166 resultados para exponential decay


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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

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For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).

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In this work Ba0.99Eu0.01MoO4 (BEMO) powders were prepared by the first time by the Complex Polymerization Method. The structural and optical properties of the BEMO powders were characterized by Fourier Transform Infra-Red (FTIR), X-ray Diffraction (XRD), Raman Spectra, High-Resolution Scanning Electron Microscopy (HR-SEM) and Photoluminescent Measurements. XRD show a crystalline scheelite-type phase after the heat treatment at temperatures greater than 400 degrees C. The ionic radius of Eu3+ (0.109 nm) is lower than the Ba2+ (0.149 nm) one. This difference is responsible for the decrease in the lattice parameters of the BEMO compared to the pure BaMoO4 matrix. This little difference in the lattice parameters show that Eu3+ is expected to occupy the Ba2+ site at different temperatures, stayed the tetragonal (S-4) symmetry characteristic of scheelite-type crystalline structures of BaMoO4. The emission spectra of the samples, when excited at 394 nm, presented the D-5(1)-> F-7(0, 1 and 2) and D-5(0)-> F-7(0, 1, 2, 3 and 4) Eu3+ transitions at 523, 533, 554, 578, 589, 614, 652 and 699 nm, respectively. The emission spectra of the powders heat-treated at 800 and 900 degrees C showed a marked increase in its intensities compared to the materials heat-treated from 400 to 700 C. The decay times for the sample were evaluated and all of them presented the average value of 0.61 ms. Eu3+ luminescence decay time follows one exponential curve indicating the presence of only one type of Eu3+ symmetry site.

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The temperature dependence of photoinduced birefringence was investigated for mixed Langmuir-Blodgett (LB) films from the homopolymer poly[4'-[[2-(methacryloyloxy)ethyl]ethyl-amino]-2-chloro-4-nitroazobenzene] (HPDR13) and cadmium stearate (Cdst) and from the copolymer 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2'-chloro-4'-nitroazobenzene (MMA-DR13) and CdSt. Birefringence was achieved by impinging a linearly polarized light on the LB films. The maximum birefringence achieved decreased with temperature as thermal relaxation of the chromophores was facilitated. The buildup curves for birefringence were fitted with biexponential functions representing distinctly different mechanisms with time constants. The first, fast process is thermally activated and may be represented by an Arrhenius process. The decay of birefringence after switching off the laser source was described by a Kohlraush-Williams-Watts (KWW) function, consistent with a distribution of relaxation times for the polymer system. Activation energies were obtained from Arrhenius plots of the rate constant of the exponential functions and KWW function, which showed that the buildup of birefringence was very similar for the two polymer systems. The decay, however, was slower for the LB film from MMA-DR13/CdSt. (C) 2002 Published by Elsevier B.V. Ltd.