The Schrodinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Construction of time-dependent dynamical invariants: A new approach

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

Basins of attraction changes by amplitude constraining of oscillators with limited power supply

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity. (c) 2005 Elsevier Ltd. All rights reserved.

On the appearance of a Hopf bifurcation in a non-ideal mechanical problem

In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. (C) 2003 Elsevier Ltd. All rights reserved.

A theoretical study of the A(2)Sigma(+)-X-2 Pi system of the SiP molecule

The A (2)Sigma(+) and X(2)Pi electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrodinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A(2)Sigma(+)-X(2)Pi system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A(2)Sigma(+) state, taking into account the spin-orbit diagonal correction to the X(2)Pi state, decrease from a value of 138 ms at v' = 0 to 0.48 ms at v' = 8, and, for the X(2)Pi state, from 2.32 s at v = 1 to 0.59 s at v = 5. Vibrational and rotational transitions are expected to be relatively strong.

Control and chaos for vibro-impact and non-ideal oscillators

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

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper The mathematical model of the system is represented by coupled non-linear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation. [DOI: 10.1115/1.3124783]

On energy transfer between vibrating systems under linear and nonlinear interactions

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

On energy transfer between linear and nonlinear oscillators

In this paper energy transfer in a dissipative mechanical system is analysed. Such system is composed of a linear and a nonlinear oscillator with a nonlinearizable cubic stiffness. Depending on initial conditions, we find energy transfer either from linear to nonlinear oscillator (energy pumping) or from nonlinear to linear. Such results are valid for two different potentials. However, under resonance and absence of external excitation, if the mass of the nonlinear oscillator is adequately small then the linear oscillator always loses energy. Our approach uses rigorous Regular Perturbation Theory. Besides, we have included the case of two linear oscillators under linear or cubic interactions. Comparisons with the earlier case are made. (c) 2008 Elsevier Ltd. All rights reserved.

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Contadores eletrônicos no laboratório didático: parte II. Medida de intervalos de tempo sucessivos

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

Contadores eletrônicos no laboratório didático: parte I. Montagem e aplicações

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

Serotonin and circadian rhythms

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

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Force-versus-time curves during collisions between two identical steel balls

We describe a numerical procedure for plotting the force-versus-time curves in elastic collisions between identical conducting balls. A system of parametric equations relating the force and the time to a dimensionless parameter is derived from the assumption of a force compatible with Hertz's theory of collision. A simple experimental arrangement consisting of a mechanical system of colliding balls and an electrical circuit containing a crystal oscillator and an electronic counter is used to measure the collision time as a function of the energy of impact. From the data we can determine the relevant parameters. The calculated results agree very well with the expected values and are consistent with the assumption that the collisions are elastic. (C) 2006 American Association of Physics Teachers.