multislit experiments involving matter waves may be constructed to assess dispersively generated correlations between the position and momentum of a single free particle. These correlations give rise to position dependent phases which develop dynamically as a result of dispersion and may play an important role in the interference patterns. To the extent that initial transverse coherence is preserved throughout the proposed diffraction setup, such interference patterns are noticeably different from those of a classical dispersion free wave. (c) 2007 Published by Elsevier B.V.