On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

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

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

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

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

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

Swarm Control Designs applied to a Mechanical Oscillator

This paper presented the particle swarm optimization approach for nonlinear system identification and for reducing the oscillatory movement of the nonlinear systems to periodic orbits. We analyzes the non-linear dynamics in an oscillator mechanical and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This approaches is applied in analyzes the nonlinear dynamics in an oscillator mechanical. The simulation results show the identification by particle swarm optimization is very effective.

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I-primary resonance and free response at low temperatures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Harmonical oscillator and electro-mechanical analogy: an interdiscinary experiment to high precision mass variation measurements

De forma geral, os cursos de física clássica oferecidos nas universidades carecem de exemplos de aplicações nas áreas de química e biologia, o que por vezes desmotivam os alunos de graduação destas áreas a estudarem os conceitos físicos desenvolvidos em sala de aula. Neste texto, a analogia entre os osciladores elétrico e mecânico é explorada visando possívies aplicações em química e biologia, mostrando-se de grande valia devido ao seu uso em técnicas de medição de variação de massa com alta precisão, tanto de forma direta como indireta. Estas técnicas são conhecidas como técnicas eletrogravimétricas e são de especial importância em aplicações que envolvem biossensores. Desta forma, o texto explora o estudo da analogia eletromecânica de forma interdisciplinar envolvendo as áreas de física, química e biologia. Baseado nessa analogia é proposto um experimento que permite a sua aplicação em diferentes níveis conceituais dessas disciplinas, tanto em abordagem básica como mais profunda.

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THE PARTITION-FUNCTION FOR AN ANYON-LIKE OSCILLATOR

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then re-obtained as particular cases of our function. The technique we employ is a non-relativistic version of the Green function method used in the computation of one-loop effective actions of quantum field theory.

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Energy localization in the Phi(4) oscillator chain

We study energy localization in a finite one-dimensional Phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. on the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrodinger equation approximating the dynamics, to support and explain the numerical results.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Nonadiabatic calculations of the oscillator strengths for the helium atom in the hyperspherical adiabatic approach

Energies and wavefunctions are calculated for the bound states of the helium atom in the hyperspherical adiabatic approach by the full inclusion of nonadiabatic couplings. We show that the use of appropriate asymptotic radial boundary conditions not only allows the efficient calculation of energies accurate up to a few ppm for the ground state but also gives increasingly precise results for high-lying excited states with a unique set of equations. The accuracy of the wavefunctions is demonstrated by the calculation of oscillator strengths in the length form for transitions between stares ii S-1(e) and (n + 1) P-1(0) up to n = 29, in agreement with variational calculations.

Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = -V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this, symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

The propagator for a charged oscillator with a time-dependent mass in a time-varying electromagnetic field

We make a change of variables and a time reparametrization in the Schrödinger equation in order to obtain the propagator of a charged oscillator with a time-dependent mass and frequency under the influence of time-varying electric and magnetic fields, in terms of the simple propagators of harmonic oscillators with constant frequencies and masses. We also discuss the Jackiw transformation and others as a particular case of ours. © 1991.