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.

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.

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.

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.

The Schenberg data acquisition and analysis: results from its first commissioning run

The Mario Schenberg gravitational wave detector has started its commissioning phase at the Physics Institute of the University of Sao Paulo. We have collected almost 200 h of data from the instrument in order to check out its behavior and performance. We have also been developing a data acquisition system for it under a VXI System. Such a system is composed of an analog-to-digital converter and a GPS receiver for time synchronization. We have been building the software that controls and sets up the data acquisition. Here we present an overview of the Mario Schenberg detector and its data acquisition system, some results from the first commissioning run and solutions for some problems we have identified.

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

Development of a sequential injection-square wave voltammetry method for determination of paraquat in water samples employing the hanging mercury drop electrode

This work describes the development and optimization of a sequential injection method to automate the determination of paraquat by square-wave voltammetry employing a hanging mercury drop electrode. Automation by sequential injection enhanced the sampling throughput, improving the sensitivity and precision of the measurements as a consequence of the highly reproducible and efficient conditions of mass transport of the analyte toward the electrode surface. For instance, 212 analyses can be made per hour if the sample/standard solution is prepared off-line and the sequential injection system is used just to inject the solution towards the flow cell. In-line sample conditioning reduces the sampling frequency to 44 h(-1). Experiments were performed in 0.10 M NaCl, which was the carrier solution, using a frequency of 200 Hz, a pulse height of 25 mV, a potential step of 2 mV, and a flow rate of 100 mu L s(-1). For a concentration range between 0.010 and 0.25 mg L(-1), the current (i(p), mu A) read at the potential corresponding to the peak maximum fitted the following linear equation with the paraquat concentration (mg L(-1)): ip = (-20.5 +/- 0.3) Cparaquat -(0.02 +/- 0.03). The limits of detection and quantification were 2.0 and 7.0 mu g L(-1), respectively. The accuracy of the method was evaluated by recovery studies using spiked water samples that were also analyzed by molecular absorption spectrophotometry after reduction of paraquat with sodium dithionite in an alkaline medium. No evidence of statistically significant differences between the two methods was observed at the 95% confidence level.

Square wave adsorptive cathodic stripping voltarnmetry automated by sequential injection analysis - Potentialities and limitations exemplified by the determination of methyl parathion in water samples

This paper describes the development and evaluation of a sequential injection method to automate the determination of methyl parathion by square wave adsorptive cathodic stripping voltammetry exploiting the concept of monosegmented flow analysis to perform in-line sample conditioning and standard addition. Accumulation and stripping steps are made in the sample medium conditioned with 40 mmol L-1 Britton-Robinson buffer (pH 10) in 0.25 mol L-1 NaNO3. The homogenized mixture is injected at a flow rate of 10 mu Ls(-1) toward the flow cell, which is adapted to the capillary of a hanging drop mercury electrode. After a suitable deposition time, the flow is stopped and the potential is scanned from -0.3 to -1.0 V versus Ag/AgCl at frequency of 250 Hz and pulse height of 25 mV The linear dynamic range is observed for methyl parathion concentrations between 0.010 and 0.50 mgL(-1), with detection and quantification limits of 2 and 7 mu gL(-1), respectively. The sampling throughput is 25 h(-1) if the in line standard addition and sample conditioning protocols are followed, but this frequency can be increased up to 61 h(-1) if the sample is conditioned off-line and quantified using an external calibration curve. The method was applied for determination of methyl parathion in spiked water samples and the accuracy was evaluated either by comparison to high performance liquid chromatography with UV detection, or by the recovery percentages. Although no evidences of statistically significant differences were observed between the expected and obtained concentrations, because of the susceptibility of the method to interference by other pesticides (e.g., parathion, dichlorvos) and natural organic matter (e.g., fulvic and humic acids), isolation of the analyte may be required when more complex sample matrices are encountered. (C) 2007 Elsevier B.V. All rights reserved.

Electroanalytical determination of promethazine hydrochloride in pharmaceutical formulations on highly boron-doped diamond electrodes using square-wave adsorptive voltammetry

The electrochemical oxidation of promethazine hydrochloride was made on highly boron-doped diamond electrodes. Cyclic voltammetry experiments showed that the oxidation mechanisms involved the formation of an adsorbed product that is more readily oxidized, producing a new peak with lower potential values whose intensity can be increased by applying the accumulation potential for given times. The parameters were optimized and the highest current intensities were obtained by applying +0.78 V for 30 seconds. The square-wave adsorptive voltammetry results obtained in BR buffer showed two well-defined peaks, dependent on the pH and on the voltammetric parameters. The best responses were obtained at pH 4.0, frequency of 50 s(-1), step of 2 mV, and amplitude of 50 mV. Under these conditions, linear responses were obtained for concentrations from 5.96 x 10(-7) to 4.76 x 10(-6) mol L-1, and calculated detection limits of 2.66 x 10(-8) mol L-1 (8.51 mu g L-1) for peak 1 and of 4.61 x 10(-8) mol L-1 (14.77 mu g L-1) for peak 2. The precision and accuracy were evaluated by repeatability and reproducibility experiments, which yielded values of less than 5.00% for both voltammetric peaks. ne applicability of this procedure was tested on commercial formulations of promethazine hydrochloride by observing the stability, specificity, recovery and precision of the procedure in complex samples. All results obtained were compared to recommended procedure by British Pharmacopeia. The voltammetric results indicate that the proposed procedure is stable and sensitive, with good reproducibility even when the accumulation steps involve short times. It is therefore very suitable for the development of the electroanalytical procedure, providing adequate sensitivity and a reliable method.