Generalized neighbor-interaction models induced by nonlinear lattices

It is shown that the tight-binding approximation of the nonlinear Schrodinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrodinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Effective nonlinear Schrodinger equations for cigar-shaped and disc-shaped Fermi superfluids at unitarity

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

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

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

Nonlinear two-field models from orbit equation deformations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A simple feedback control for a chaotic oscillator with limited power supply

We proposed a simple feedback control method to suppress chaotic behavior in oscillators with limited power supply. The small-amplitude controlling signal is applied directly to the power supply system, so as to alter the characteristic curve of the driving motor. Numerical results are presented showing the method efficiency for a wide range of control parameters. Moreover, we have found that, for some parameters, this kind of control may introduce coexisting periodic attractors with complex basins of attraction and, therefore, serious problems with predictability of the final state the system will asymptote to. (c) 2006 Elsevier Ltd. All rights reserved.

On Nonlinear Dynamics and an Optimal Control Design to a Longitudinal Flight

In this work, we analyzed a bifurcational behavior of a longitudinal flight nonlinear dynamics, taking as an example the F-8 aircraft Crusader. We deal with an analysis of high angles of attack in order to stabilize the oscillations; those were close to the critical angle of the aircraft, in the flight conditions, established. We proposed a linear optimal control design applied to the considered nonlinear aircraft model below angle of stall, taking into account regions of Hopf and saddled noddle bifurcations.

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

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)

The rigid-flexible nonlinear robotic manipulator: Modeling and control

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

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper The mathematical model of the system is represented by coupled non-linear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation. [DOI: 10.1115/1.3124783]