Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Criação da matéria em cosmologias com velocidade da luz variável e eletrônico não-linear

In this work we obtain the cosmological solutions and investigate the thermodynamics of matter creation in two diferent contexts. In the first we propose a cosmological model with a time varying speed of light c. We consider two diferent time dependence of c for a at Friedmann-Robertson- Walker (FRW) universe. We write the energy conservation law arising from Einstein equations and study how particles are created as c decreases with cosmic epoch. The variation of c is coupled to a cosmological Λ term and both singular and non-singular solutions are possible. We calculate the "adiabatic" particle creation rate and the total number of particles as a function of time and find the constrains imposed by the second law of thermodynamics upon the models. In the second scenario, we study the nonlinearity of the electrodynamics as a source of matter creation in the cosmological models with at FRW geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ α H2 (cosmological term proportional to the Hubble parameter). In all cases, the second law of thermodynamics demands that the universe is not contracting (H ≥ 0). The first two solutions are non-singular and exhibit in ationary periods. The third case studied allows an always in ationary universe for a suficiently large cosmological term

High sensitivity fiber optic angular displacement sensor and its application for detection of ultrasound

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mesoscopic structure evidenced by AC dielectric nonlinearities in Sr(0.75)Ba(0.25)Nb(2)O(6) relaxor ferroelectric thin films

The AC electric field and temperature dependences of the dielectric permittivity for strontium barium niobate (Sr(0.75)Ba(0.25)Nb(2)O(6)) relaxor ferroelectric thin films have been investigated. The results indicate the existence of a true mesoscopic structure evidenced by the nonlinear dielectric response of these films, which is similar to those observed for bulk relaxor ferroelectrics. A tendency for a temperature dependent crossover from a linear to a quadratic behaviour of the dielectric nonlinearity was observed, indicating an evolution from paraelectric to glass-like behaviour on cooling the samples towards the freezing temperature transition.

On the spectrum of stochastic perturbations of the shift and Julia sets

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

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

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.

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity), we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially screened radially symmetric harmonic potential well in two and three dimensions. We also consider an axially symmetric configuration with zero axial trap and a exponentially screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence, these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillations of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.

Finite-well potential in the 3D nonlinear Schrodinger equation: application to Bose-Einstein condensation

Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schrodinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Fresnel analysis of wave propagation in nonlinear electrodynamics

We study wave propagation in local nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of local nonlinear Lagrangian nondispersive models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains nontrivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.