Interaction of Hawking radiation with static sources in de Sitter and Schwarzschild-de Sitter spacetimes

We study and look for similarities between the response rates R-dS(a(0),Lambda) and R-SdS(a(0),Lambda,M) of a static scalar source with constant proper acceleration a(0) interacting with a massless, conformally coupled Klein-Gordon field (i) in de Sitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the de Sitter cosmological horizon and (ii) in Schwarzschild-de Sitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where Lambda is the cosmological constant and M is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of de Sitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild-de Sitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that R-dS(a(0),Lambda) and R-SdS(a(0),Lambda,M) do not coincide in general, but tend to each other when Lambda-->0 or a(0)-->infinity. Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.

The nonlinear essence of gravitational waves

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that-analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge-a gravitational wave must necessarily be nonlinear to transport its own charge-that is, energy-momentum.

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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 the dynamical properties of an elliptical-oval billiard with static boundary

Some dynamical properties for a classical particle confined inside a closed region with an elliptical-oval-like shape are studied. The dynamics of the model is made by using a two-dimensional nonlinear mapping. The phase space of the system is of mixed kind and we have found the condition that breaks the invariant spanning curves in the phase space. We have discussed also some statistical properties of the phase space and obtained the behaviour of the positive Lyapunov exponent. (C) 2009 Elsevier B.V. All rights reserved.

A family of stadium-like billiards with parabolic boundaries under scaling analysis

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.

Comments on a nonlinear and nonideal electromechanical damping vibration absorber, Sommerfeld effect and energy transfer

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

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I-primary resonance and free response at low temperatures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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)

Three-parameter soil-water transient equations in horizontal water-transport analysis

For data obtained from horizontal soil column experiments, the determination of soil-water transport characteristics and functions would be aided by a single-form equation capable of objectively describing water content theta vs. time t at given position x(f). Our study was conducted to evaluate two such possible equations, one having the form of the Weibull frequency distribution, and the other being called a bipower form. Each equation contained three parameters, and was fitted by nonlinear least squares to the experimental data from three separate columns of a single soil. Across the theta range containing the measured data points obtained by gamma-ray attenuation, the two equations were in close agreement. The resulting family of theta(x(f),t) transients, as obtained from either equation, enabled the evaluation of exponent n in the t(n) dependence of the positional advance of a given theta. Not only was n found to be <0.5 at low theta values, but it also increased with theta and tended toward 0.5 as theta approached its sated (near-saturated) value. Some quantitative uncertainty in n(theta) does arise due to the reduced number of data points available at the higher water contents. Without claiming non-Boltzmann behavior (n < 0.5) as necessarily representative of all soils, we nonetheless consider n(theta) to be worthy of further study for evaluating its significance and implications.

Structural and vibrational analysis of nanocrystalline Ga1-xMnxN films deposited by reactive magnetron sputtering

The structural and vibrational properties of nanocrystalline Ga1-xMnxN films deposited by reactive magnetron sputtering were analyzed in a wide composition range (0 < x < 0.18). The films were structurally characterized using x-ray diffraction with Rietveld refinement. The corresponding vibrational properties were investigated using micro-Raman and Fourier transform infrared spectroscopies. The films present a high crystallized fraction, crystallites having wurtzite structure, and high orientation texture with the c axis oriented perpendicular to the substrate surface. Rietveld analysis indicates that Mn atoms are incorporated substitutionally into Ga positions and show that the ionic character of cation-N bonds along the c axis is favored by the Mn incorporation. No evidence for Mn segregation or Mn rich phases was found in the composition range analyzed. Micro-Raman scattering spectra and infrared absorption experiments showed progressive changes with the increase of x and monotonic shifts of the GaN TO and LO peaks to lower frequencies. The structural and vibrational analyses are compared and the influence of Mn on the static and dynamic properties of the lattice is analyzed. (C) 2007 American Institute of Physics.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)