Many-body system with a four-parameter family of point interactions in one dimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual delta-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the delta-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is nor satisfied except when the four-parameter family is essentially reduced to the delta-function potential.

Charged three-body system with arbitrary masses near conformal invariance

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

On the control of a non-ideal engineering system: A friction-driven oscillating system with limited power supply

In this work a switching feedback controller for stick-slip compensation of a 2-DOF mass-spring-belt system which interacts with an energy source of limited power supply (non-ideal case) is developed. The system presents an oscillatory behavior due to the stick-slip friction. As the system equilibrium for a conventional feedback controller is not the origin, a switching control law combining a state feedback term and a discontinuous term is proposed to regulate the position of the mass. The problem of tracking a desired periodic trajectory is also considered. The feedback system is robust with respect to the friction force that is assumed to be within known upper and lower bounds.

On stick-slip homoclinic chaos and bifurcations in a mechanical system with dry friction

In this paper we consider a self-excited mechanical system by dry friction in order to study the bifurcational behavior of the arisen vibrations. The oscillating system consists of a mass block-belt-system which is self-excited by static and Coulomb friction. We analyze the system behavior numerically through bifurcation diagrams, phase portraits, frequency spectra and Poincare maps, which show the existence of nonhomoclinic and homoclinic chaos and a route to homoclinic chaos. The homoclinic chaos is also analyzed analytically via the Melnikov prediction method. The system dynamic is characterized by the existence of two potential wells in the phase plane which exhibit rich bifurcational and chaotic behavior.

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sequential injection analysis system with spectrophotometric detection for determination of norfloxacin and ciprofloxacin in pharmaceutical formulations

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

Solution of the Poisson-Boltzmann equation for a system with four ionic species

The analytical solution of the Poisson-Boltzmann equation in an electrolyte with four ionic species (2:2:1:1), in the presence of a charged planar membrane or surface is presented. The function describing the mean electrical potential provides a convenient description that helps the understanding of electrical processes of biological interest.

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.

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].

3-BOSON SYSTEM WITH ABSORPTIVE SHORT-RANGE POTENTIAL

We study the properties of the three-boson system with absorption, through a short range interaction in the limit where the range reduces to zero. We derive an analytic expression for the three-boson width that relates it to the real part of the three-boson energy, two-boson binding energy and decay constant. One of the characteristics of this expression is that, in this limit, the ratio between the width and the three-boson binding energy is proportional to the range.

Spectrophotometric determination of phosphite in fertilizers in a flow injection system with online sample preparation

A flow injection system with online sample preparation is proposed for the determination of phosphite in liquid fertilizers by spectrophotometry. After loop-based injection, phosphite is oxidized by an acidic permanganate solution (1.0 10(-2) mol L-1 KMnO4 + 1.0 mol L-1 H2SO4) in a heated reactor (50 degreesC). The phosphate generated is then determined by the molybdenum blue method. Influence of flow rates, temperature, and concentration and order of addition of reagents, sample volume, and reactor configuration for the blue complex formation on recorded signals were investigated. The pow system was applied to phosphite determination in commercial samples of liquid fertilizers. The proposed system handles about 80 samples per hour [0.05-0.40% (w/v) H3PO3; R = 0,9998], consuming about 80 muL sample, 1 mg KMnO4, 25 mg (NH)(6)Mo7O24, and Ia mg ascorbic acid per determination. Results are precise [relative standard deviation less than or equal to 3.5% for 0.1% (w/v) H3PO3, n = 12] and in agreement with those obtained by gravimetry at 95% confidence level. (C) 2000 John Wiley & Sons, Inc.