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.

On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier B.V. All rights reserved.

Sliding Vector Fields via Slow-Fast Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wide localized solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

Chaos in collapsing Bose-condensed gas

We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schrödinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos. ©2000 The American Physical Society.

Object oriented modeling of piston engines

This work reports a conception phase of a piston engine global model. The model objective is forecast the motor performance (power, torque and specific consumption as a function of rotation and environmental conditions). Global model or Zero-dimensional is based on flux balance through each engine component. The resulting differential equations represents a compressive unsteady flow, in which, all dimensional variables are areas or volumes. A review is presented first. The ordinary differential equation system is presented and a Runge-Kutta method is proposed to solve it numerically. The model includes the momentum conservation equation to link the gas dynamics with the engine moving parts rigid body mechanics. As an oriented to objects model the documentation follows the UML standard. A discussion about the class diagrams is presented, relating the classes with physical model related. The OOP approach allows evolution from simple models to most complex ones without total code rewrite. Copyright © 2001 Society of Automotive Engineers, Inc.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

Detecção de bordas em imagens digitais através de um processo de difusão anisotrópica não linear

The edges detection model by a non-linear anisotropic diffusion, consists in a mathematical model of smoothing based in Partial Differential Equation (PDE), alternative to the conventional low-pass filters. The smoothing model consists in a selective process, where homogeneous areas of the image are smoothed intensely in agreement with the temporal evolution applied to the model. The level of smoothing is related with the amount of undesired information contained in the image, i.e., the model is directly related with the optimal level of smoothing, eliminating the undesired information and keeping selectively the interest features for Cartography area. The model is primordial for cartographic applications, its function is to realize the image preprocessing without losing edges and other important details on the image, mainly airports tracks and paved roads. Experiments carried out with digital images showed that the methodology allows to obtain the features, e.g. airports tracks, with efficiency.

Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Forced oscillations with continuum models of atomic force microscopy

The dynamics of the AFM-atomic force microscope follows a model based in a Timoshenko cantilever beam with a tip attached at the free end and acting with the surface of a sample. General boundary conditions arise when the tip is either in contact or non-contact with the surface. The governing equations are given in matrix conservative form subject to localized loads. The eigenanalysis is done with a fundamental matrix response of a damped second-order matrix differential equation. Forced responses are found by using a Galerkin approximation of the matrix impulse response. Simulations results with harmonic and pulse forcing show the filtering character and the effects of the tip-sample interaction at the end of the beam. © 2012 American Institute of Physics.

Método das aproximações sucessivas e aplicações

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)