A Equação-Mestra: atingindo o equilíbrio

In the last years, a great interest in nonequilibrium systems has been witnessed. Although the Master Equations are one of the most common methods used to describe these systems, the literature about these equations is not straightforward due to the mathematical framework used in their derivations. The goals of this work are to present the physical concepts behind the Master Equations development and to discuss their basic proprieties via a matrix approach. It is also shown how the Master Equations can be used to model typical nonequilibrium processes like multi-wells chemical reactions and radiation absorption processes.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Turbulent magnetic pumping in a Babcock-Leighton solar dynamo model

Context. The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. Aims. We explore the effects of turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. Methods. As a first step, only vertical pumping has been considered through the inclusion of a radial diamagnetic term in the induction equation. In the second step, a latitudinal pumping term was included and then, a near-surface shear was included. Results. The results reveal the importance of the pumping mechanism in solving current limitations in mean field dynamo modeling, such as the storage of the magnetic flux and the latitudinal distribution of the sunspots. If a meridional flow is assumed to be present only in the upper part of the convective zone, it is the full turbulent pumping that regulates both the period of the solar cycle and the latitudinal distribution of the sunspot activity. In models that consider shear near the surface, a second shell of toroidal field is generated above r = 0.95 R(circle dot) at all latitudes. If the full pumping is also included, the polar toroidal fields are efficiently advected inwards, and the toroidal magnetic activity survives only at the observed latitudes near the equator. With regard to the parity of the magnetic field, only models that combine turbulent pumping with near-surface shear always converge to the dipolar parity. Conclusions. This result suggests that, under the Babcock-Leighton approach, the equartorward motion of the observed magnetic activity is governed by the latitudinal pumping of the toroidal magnetic field rather than by a large scale coherent meridional flow. Our results support the idea that the parity problem is related to the quadrupolar imprint of the meridional flow on the poloidal component of the magnetic field and the turbulent pumping positively contributes to wash out this imprint.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Scalar resonances in a unitary pi pi S-wave model for D(+)->pi(+)pi(-)pi(+)

We propose a model for D(+)->pi(+)pi(-)pi(+) decays following experimental results which indicate that the two-pion interaction in the S wave is dominated by the scalar resonances f(0)(600)/sigma and f(0)(980). The weak decay amplitude for D(+)-> R pi(+), where R is a resonance that subsequently decays into pi(+)pi(-), is constructed in a factorization approach. In the S wave, we implement the strong decay R ->pi(+)pi(-) by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range m(pi pi)(2) from threshold to about 3 GeV(2). In order to reproduce the experimental Dalitz plot for D(+)->pi(+)pi(-)pi(+), we include contributions beyond the S wave. For the P wave, dominated by the rho(770)(0), we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the f(2)(1270) and rho(1450)(0). The major achievement is a good reproduction of the experimental m(pi pi)(2) distribution, and of the partial as well as the total D(+)->pi(+)pi(-)pi(+) branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a by-product, we predict a value for the poorly known D ->sigma transition form factor at q(2)=m pi(2).

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

An improved continuous medium technique for structural frame analysis

This paper presents an improved constitutive equation of frame in the context of continuous medium technique. This improved constitutive equation, which is a consistent formulation of column global bending, is applicable to a complete class of frameworks including the ideal shear frame panel, for which the beams are assumed to be rigid, and the associated column system, for which the rigidity of beams is negligible. Global buckling and second-order effects of the frame structure are discussed. The main results can be extended to other types of lateral stiffening elements as built-up columns. A worked example is presented in order to compare the main results with those obtained by the classic matrix method. Copyright (C) 2007 John Wiley & Sons, Ltd.

Further improvements on impedance-based fault location for power distribution systems

In this study, further improvements regarding the fault location problem for power distribution systems are presented. The proposed improvements relate to the capacitive effect consideration on impedance-based fault location methods, by considering an exact line segment model for the distribution line. The proposed developments, which consist of a new formulation for the fault location problem and a new algorithm that considers the line shunt admittance matrix, are presented. The proposed equations are developed for any fault type and result in one single equation for all ground fault types, and another equation for line-to-line faults. Results obtained with the proposed improvements are presented. Also, in order to compare the improvements performance and demonstrate how the line shunt admittance affects the state-of-the-art impedance-based fault location methodologies for distribution systems, the results obtained with two other existing methods are presented. Comparative results show that, in overhead distribution systems with laterals and intermediate loads, the line shunt admittance can significantly affect the state-of-the-art methodologies response, whereas in this case the proposed developments present great improvements by considering this effect.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Computer-Assisted Numerical Analysis for Oxygen and Carbon Dioxide Mass Transfer in Blood Oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that V(CO2) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO2), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (Q(G)/Q(B)) shows that V(CO2) variation with the gas flow is almost linear up to Q(G)/Q(B) = 2.0. V(O2) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the V(O2) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G)/Q(B) > 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO2) comprise the whole fiber bundle.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Development and In Vitro Evaluation of Propranolol Hydrochloride Controlled Release Tablets Using HPMC as Matrix Former

The purpose of this paper was to produce controlled-release matrices with 120 mg of propranolol hydrochloride (PHCl) employing hydroxypropyl methylcellulose (HPMC, Methocel (R) K100) as the gel forming barrier. Although this class of polymers has been commonly used for direct compression, with the intent of use reduced polymer concentrations to achieve controlled drug release, in this study tablets were produced by the wet granulation process. HPMC percentages ranged from 15-34 % and both soluble and non soluble diluents were tested in the 10 proposed tablet compositions. Dissolution testing of matrices was performed over a 12 h period in 1.2 pH medium (the first 2 h) and in pH 6.8 (10 h). Dissolution kinetic analysis was performed by applying Zero-order, First-order and Higuchi models with the aim of elucidating the drug release mechanism. All physical-chemical characteristics such as average weight, friability, hardness, diameter, height, and drug content were in accordance to the pharmacopeial specifications. Taking into account that PHCl is a very soluble drug, low concentrations (15 %) of HPMC were sufficient to reduce the drug release and to promote controlled release of PHCl, presenting good dissolution efficiencies, between 50 % and 63 %. The Higuchi model has presented the best fit to the 15 % HPMC formulations, indicating that the main release mechanism was diffusion. It could be concluded that the application of the wet granulation method reduced matrices erosion and promoted controlled release of the drug at low HPMC percentages.