PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

An integrable evolution equation for surface waves in deep water

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed.

Simplified design methods of treated timber structures for shore, beach, and marina construction /

"March 1976."

Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.

Comparison of Photovoltaic panel’s standard and simplified models

Shockley diode equation is basic for single diode model equation, which is overly used for characterizing the photovoltaic cell output and behavior. In the standard equation, it includes series resistance (Rs) and shunt resistance (Rsh) with different types of parameters. Maximum simulation and modeling work done previously, related to single diode photovoltaic cell used this equation. However, there is another form of the standard equation which has not included Series Resistance (Rs) and Shunt Resistance (Rsh) yet, as the Shunt Resistance is much bigger than the load resistance and the load resistance is much bigger than the Series Resistance. For this phenomena, very small power loss occurs within a photovoltaic cell. This research focuses on the comparison of two forms of basic Shockley diode equation. This analysis describes a deep understanding of the photovoltaic cell, as well as gives understanding about Series Resistance (Rs) and Shunt Resistance (Rsh) behavior in the Photovoltaic cell. For making estimation of a real time photovoltaic system, faster calculation is needed. The equation without Series Resistance and Shunt Resistance is appropriate for the real time environment. Error function for both Series resistance (Rs) and Shunt resistances (Rsh) have been analyzed which shows that the total system is not affected by this two parameters' behavior.

Modelagem matemática e simulação numérica do resfriamento rápido de morango com ar forçado

This work approaches the forced air cooling of strawberry by numerical simulation. The mathematical model that was used describes the process of heat transfer, based on the Fourier's law, in spherical coordinates and simplified to describe the one-dimensional process. For the resolution of the equation expressed for the mathematical model, an algorithm was developed based on the explicit scheme of the numerical method of the finite differences and implemented in the scientific computation program MATLAB 6.1. The validation of the mathematical model was made by the comparison between theoretical and experimental data, where strawberries had been cooled with forced air. The results showed to be possible the determination of the convective heat transfer coefficient by fitting the numerical and experimental data. The methodology of the numerical simulations was showed like a promising tool in the support of the decision to use or to develop equipment in the area of cooling process with forced air of spherical fruits.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

Simplified flow cytometric assay to detect minimal residual disease in childhood with acute lymphoblastic leukemia

The detection of minimal residual disease (MRD) is an important prognostic factor in childhood acute lymphoblastic leukemia (ALL) providing crucial information on the response to treatment and risk of relapse. However, the high cost of these techniques restricts their use in countries with limited resources. Thus, we prospectively studied the use of flow cytometry (FC) with a simplified 3-color assay and a limited antibody panel to detect MRD in the bone marrow (BM) and peripheral blood (PB) of children with ALL. BM and PB samples from 40 children with ALL were analyzed on days (d) 14 and 28 during induction and in weeks 24-30 of maintenance therapy. Detectable MRD was defined as > 0.01% cells expressing the aberrant immunophenotype as characterized at diagnosis among total events in the sample. A total of 87% of the patients had an aberrant immunophenotype at diagnosis. On d14, 56% of the BM and 43% of the PB samples had detectable MRD. On d28, this decreased to 45% and 31%, respectively. The percentage of cells with the aberrant phenotype was similar in both BM and PB in T-ALL but about 10 times higher in the BM of patients with B-cell-precursor ALL. Moreover, MRD was detected in the BM of patients in complete morphological remission (44% on d14 and 39% on d28). MRD was not significantly associated to gender, age, initial white blood cell count or cell lineage. This FC assay is feasible, affordable and readily applicable to detect MRD in centers with limited resources.

Fracionamento dos carboidratos pelas equações do Cornell Net Carbohydrate and Protein System de três cultivares de girassol na presença ou não de irrigação

Objetivou-se quantificar as frações de carboidratos pelas equações do Cornell Net Carbohydrate and Protein System (CNCPS) de três cultivares de girassol (Helianthus annuus L.) cultivados na presença ou não de irrigação. A utilização de uma preparação fibrosa, denominada parede celular (PC), nas equações da CNCPS, em substituição à fibra em detergente neutro (FDN) não promoveu diferenças nas frações de carboidratos B1 e C, mas influenciou as frações A e B2. Como os valores da fração B1, obtidos pelo modelo CNCPS foram menores que os teores de amido e pectina determinados em laboratório, supõe-se que a pectina e outros oligossacarídeos da parede celular, solubilizados pela solução de detergente neutro (fibra solúvel), nunca fizeram parte da fração B1, e sim da fração A. Apesar de os carboidratos da fibra solúvel apresentarem elevadas taxas de degradação, não parece adequada a caracterização da fibra solúvel na fração A. Parece mais adequado que a fibra solúvel (que inclui a pectina) seja alocada a uma fração exclusivamente sua, que pode ser a fração B2, e que seja criada uma nova fração, a B3, para os carboidratos digeríveis da parede celular. Assim, a fração B1 seria composta apenas de amido. A equação da fração C, que estima os carboidratos indigeríveis da parede celular, pode ser simplificada, relacionando a fração indigerível ao teor de lignina na matéria seca, e não à FDN isenta de cinzas e proteína, como atualmente utilizado. Esta proposta tem implicações práticas, uma vez que a fração indigerível da parede celular tem sido expressa em relação à FDN, e não na MS, com base no fato de que os efeitos inibitórios da lignina ocorrem sobre os componentes fibrosos da parede celular vegetal, e não sobre o conteúdo celular.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

A simplified minimal residual disease polymerase chain reaction method at early treatment points can stratify children with acute lymphoblastic leukemia into good and poor outcome groups

Background Minimal residual disease is an important independent prognostic factor in childhood acute lymphoblastic leukemia. The classical detection methods such as multiparameter flow cytometry and real-time quantitative polymerase chain reaction analysis are expensive, time-consuming and complex, and require considerable technical expertise. Design and Methods We analyzed 229 consecutive children with acute lymphoblastic leukemia treated according to the GBTLI-99 protocol at three different Brazilian centers. Minimal residual disease was analyzed in bone marrow samples at diagnosis and on days 14 and 28 by conventional homo/heteroduplex polymerase chain reaction using a simplified approach with consensus primers for IG and TCR gene rearrangements. Results At least one marker was detected by polymerase chain reaction in 96.4%, of the patients. By combining the minimal residual disease results obtained on days 14 and 28, three different prognostic groups were identified: minimal residual disease negative on days 14 and 28, positive on day 14/negative on day 28, and positive on both. Five-year event-free survival rates were 85%, 75.6%,, and 27.8%, respectively (p<0.0001). The same pattern of stratification held true for the group of intensively treated children. When analyzed in other subgroups of patients such as those at standard and high risk at diagnosis, those with positive B-derived CD10, patients positive for the TEL/AML1 transcript, and patients in morphological remission on a day 28 marrow, the event-free survival rate was found to be significantly lower in patients with positive minimal residual disease on day 28. Multivariate analysis demonstrated that the detection of minimal residual disease on day 28 is the most significant prognostic factor. Conclusions This simplified strategy for detection of minimal residual disease was feasible, reproducible, cheaper and simpler when compared with other methods, and allowed powerful discrimination between children with acute lymphoblastic leukemia with a good and poor outcome.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.