On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled 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 non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Antimony orthophosphate glasses with large nonlinear refractive indices, low two-photon absorption coefficients, and ultrafast response

Antimony glasses based on the composition Sb2O3-SbPO4 were prepared and characterized. The samples present high refractive index, good transmission from 380 to 2000 nm, and high thermal stability. The nonlinear refractive index, n(2), of the samples was studied using the optical Kerr shutter technique at 800 nm. The third-order correlation signals between pump and probe pulses indicate ultrafast response (<100 fs) for all compositions. Enhancement of n(2) was observed by adding lead oxide to the Sb2O3-SbPO4 composition. Large values of n(2)approximate to10(-14) cm(2)/W and negligible two-photon absorption coefficients (smaller than 0.01 cm/GW) were determined for all samples. The glass compositions studied present appropriate figure-of-merit for all-optical switching applications. (C) 2005 American Institute of Physics.

Diffusion coefficients during osmotic dehydration of tomatoes in ternary solutions

The apparent diffusion coefficients for sucrose, NaCl and water during osmotic dehydration of tomatoes in ternary solutions were determined. Long time experiments (up to 60 h) were carried out in order to determine equilibrium concentrations inside tomatoes, whereas short time experiments (up to 4 h) were performed to provide detailed information on kinetics of water loss and solids gain at the beginning of osmotic treatment. The mass transfer rates for water and solutes showed to be dependent of NaCl and sucrose concentrations in osmotic solution and simple regression models as functions of solutes concentration were determined for diffusion coefficients. Salt and sucrose diffusivities showed to be interdependent, with increasing NaCl concentration causing the enhancement of water loss, at the same time that higher sucrose contents hindered the excessive salt penetration. (C) 2003 Elsevier Ltd. All rights reserved.

GENERATING FUNCTION FOR CLEBSCH-GORDAN-COEFFICIENTS, OF THE SUQ(2) QUANTUM ALGEBRA

Some methods have been developed to calculate the su(q)(2) Clebsch-Gordan coefficients (CGC). Here we develop a method based on the calculation of Clebsch-Gordan generating functions through the use of 'quantum algebraic' coherent states. Calculating the su(q)(2) CGC by means of this generating function is an easy and straightforward task.

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].

Orbital perturbations using geopotential coefficients up to high degree and order: Highly eccentric orbits

Several methods have been proposed for calculations of the eccentricity function for a high value of the eccentricity, however they cannot be used when the high degree and order coefficients of gravity fields are taken into account. The method proposed by Wnuk(1) is numerically stable in this case, but when is used. a large number of terms occurs in formulas for geopotential perturbations. In this paper we propose an application of expansions of some functions of the eccentric anomaly E as well as Hansen coefficients in power series of (e - e*), where e* is a fixed value of the eccentricity derived by da Silva Fernandes(2,3,4). These series are convergent for all e < 1.

Concentration profiles and effective diffusion coefficients of sucrose and water in osmo-dehydrated apples

The spatial distribution of water and sugars in half-fresh apples dehydrated in sucrose solutions (30% and 50% w/w, 27 degrees C) for 2, 4 and 8 h, was determined. Each half was sliced as from the exposed surface. The density, water and sugar contents were determined for each piece. A mathematical model was fitted to the experimental data of the water and sucrose contents considering the overall flux and tissue shrinkage. A numerical method of finite differences permitted the calculation of the effective diffusion coefficients as a function of concentration, using material coordinates and integrating the two differential equations (for water and sucrose) simultaneously. The coefficients obtained were one or even two orders of magnitude lower than those for pure solutions and presented unusual concentration dependence. The behaviour of the apple tissue was also studied using light microscopy techniques to obtain images of the osmotically treated pieces (20%, 30% and 50% w/w sucrose solutions for 2, 4 and 8 h). (c) 2006 Elsevier Ltd. All rights reserved.

Evaluation of water and sucrose diffusion coefficients in potato tissue during osmotic concentration

The water and sucrose effective diffusion coefficients behavior were studied in potato tubers immersed in aqueous sucrose solution, 50% (w/,A), at 27 degreesC. Water and sucrose concentration profiles were measured as function of the position for 3, 6 and 12 h of immersion. These were adjusted to a mathematical model for three components that take into account the bulk flow in a shrinking tissue and the concentration dependence of the diffusion coefficients.The binary effective coefficients were an order of magnitude lower than those for pure solutions of sucrose. These coefficients show an unusual concentration dependence. Analysis of these coefficients as functions of the concentration and position demonstrates that, cellular tissue promotes high resistance to diffusion in the tuber and also the elastic contraction of material influences the species diffusion. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

EVALUATION OF DIFFUSION-COEFFICIENTS IN OSMOTIC CONCENTRATION OF BANANAS (MUSA-CAVENDISH LAMBERT)

The effect of time of exposure, solution concentration and temperature on the osmotic concentration of banana (slices of 11 mm thickness) was studied in aqueous sucrose solutions. The selectivity of the cellular tissues was reduced by steam blanching the banana slices before osmotic treatment. Effective diffusion coefficients for the loss of water and the increase in sucrose content were determined according to Fick's Law applied to a two-dimensional body; calculated on the basis of the concentration of various components in the liquid phase impenetrating the fruit. These coefficients revealed values similar to binary diffusion coefficients for pure sucrose solutions.