Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Effects of 10% carbamide peroxide bleaching materials on enamel microhardness

Purpose: To evaluate the microhardness of enamel treated with two different 10% carbamide peroxide bleaching materials at different time intervals. Materials and Methods: Two bleaching agents were analyzed: Opalescence (OPA) and Rembrandt (REM). The control group (CON) consisted of dental fragments maintained in artificial saliva. Bleaching was accomplished for 8 hrs per day and stored during the remaining time in an individual recipient with artificial saliva. Enamel microhardness testing was performed before the initial exposure to the treatments and after 1, 7, 14, 21, 28, 35 and 42 days. Results: the ANOVA, followed by the Bartlet and Tukey tests, showed significant differences for treatments (P < 0.00001) from day 7-day 42. From the 7th to the 14th day, OPA presented an increase of enamel microhardness over time while REM presented a decrease of microhardness. Statistical differences were not found between REM and the control group (OPA > CON = REM). From the 21st-35th day, enamel fragments bleached with OPA and REM presented a decrease of microhardness. Statistical differences of microhardness were verified among all the treatments (OPA > CON > REM). on the day 42, statistical differences were not found between OPA and the control group, but they were found between REM and the control group (OPA = CON > REM). The polynomial regression showed an increase of microhardness for OPA until the 21st day, followed by a decrease of microhardness up to the 42nd day. A decrease of microhardness for REM was verified. There were alterations in enamel microhardness as a function of bleaching time when using the two different 10% carbamide peroxide whiteners. Over a 42-day treatment time, bleaching with REM agent caused a decrease in enamel microhardness. The OPA agent initially increased the microhardness, then returned to the control level. Different bleaching materials with the same concentration of carbamide peroxide have different effects on the enamel.

Buffalos milk yield analysis using random regression models

Data comprising 1,719 milk yield records from 357 females (predominantly Murrah breed), daughters of 110 sires, with births from 1974 to 2004, obtained from the Programa de Melhoramento Genetic de Bubalinos (PROMEBUL) and from records of EMBRAPA Amazonia Oriental - EAO herd, located in Belem, Para, Brazil, were used to compare random regression models for estimating variance components and predicting breeding values of the sires. The data were analyzed by different models using the Legendre's polynomial functions from second to fourth orders. The random regression models included the effects of herd-year, month of parity date of the control; regression coefficients for age of females (in order to describe the fixed part of the lactation curve) and random regression coefficients related to the direct genetic and permanent environment effects. The comparisons among the models were based on the Akaike Infromation Criterion. The random effects regression model using third order Legendre's polynomials with four classes of the environmental effect were the one that best described the additive genetic variation in milk yield. The heritability estimates varied from 0.08 to 0.40. The genetic correlation between milk yields in younger ages was close to the unit, but in older ages it was low.

Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Row-column response surface designs

Factorial experiments are widely used in industry to investigate the effects of process factors on quality response variables. Many food processes, for example, are not only subject to variation between days, but also between different times of the day. Removing this variation using blocking factors leads to row-column designs. In this paper, an algorithm is described for constructing factorial row-column designs when the factors are quantitative, and the data are to be analysed by fitting a polynomial model. The row-column designs are constructed using an iterative interchange search, where interchanges that result in an improvement in the weighted mean of the efficiency factors corresponding to the parameters of interest are accepted. Some examples illustrating the performance of the algorithm are given.

Modeling thermal conductivity, specific heat, and density of milk: A neural network approach

The accurate determination of thermophysical properties of milk is very important for design, simulation, optimization, and control of food processing such as evaporation, heat exchanging, spray drying, and so forth. Generally, polynomial methods are used for prediction of these properties based on empirical correlation to experimental data. Artificial neural networks are better Suited for processing noisy and extensive knowledge indexing. This article proposed the application of neural networks for prediction of specific heat, thermal conductivity, and density of milk with temperature ranged from 2.0 to 71.0degreesC, 72.0 to 92.0% of water content (w/w), and 1.350 to 7.822% of fat content (w/w). Artificial neural networks presented a better prediction capability of specific heat, thermal conductivity, and density of milk than polynomial modeling. It showed a reasonable alternative to empirical modeling for thermophysical properties of foods.

Monotonicity of the zeros of orthogonal polynomials through related measures

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered. (c) 2005 Elsevier B.V. All rights reserved.

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

Influence of temperature and water and fat contents on the thermophysical properties of milk

Heat capacity, thermal conductivity, and density of whole milk, skimmed milk, and partially skimmed milk were determined at concentrations varying from (72.0 to 92.0) mass % water content and from (0.1 to 7.8) mass % fat content, at temperatures ranging from (275.15 to 344.15) K. Heat capacity and thermal conductivity varied from (3.4 to 4.1) J(.)g(-) K-1.(-1) and from (0.5 to 0.6) W(.)m(-1) K-1.(-1), respectively. Density varied from (1011.8 to 1049.5) kg(.)m(-3). Polynomial functions were used to model the dependence of the properties upon the studied variables. A linear relationship was obtained for all the properties. In the tested range, water content exhibited a greater influence on the properties, while fat content showed a smaller influence.

Density, heat capacity and thermal conductivity of liquid egg products

Density, heat capacity and thermal conductivity of liquid egg products, such as egg white, egg yolk, whole egg and various white and yolk blends, were determined as affected by temperature and water content ranging from 273 to 311 K and 51.8 to 88.2% (mass), respectively. Polynomial models fitted the experimental data very well, showing a linear relationship both for temperature and water content. (c) 2005 Published by Elsevier Ltd.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

Optimal capacitor placement in radial distribution networks

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (Non Polynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

ANALYSIS OF CURVED EDGE PLATES BY THE BOUNDARY-ELEMENT METHOD

The aim of this work is to present a formulation of the boundary element method to analyse elastic and isotropic plates with curved boundaries. In this study the plate boundary is approximated, along each element, by a second degree polynomial relation or by a circular arch, in order to better represent the real boundary. The numerical integration is performed by the self-adaptive coordinate transformation proposed by Telles. The effective shear forces are approximated by concentrated reactions applied at the boundary element nodes, according to the alternative formulation introduced by Paiva. Some examples are presented to demonstrate the better accuracy obtained with the proposed elements.