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.

Renal ischemia in rats: Mitochondria function and laser autofluorescence

Ischemia-reperfusion injury is the major cause of organ dysfunction or even nonfunction following transplantation. It can attenuate the long-term survival of transplanted organs. To evaluate the severity of renal ischemia injury determined by histology, we applied laser(442 nm and 532 nm) induced fluorescence (LIF), mitochondria respiration, and membrane swelling to evaluate 28 Wistar rats that underwent left kidney warm ischemia for 20, 40, 60, or 80 minutes. LIF performed before ischemia (control) was repeated at 20, 40, 60, and 80 minutes thereafter. We harvested left kidney tissue samples immediately after LIF determination for histology and mitochondrial analyses: state 3 and 4 respiration, respiration control rate (RCR), and membrane swelling. The association of optic spectroscopy with histological damage showed: LIF, 442 nm (r(2) = 0.39, P < .001) and 532 nm, (r(2) = 0.18, P = .003); reflecting laser/fluorescence-induced, 442 nm (r(2) = 0.20, P = .002) and 532 nm (r(2) = 0.004, P = .67). The associations between mitochondria function and tissue damage were: state 3 respiration (r(2) = 0.43, P = .0004), state 4 respiration (r(2) = 0.03, P = 0.38), RCR (r(2) = 0.28, P = .007), and membrane swelling (r(2) = 0.02, P = .43). The intensity of fluorescence emitted by tissue excited by laser, especially at a wave length of 442 nm, was determined in real time. Mitochondrial state 3 respiration and respiratory control ratio also exhibited good correlations with the grade of ischemic tissue damage.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Immunologic aspects of West syndrome and evidence of plasma inhibitory effects on T cell function

OBJETIVO: O objetivo deste estudo foi determinar o perfil da deficiência imune em um grupo bem definido de epilepsia: crianças com síndrome de West (SW) e seus padrões EEG de evolução, idade-dependentes, como os complexos onda-aguda- onda lenta generalizadas da síndrome de Lenox-Gastaut (SLG) e as pontas multifocais independentes (PMI). MÉTODO: Um grupo de 50 crianças, 33 com SW, 10 com SLG, 7 com PMI e 20 crianças sadias (controle) foram avaliadas em relação aos seguintes parâmetros:determinação de subpopulações de linfócitos T (CD1, CD3, CD4 e CD8), relação CD4/CD8 e resposta proliferativa de linfócitos frente a fitohemaglutinina (PHA), na presença de plasma autólogo ou de plasma AB (homólogo). A prova cutânea de sensibilização ao Dinitroclorobenzeno (DNCB) foi realizada apenas nos pacientes. Os níveis séricos de IgG, IgA e IgM foram comparados aos valores normais em crianças Brasileiras, em diferentes faixas etárias. RESULTADOS: A resposta ao DNCB foi ausente ou fracamente reativa em 76% dos pacientes. Níveis séricos elevados de IgG (45,7%) e de IgM (61,4%) e baixos de IgA (23,9%) foram detectados nos pacientes. A determinação das subpopulações de linfócitos T em sangue periférico mostrou: deficiência nas proporções de células CD3+ (p<0,05) e de CD4+ (p<0,05), aumento de CD8+ (p<0,01) e diminuição da relação CD4 / CD8 (p<0,001). A proporção de células CD1+ no grupo controle manteve-se menor que 3%, enquanto que em 18% dos pacientes esses níveis variaram entre 3 e 11%. A resposta proliferativa de linfócitos frente a PHA revelou índices blastogênicos significativamente mais baixos apenas quando células dos pacientes foram cultivadas na presença do próprio plasma (plasma autólogo). Quando estas células foram cultivadas na presença de plasma AB, não se evidenciou diferença significativa em relação ao grupo controle. CONCLUSÃO: A imunodeficiência na SW caracterizou-se por: anergia, alteração de imunidade mediada por células e dos níveis de imunoglobulinas, presença de timócitos imaturos na circulação periférica e deficiência funcional de linfócitos T induzida por fatores plasmáticos inibidores. Discutem-se as principais evidências de disfunção imune como imunodeficiência e autoimunidade.

Transport properties of the transverse charge-density-wave system Fe3O2BO3

We study the transport properties of the charge-density-wave system Fe3O2BO3. ac conductivity measurements for different frequencies are presented for temperatures above and below the structural transition. dc conductivity, as a function of temperature and pressure, yields the variation of the transition temperature with external pressure. Below this transition the conductivity is thermally activated in a wide range of temperature and the gap obtained is strongly pressure dependent. The ac conductivity at sufficiently low temperatures below the transition is ascribed to the excitation of local defects associated with domain walls and which are characteristic of the one-dimensional nature of the Fe3O2BO3 system.

A PZT-based technique for SHM using the coherence function

This paper presents a new approach for damage detection in structural health monitoring systems exploiting the coherence function between the signals from PZT (Lead Zirconate Titanate) transducers bonded to a host structure. The physical configuration of this new approach is similar to the configuration used in Lamb wave based methods, but the analysis and operation are different. A PZT excited by a signal with a wide frequency range acts as an actuator and others PZTs are used as sensors to receive the signal. The coherences between the signals from the PZT sensors are obtained and the standard deviation for each coherence function is computed. It is demonstrated through experimental results that the standard deviation of the coherence between the signals from the PZTs in healthy and damaged conditions is a very sensitive metric index to detect damage. Tests were carried out on an aluminum plate and the results show that the proposed methodology could be an excellent approach for structural health monitoring (SHM) applications.

Asymptotic approach for the nonlinear equatorial long wave interactions

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are disccussed. In particular, we discuss the implications of the results for El Nĩo and the Madden-Julian in connection with other scales of time and spatial variability. © Published under licence by IOP Publishing Ltd.

Detection of buried pipes using a shear wave ground surface vibration technique

A major UK initiative, entitled 'Mapping the Underworld', is seeking to address the serious social, environmental and economic consequences arising from an inability to locate the buried utility service infrastructure without resorting to extensive excavations. Mapping the Underworld aims to develop and prove the efficacy of a multi-sensor device for accurate remote buried utility service detection, location and, where possible, identification. One of the technologies to be incorporated in the device is low-frequency vibro-acoustics, and the application of this technology for detecting buried infrastructure is currently being investigated. Here, a shear wave ground vibration technique for detecting buried pipes is described. For this technique, shear waves are generated at the ground surface, and the resulting ground surface vibrations measured, using geophones, along a line traversing the anticipated run of the pipe. Measurements were made at a test site with a single pressurized polyethylene mains water pipe. Time-extended signals were employed to generate the illuminating wave. Cross-correlation functions between the measured ground velocities and a reference measurement adjacent to the excitation were then calculated and summed using a stacking method to generate a cross-sectional image of the ground. The wide cross-correlation peaks caused by high ground attenuation were partially compensated for by using a generalized cross-correlation function called the smoothed coherence transform. To mitigate the effects of other potential sources of vibration in the vicinity, the excitation signal was used as an additional reference when calculating the generalized cross-correlation functions. For two out of three tests, the pipe was detected, indicating that this technique will be a valuable addition to the Mapping the Underworld armoury.

The calcium wave model of the perception-action cycle: Evidence from semantic relevance in memory experiments

We present a general model of brain function (the calcium wave model), distinguishing three processing modes in the perception-action cycle. The model provides an interpretation of the data from experiments on semantic memory conducted by the authors. © 2013 Pereira Jr, Santos and Barros.

Reconstruction of the gravitational wave signal h(t) during the Virgo science runs and independent validation with a photon calibrator

The Virgo detector is a kilometer-scale interferometer for gravitational wave detection located near Pisa (Italy). About 13 months of data were accumulated during four science runs (VSR1, VSR2, VSR3 and VSR4) between May 2007 and September 2011, with increasing sensitivity. In this paper, the method used to reconstruct, in the range 10 Hz-10 kHz, the gravitational wave strain time series h(t) from the detector signals is described. The standard consistency checks of the reconstruction are discussed and used to estimate the systematic uncertainties of the h(t) signal as a function of frequency. Finally, an independent setup, the photon calibrator, is described and used to validate the reconstructed h(t) signal and the associated uncertainties. The systematic uncertainties of the h(t) time series are estimated to be 8% in amplitude. The uncertainty of the phase of h(t) is 50 mrad at 10 Hz with a frequency dependence following a delay of 8 mu s at high frequency. A bias lower than 4 mu s and depending on the sky direction of the GW is also present.

Long-term obesity promotes alterations in diastolic function induced by reduction of phospholamban phosphorylation at serine-16 without affecting calcium handling

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

Ultrasound Transient Shear Wave Elasticity Imaging for Tendon Tissue

Degeneration of tendon tissue is a common cause of tendon dysfunction with the symptoms of repeated episodes of pain and palpable increase of tendon thickness. Tendon mechanical properties are directly related to its physiological composition and the structural organization of the interior collagen fibers which could be altered by tendon degeneration due to overuse or injury. Thus, measuring mechanical properties of tendon tissue may represent a quantitative measurement of pain, reduced function, and tissue health. Ultrasound elasticity imaging has been developed in the last two decades and has proved to be a promising tool for tissue elasticity imaging. To date, however, well established protocols of tendinopathy elasticity imaging for diagnosing tendon degeneration in early stages or late stages do not exist. This thesis describes the re-creation of one dynamic ultrasound elasticity imaging method and the development of an ultrasound transient shear wave elasticity imaging platform for tendon and other musculoskeletal tissue imaging. An experimental mechanical stage with proper supporting systems and accurate translating stages was designed and made. A variety of high-quality tissue-mimicking phantoms were made to simulate homogeneous and heterogeneous soft tissues as well as tendon tissues. A series of data acquisition and data processing programs were developed to collect the displacement data from the phantom and calculate the shear modulus and Young’s modulus of the target. The imaging platform was found to be capable of conducting comparative measurements of the elastic parameters of the phantoms and quantitatively mapping elasticity onto ultrasound B-Mode images. This suggests the system has great potential for not only benefiting individuals with tendinopathy with an earlier detection, intervention and better rehabilitation, but also for providing a medical tool for quantification of musculoskeletal tissue dysfunction in other regions of the body such as the shoulder, elbow and knee.

Modulation transfer function and optical quality after bilateral implantation of a+3.00 D versus a+4.00 D multifocal intraocular lens

PURPOSE: To determine whether the improvement in intermediate vision after bilateral implantation of an aspheric multifocal intraocular lens (IOL) with a +3.00 diopter (D) addition (add) occurs at the expense of optical quality compared with the previous model with a +4.00 D add. SETTING: Department of Ophthalmology, University of Sao Paulo, Sao Paulo, Brazil. DESIGN: Prospective randomized double-masked comparative clinical trial. METHODS: One year after bilateral implantation of Acrysof Restor SN6AD1 +3.00 D IOLs or Acrysof Restor SN6AD3 +4.00 D IOLs, optical quality was evaluated by analyzing the in vivo modulation transfer function (MTF) and point-spread function (expressed as Strehl ratio). The Strehl ratio and MTF curve with a 4.0 pupil and a 6.0 mm pupil were measured by dynamic retinoscopy aberrometry. The uncorrected and corrected distance visual acuities at 4 m, uncorrected and distance-corrected near visual acuities at 40 cm, and uncorrected and distance-corrected intermediate visual acuities at 50 cm, 60 cm, and 70 cm were measured. RESULTS: Both IOL groups comprised 40 eyes of 20 patients. One year postoperatively, there were no statistically significant between-group differences in the MTF or Strehl ratio with either pupil size. There were no statistically significant between-group differences in distance or near visual acuity. Intermediate visual acuity was significantly better in the +3.00 D IOL group. CONCLUSION: Results indicate that the improvement in intermediate vision in eyes with the aspheric multifocal +3.00 D add IOL occurred without decreasing optical quality over that with the previous version IOL with a +4.00 D add.