Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Nonlinear two-field models from orbit equation deformations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

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

Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

Dynamical systems of the billiard type are of fundamental importance for the description of numerous phenomena observed in many different fields of research, including statistical mechanics, Hamiltonian dynamics, nonlinear physics, and many others. This Focus Issue presents the recent progress in this area with contributions from the mathematical as well as physical stand point. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730155]

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Nonlinear optimization using a modified Hopfield model

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements. Neural networks with feedback connections provide a computing model capable of solving a rich class of optimization problems. In this paper, a modified Hopfield network is developed for solving constrained nonlinear optimization problems. The internal parameters of the network are obtained using the valid-subspace technique. Simulated examples are presented as an illustration of the proposed approach.

Primal-dual logarithmic barrier and augmented Lagrangian function to the loss minimization in power systems

This article presents a new approach to minimize the losses in electrical power systems. This approach considers the application of the primal-dual logarithmic barrier method to voltage magnitude and tap-changing transformer variables, and the other inequality constraints are treated by augmented Lagrangian method. The Lagrangian function aggregates all the constraints. The first-order necessary conditions are reached by Newton's method, and by updating the dual variables and penalty factors. Test results are presented to show the good performance of this approach.

Influence of La2O3, Pr2O3 and CeO2 on the nonlinear properties of SnO2 multicomponent varistors

The influence of La2O3, Pr2O3 and CeO2 on a new class of polycrystalline ceramics with nonlinear properties based on SnO2, was investigated. La2O3 and Pr2O3 were found to precipitate at the grain boundary region, causing a considerable increase in the nonlinear behavior. It was found that CeO2 forms a solid solution in the bulk but. unlike La2O3 and Pr2O3, it does not increase the nonlinear behavior. A higher nonlinear coefficient of similar to80 was obtained for La2O3-doped SnO2-based systems. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Effect of atmosphere on the electrical properties of TiO2-SnO2 varistor systems

This work illustrates the advancement of research on TiO2-based electroceramics. In this work will be presented that the addition of different dopants, as well as thermal treatments at oxidizing and inert atmosphere, influences of the densification, the mean grain size and the electrical properties of the TiO2-based varistor ceramics. Dopants like Ta2O5, Nb2O5, and Cr2O3 have an especial role in the barrier formation at the grain boundary in the TiO2 varistors, increasing the nonlinear coefficient and decreasing the breakdown electric field. The influence of Cr'(Ti) is to increase the O' and O'(2) adsorption at the grain boundary interface and to promote a decrease in the conductivity by donating electrons to O-2 adsorbed at the grain boundary. In this paper, TiO2 and (Sn,Ti)O-2-based studies of polycrystalline ceramics, which show a non-linear I-V electrical response typical of low voltage varistor systems are also presented. All these systems are potentially promising for varistor applications. (C) 2004 Kluwer Academic Publishers.

Harmonic identification using parallel neural networks in single-phase systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.