Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Pseudospin and spin symmetries in the relativistic harmonic oscillator

We compute the analytical solutions of the generalized relativistic harmonic oscillator in 1+1 dimensions, including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs These are the conditions in which pseudospin or spin symmetries can be realized We consider positive and negative quadratic potentials and present their bound-state solutions for fermions and an-tifermions. We relate the spin-type and pseudospin-type spectra through charge conjugation and γ5 chiral transformations. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with tensor interactions and discuss the conditions in which one may have both nucleon and antin-ucleon bound states.

Radial basis function network applied to the linearization of a voltage controlled oscillator

An analog circuit that implements a radial basis function network is presented. The proposed circuit allows the adjustment of all shape parameters of the radial functions, i.e., amplitude, center and width. The implemented network was applied to the linearization of a nonlinear circuit, a voltage controlled oscillator (VCO). This application can be classified as an open-loop control in which the network plays the role of the controller. Experimental results have proved the linearization capability of the proposed circuit. Its performance can be improved by using a network with more basis functions. Copyright 2007 ACM.

Dynamics of a piecewise-linear oscillator with limited power supply

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction. © 2009 by ASME.

An investigations on local and global behavior of a (SMA) oscillator of 3 - DOF driven by a limited power supply

SMART material systems offer great possibilities in terms of providing novel and economical solutions to engineering problems. The technological advantages of these materials over traditional ones are due to their unique microstructure and molecular properties. Smart materials such as shape memory alloys (SMA), has been used in such diverse areas of engineering science, nowadays. In this paper, we present a numerical investigation of the dynamics interaction of a nonideal structure (NIS). We analyze the phenomenon of the passage through resonance region in the steady state processes. We remarked that this kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the DC motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. The results obtained by using numerical simulations are discussed in details. Copyright © 2009 by ASME.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

A note on non-linear phenomena in a non-ideal oscillator, with a snap-through truss absorber, including parameter uncertainties

This work considers the vibrating system that consists of a snap-through truss absorber coupled to an oscillator under excitation of an electric motor with an eccentricity and limited power, characterizing a non-ideal oscillator. It is aimed to use the non-linearity and quasi-zero stiffness of absorber (snap-through truss absorber) to obtain a significantly attenuation the jump phenomenon. There is also an interest to exhibit the reduction of Sommerfeld effect, to confirm the saturation phenomenon occurrence and show the power transfer in a non-linear structure, evidencing the pumping energy. As shown by simulations in this work, this absorber allows the energy pumping before and during the jump phenomenon, decreasing the higher amplitudes of considered system. Additionally, the occurrence of saturation phenomenon due use of snap-through truss absorber is verified. The analysis of parameter uncertainties was introduced. Sensitivity of system with parametric errors demonstrated a trustable system. © IMechE 2012.

Soluções da equação de Fokker-Planck para um potencial isoespectral ao potencial de Morse

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solução analítica da equação de movimento clássica para o potencial de Morse generalizado e potenciais de Morse simétricos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso de uma rede unidimensional harmônica com o potencial de Rosen-Morse on site para modelar o DNA

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Extensometria: estudo das deformações ao redor de três implantes cone morse, com posicionamento linear, sob carga axial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Distribuição das tensões geradas ao redor de implantes osseointegrados de diferentes conexões cone morse: análise fotoelástica e pelo método dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise fotoelástica da distribuição de tensões em próteses implantossuportadas cimentadas ou parafusadas em implantes de hexágono externo, interno ou cone-morse

Pós-graduação em Odontologia - FOA

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

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

A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)