Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spin-Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vibration energy harvesting using piezoelectric transducer and non-controlled rectifiers circuits

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Crossover between macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors

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

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Modelling the lethargic crab disease.

The lethargic crab disease (LCD) is an emergent infirmity that has decimated native populations of the mangrove land crab (Ucides cordatus, Decapoda: Ocypodidae) along the Brazilian coast. Several potential etiological agents have been linked with LCD, but only in 2005 was it proved that it is caused by an ascomycete fungus. This is the first attempt to develop a mathematical model to describe the epidemiological dynamics of LCD. The model presents four possible scenarios, namely, the trivial equilibrium, the disease-free equilibrium, endemic equilibrium, and limit cycles arising from a Hopf bifurcation. The threshold values depend on the basic reproductive number of crabs and fungi, and on the infection rate. These scenarios depend on both the biological assumptions and the temporal evolution of the disease. Numerical simulations corroborate the analytical results and illustrate the different temporal dynamics of the crab and fungus populations.

CHARGED PARTICLE DYNAMICS IN TIME DEPENDENT MAGNETIC FIELDS

In this work we study the behavior of charged particles immersed in a peculiar configuration of magnetic fields, which has a main constant field B(0) and a superimposed, transversal perturbation field B(1) sin(omega(p)t), with B(1) << B(0). By taking Cartesian coordinates and placing B(0) along the z axis and B(1) sin (omega(p)t) on the x axis, an analytical solution for y(t) may be obtained by solving an integrodifferential equation. Besides, the solution z(t) also exhibits a very interesting dynamics, and the entire system is conditioned by resonances between the particle orbit frequencies and the frequency of the magnetic transversal perturbation, omega(p). In this work we also discuss numerical simulations for the related particle trajectories, as well as potential applications in the context of separation phenomena.

Dynamics of the deconfinement transition of quarks and gluons in a finite volume

We employ finite elements methods for the approximation of solutions of the Ginzburg-Landau equations describing the deconfinement transition in quantum chromodynamics. These methods seem appropriate for situations where the deconfining transition occurs over a finite volume as in relativistic heavy ion collisions. where in addition expansion of the system and flow of matter are important. Simulation results employing finite elements are presented for a Ginzburg-Landau equation based on a model free energy describing the deconfining transition in pure gauge SU(2) theory. Results for finite and infinite system are compared. (C) 2009 Elsevier B.V. All rights reserved.

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

Vortices in nonlocal Gross-Pitaevskii equation

We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to the polar angle, the unstable modes of the axial n-fold vortex have orbital numbers l satisfying 0 < \l\ < 2\n\, as in the local model. Numerical simulations show that nonlocality slightly decreases the threshold rotation frequency above which the nonvortex state ceases to be the global energy minimum and decreases the frequency of the anomalous mode of the 1-vortex. In the case of higher axial vortices, nonlocality leads to instability against splitting with the creation of antivortices and gives rise to additional anomalous modes with higher orbital numbers. Despite new instability channels with the creation of antivortices, for a stationary solution comprised of vortices and antivortices there always exists another vortex solution, composed solely of vortices, with the same total vorticity but with a lower energy.

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is investigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. (c) 2007 Elsevier B.V. All rights reserved.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.