Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

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.

Analytical study of the nonlinear behavior of a shape memory oscillator: Part II-resonance secondary

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On energy transfer phenomena, in a nonlinear ideal and nonideal essential vibrating systems, coupled to a (MR) magneto-rheological damper

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

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Local order around rare earth ions during the devitrification of oxyfluoride glasses

Erbium L-3-edge extended x-ray absorption fine structure (EXAFS) measurements were performed on rare earth doped fluorosilicate and fluoroborate glasses and glass ceramics. The well known nucleating effects of erbium ions for the crystallization of cubic lead fluoride (based on x-ray diffraction measurements) and the fact that the rare earth ions are present in the crystalline phase (as indicated by Er3+ emission spectra) seem in contradiction with the present EXAFS analysis, which indicates a lack of medium range structural ordering around the Er3+ ions and suggests that the lead fluoride crystallization does not occur in the nearest neighbor distance of the rare earth ion. Molecular dynamics simulations of the devitrification process of a lead fluoride glass doped with Er3+ ions were performed, and results indicate that Er3+ ions lower the devitrification temperature of PbF2, in good agreement with the experimental results. The genuine role of Er3+ ions in the devitrification process of PbF2 has been investigated. Although Er3+ ions could indeed act as seeds for crystallization, as experiments suggest, molecular dynamics simulation results corroborate the experimental EXAFS observation that the devitrification does not occur at its nearest neighbor distance. (c) 2008 American Institute of Physics.

Methods to verify parameter equality in nonlinear regression models

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

Antimony orthophosphate glasses with large nonlinear refractive indices, low two-photon absorption coefficients, and ultrafast response

Antimony glasses based on the composition Sb2O3-SbPO4 were prepared and characterized. The samples present high refractive index, good transmission from 380 to 2000 nm, and high thermal stability. The nonlinear refractive index, n(2), of the samples was studied using the optical Kerr shutter technique at 800 nm. The third-order correlation signals between pump and probe pulses indicate ultrafast response (<100 fs) for all compositions. Enhancement of n(2) was observed by adding lead oxide to the Sb2O3-SbPO4 composition. Large values of n(2)approximate to10(-14) cm(2)/W and negligible two-photon absorption coefficients (smaller than 0.01 cm/GW) were determined for all samples. The glass compositions studied present appropriate figure-of-merit for all-optical switching applications. (C) 2005 American Institute of Physics.

Pattern recognition theory in nonlinear signal processing

A body of research has developed within the context of nonlinear signal and image processing that deals with the automatic, statistical design of digital window-based filters. Based on pairs of ideal and observed signals, a filter is designed in an effort to minimize the error between the ideal and filtered signals. The goodness of an optimal filter depends on the relation between the ideal and observed signals, but the goodness of a designed filter also depends on the amount of sample data from which it is designed. In order to lessen the design cost, a filter is often chosen from a given class of filters, thereby constraining the optimization and increasing the error of the optimal filter. To a great extent, the problem of filter design concerns striking the correct balance between the degree of constraint and the design cost. From a different perspective and in a different context, the problem of constraint versus sample size has been a major focus of study within the theory of pattern recognition. This paper discusses the design problem for nonlinear signal processing, shows how the issue naturally transitions into pattern recognition, and then provides a review of salient related pattern-recognition theory. In particular, it discusses classification rules, constrained classification, the Vapnik-Chervonenkis theory, and implications of that theory for morphological classifiers and neural networks. The paper closes by discussing some design approaches developed for nonlinear signal processing, and how the nature of these naturally lead to a decomposition of the error of a designed filter into a sum of the following components: the Bayes error of the unconstrained optimal filter, the cost of constraint, the cost of reducing complexity by compressing the original signal distribution, the design cost, and the contribution of prior knowledge to a decrease in the error. The main purpose of the paper is to present fundamental principles of pattern recognition theory within the framework of active research in nonlinear signal processing.

Nonlinear optical properties of tungstate fluorophosphate glasses

The optical nonlinearity of tungstate fluorophosphate glasses, synthesized in the NaPO3-BaF2-WO3 system, was investigated through experiments based on the third-order susceptibility, chi((3)). Nonlinear (NL) refraction and NL absorption measurements in the picosecond regime were performed using the Z-scan technique at 532 nm. NL refractive index, n(2)proportional toRe chi((3)), ranging from 0.4x10(-14) cm(2)/W to 0.6x10(-14) cm(2)/W were determined. The two-photon absorption coefficient, alpha(2)proportional toIm chi((3)), for excitation at 532 nm, vary from 0.3 to 0.5 cm/GW. Light induced birefringence experiments performed in the femtosecond regime indicate that the response time of the nonlinearity at 800 nm is faster than 100 fs. The experiments show that chi((3)) is enhanced when the WO3 concentration increases and this behavior is attributed to the hyperpolarizabilities associated to W-O bonds. (C) 2004 American Institute of Physics.

Exchange and crystal field effects in the ESR spectra of Eu(2+) in LaB(6)

Electron spin resonance of Eu(2+) (4f(7), S=7/2) in a La hexaboride (LaB(6)) single crystal shows a single anisotropic Dysonian resonance. From the observed negative g shift of the resonance, it is inferred that the Eu(2+) ions are covalent exchange coupled to the B 2p-like host conduction electrons. From the anisotropy of the spectra (linewidth and field for resonance), we found that the S ground state of Eu(2+) ions experience a cubic crystal field of a negative fourth order crystal field parameter (CFP), b(4)=-11.5(2.0) Oe, in agreement with the negative fourth order CFP, A(4), found for the non-S ground state R hexaborides. These results support covalency as the dominant contribution to the fourth order CFP for the whole R hexaboride family.

4f-4f intensities of the Tm3+ ions in fluoroindate glasses: the influence of third-order effects through odd intensity parameters

In this work an analysis of the phenomenological Omega(lambda) intensity parameters for the Tm3+ ion in fluoroindate glass is made using the standard Judd-Ofelt theory, and a modified oscillator strength taking into account odd-order contributions is utilized. Different sets of phenomenological intensity parameters Omega(lambda) (lambda=1,2,3,4,5,6) are discussed. The set of better quality is used to analyze the influence of third-order effects through odd intensity parameters in the new approximation. Fluoroindate glasses of compositions (40-x)InF3-20ZnF(2)-20SrF(2)-16BaF(2)-2GdF(3)-2NaF-xTmF(3) with x=1, 2 and 3 mol% were prepared, and the absorption spectra at room temperature in the spectral range from 300 to 2500 nm were obtained. The experimental oscillator strengths determined from the area under the absorption band are compared to the calculated ones. (C) 1998 Elsevier B.V. S.A.

Properties and one-step synthesis of (2-acetylpyridine)tetraammineruthenium(II), [Ru-II(2-acpy)(NH3)(4)](2+) and tetraammine(2-benzoylpyridine)ruthenium(II), [Ru-II(NH3)(4)(2-bzpy)](2+) Redox potentials, UV-Vis and NMR spectra

A more direct and efficient route to the syntheses of [Ru(NH3)(4)(X-Y)](BF4)(2), where X-Y can be 2-acetylpyridine (2-acpy) or 2-benzoylpyridine (2-bzpy), based on the reactions of [RuCl(NH3)(5)]Cl-2 with these ortho-substituted azines is described. The [Ru(2-acpy)(NH3)(4)](BF4)(2) and [Ru(NH3)(5)(2-bzpy)](BF4)(2) complexes have a molar conductance of 328 and 292 Ohm(-1) cm(2) mol(-1), respectively, corresponding to a 1:2 species in solution. These complexes showed two intense absorption bands around 620-650 and 380 nm, the energies of which are solvent dependent, decreasing with the increase of the Gutman's donor number of the solvent, and were assigned as metal-to-ligand charge transfer (MLCT). The complexes have oxidation potentials (Ru-II/III) of +0.380 V vs. Ag/AgCl (2-acpy) and +0.400 V vs. Ag/AgCl (2-bzpy), and reduction potentials (X-Y0/-) of -1.10 V vs. Ag/AgCl (2-acpy) and -0.950 V vs. Ag/AgCl (2-bzpy) on CF3COOH/NaCF3COO at pH=3.0, scan rate 100 mV s(-1), [Ru]=1.0x10(-3) mol l(-1). Both processes show a coupled chemical reaction. Upon oxidation of the metal center, the MLCT absorption bands are bleached and restored upon subsequent reduction. In order to confirm the structure of the complexes a detailed LH NMR investigation was performed in d(6)-acetone. Further confirmation of the structure was obtained by recording the N-15 NMR spectrum of [Ru(NH3)(4)(2-bzpy)](2+) in d(6)-DMSO using the INEPT pulse sequence improving the sensitivity of N-15 by polarization transfer from the protons to the N-15. The Nuclear Overhauser Effect (NOE) experiments were made qualitatively for [Ru(NH3)(4)(2-acpy)](2+), and showed that H-6 of the pyridine is close to a NH3 proton, which should then be in a cis position, and, hence, confirming that acpy is acting as a bidentate ligand. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Nonlinear behavior of TiO2 center dot Ta2O5 center dot MnO2 material doped with BaO and Bi2O3

A study was made on the effect of the addition of BaO (0.025-0.05 mol%) and Bi2O3 (0.025-0.05 mol%) to the TiO2.Ta2O5.MnO2 material. The samples were characterized by X-ray diffraction, and current-voltage measurements were accomplished for determination of the nonlinear coefficient. An analysis was made to evaluate the microstructural characteristics of the materials. The most appropriate sintering conditions for the materials were analyzed with the purpose of obtaining the best nonlinear coefficient associated with the smallest breakdown electric field. After sintering at 1400 degreesC for 2 h, a low-voltage (30 V cm(-1)) varistor was obtained, which, however, presented a low nonlinear coefficient (6). It was found that the sintering conditions must be controlled in order to improve the electrical properties of these materials. (C) 2004 Elsevier B.V. All rights reserved.