An analog model for quantum lightcone fluctuations in nonlinear optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. © 2012 Elsevier Inc.

Stability of nonlinear system using takagi-sugeno fuzzy models and hyper-rectangle of LMIs

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi-Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature. © 2013 Brazilian Society for Automatics - SBA.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

On elimination of chaotic behavior in a non-ideal portal frame structural system, using both passive and active controls

In this paper, an application is considered of both active and passive controls, to suppression of chaotic behavior of a simple portal frame, under the excitation of an unbalanced DC motor, with limited power supply (non-ideal problem). The adopted active control strategy consists of two controls: the nonlinear (feedforward) in order to keep the controlled system in a desirable orbit, and the feedback control, which may be obtained by considering state-dependent Riccati equation control to bringing the system into the desired orbit using a magneto rheological (MR) damper. To control the electric current applied in control of the MR damper the Bouc-Wen mathematical model was used to the MR damper. The passive control was obtained by means of a nonlinear sub-structure with properties of nonlinear energy sink. Simulations showed the efficiency of both the passive control (energy pumping) and active control strategies in the suppression of the chaotic behavior. © The Author(s) 2012.

Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls

The optimal reactive dispatch problem is a nonlinear programming problem containing continuous and discrete control variables. Owing to the difficulty caused by discrete variables, this problem is usually solved assuming all variables as continuous variables, therefore the original discrete variables are rounded off to the closest discrete value. This approach may provide solutions far from optimal or even unfeasible solutions. This paper presents an efficient handling of discrete variables by penalty function so that the problem becomes continuous and differentiable. Simulations with the IEEE test systems were performed showing the efficiency of the proposed approach. © 1969-2012 IEEE.

Nonlinear control system applied to atomic force microscope including parametric errors

The performance of the optimal linear feedback control and of the state-dependent Riccati equation control techniques applied to control and to suppress the chaotic motion in the atomic force microscope are analyzed. In addition, the sensitivity of each control technique regarding to parametric uncertainties are considered. Simulation results show the advantages and disadvantages of each technique. © 2013 Brazilian Society for Automatics - SBA.

Nonlinear Optical Properties of Tungsten Lead-Pyrophosphate Glasses Containing Metallic Copper Nanoparticles

We have prepared heavy metal oxide glasses containing metallic copper nanoparticles with promising nonlinear optical properties which were determined by Z-scan and pump-probe measurements using femtosecond laser pulses. For the wavelengths within the plasmon band, we have observed saturable absorption and response times of 2.3 ps. For the other regions of the spectrum, reverse saturable absorption and lifetimes shorter than 200 fs were verified. The nonlinear refractive index is about 2.0 × 10-19 m2/W from visible to telecom region, thus presenting an enhancement effect at wavelengths near the plasmon and Cu+2 d-d band. © 2013 Springer Science+Business Media New York.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

A semigroups theory approach to a model of suspension bridges

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

Nonlinear optical properties of Bi2O3-GeO2 glass at 800 and 532 nm

The nonlinear (NL) optical properties of glassy xBi2O 3-(1-x) GeO2 with x = 0.72 and 0.82 were investigated. The experiments were performed with lasers at 800 nm (pulses of 150 fs) and 532 nm (pulses of 80 ps and 250 ns). Using the Kerr gate technique, we observed that the NL response of the samples at 800 nm is faster than 150 fs. NL refraction indices, | n 2 | ≈ 5 × 10-16 cm2/W, and two-photon absorption coefficients, α 2, smaller than 0.03 cm/GW, were measured at 800 nm. At 532 nm, we measured the NL transmittance of the samples. From the results obtained, we determined α 2 ≈1 cm/GW and excited-state absorption cross-sections of ≈10-22 cm2 due to free-carriers. © 2013 AIP Publishing LLC.

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Lead-germanate glasses and fibers: A practical alternative to tellurite for nonlinear fiber applications

We report on the fabrication of novel lead-germanate glasses and fibers. We have characterized these glasses in terms of their thermal properties, Raman spectra and refractive indices (both linear and nonlinear) and present them as viable alternatives to tellurite glasses for applications requiring highly nonlinear optical fibers. © 2013 Optical Society of America.

Poincaré plot indexes of heart rate variability: Relationships with other nonlinear variables

The Poincaré plot for heart rate variability analysis is a technique considered geometrical and non-linear, that can be used to assess the dynamics of heart rate variability by a representation of the values of each pair of R-R intervals into a simplified phase space that describes the system's evolution. The aim of the present study was to verify if there is some correlation between SD1, SD2 and SD1/SD2 ratio and heart rate variability nonlinear indexes either in disease or healthy conditions. 114 patients with arterial coronary disease and 65 healthy subjects underwent 30. minute heart rate registration, in supine position and the analyzed indexes were as follows: SD1, SD2, SD1/SD2, Sample Entropy, Lyapunov Exponent, Hurst Exponent, Correlation Dimension, Detrended Fluctuation Analysis, SDNN, RMSSD, LF, HF and LF/HF ratio. Correlation coefficients between SD1, SD2 and SD1/SD2 indexes and the other variables were tested by the Spearman rank correlation test and a regression analysis. We verified high correlation between SD1/SD2 index and HE and DFA (α1) in both groups, suggesting that this ratio can be used as a surrogate variable. © 2013 Elsevier B.V.

Fenômenos não-lineares, incluindo-se os não-ideias, em captura de energia utilizando-se dispositivos piezoelétricos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison between the performances of a linear isolator and an isolator with a geometrically nonlinear damper

Pós-graduação em Engenharia Mecânica - FEIS