976 resultados para anomalous subdiffusion equation
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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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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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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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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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The Fokker-Planck equation is studied through its relation to a Schrodinger-type equation. The advantage of this combination is that we can construct the probability distribution of the Fokker-Planck equation by using well-known solutions of the Schrodinger equation. By making use of such a combination, we present the solution of the Fokker-Planck equation for a bistable potential related to a double oscillator. Thus, we can observe the temporal evolution of the system describing its dynamic properties such as the time tau to overcome the barrier. By calculating the rates k = 1/tau as a function of the inverse scaled temperature 1/D, where D is the diffusion coefficient, we compare the aspect of the curve k x 1/D, with the ones obtained from other studies related to four different kinds of activated process. We notice that there are similarities in some ranges of the scaled temperatures, where the different processes follow the Arrhenius behavior. We propose that the type of bistable potential used in this study may be used, qualitatively, as a simple model, whose rates share common features with the rates of some single rate-limited thermally activated processes. (C) 2014 Elsevier B.V. All rights reserved.
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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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This work aims to study several diffusive regimes, especially Brownian motion. We deal with problems involving anomalous diffusion using the method of fractional derivatives and fractional integrals. We introduce concepts of fractional calculus and apply it to the generalized Langevin equation. Through the fractional Laplace transform we calculate the values of diffusion coefficients for two super diffusive cases, verifying the validity of the method
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In this paper we study the periodic orbits of the third-order differential equation x ′′′−µx ′′+ x ′ − µx = εF (x, x ′ , x ′′), where ε is a small parameter and the function F is of class C 2 .
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We demonstrate the supercontinuum (SC) generation in a suspended-core As2S3 chalcogenide microstructured optical fiber (MOF). The variation of SC is investigated by changing the fiber length, pump peak power and pump wavelength. In the case of long fibers (20 and 40 cm), the SC ranges are discontinuous and stop at the wavelengths shorter than 3500 nm, due to the absorption of fiber. In the case of short fibers (1.3 and 2.4 cm), the SC ranges are continuous and can extend to the wavelengths longer than 4 μm. The SC broadening is observed when the pump peak power increases from 0.24 to 1.32 kW at 2500 nm. The SC range increases with the pump wavelength changing from 2200 to 2600 nm, corresponding to the dispersion of As2S3 MOF from the normal to anomalous region. The SC generation is simulated by the generalized nonlinear Schrödinger equation. The simulation includes the SC difference between 1.3 and 2.4 cm long fiber by 2500 nm pumping, the variation of SC with pump peak power in 2.4 cm long fiber, and the variation of SC with pump wavelength in 1.3 cm long fiber. The simulation agrees well with the experiment.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)