The Experts below are selected from a list of 180 Experts worldwide ranked by ideXlab platform
M A Despósito - One of the best experts on this subject based on the ideXlab platform.
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Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.
Physical Review E, 2009Co-Authors: A D Viñales, K. G. Wang, M A DespósitoAbstract:The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace Analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
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Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise
arXiv: Statistical Mechanics, 2009Co-Authors: A D Viñales, K. G. Wang, M A DespósitoAbstract:The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace Analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
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Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation.
Physical Review E, 2008Co-Authors: M A Despósito, A D ViñalesAbstract:We investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized Langevin equation. Using Laplace Analysis together with Tauberian theorems we derive asymptotic expressions for the mean values, variances, and velocity autocorrelation function in terms of the long-time behavior of the memory kernel and the correlation function of the random force. The internal and external noise cases are analyzed. A simple criterion to determine if the diffusion process is normal or anomalous is established.
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Anomalous diffusion induced by a Mittag-Leffler correlated noise.
Physical review. E Statistical nonlinear and soft matter physics, 2007Co-Authors: A D Viñales, M A DespósitoAbstract:We introduce a Mittag-Leffler correlated random force leading to anomalous diffusion. Starting from a generalized Langevin equation, and using Laplace Analysis we derive exact expressions for the mean values, variances and diffusion coefficient for a free particle in terms of generalized Mittag-Leffler functions and its derivatives. The asymptotic behavior of these quantities are obtained, from which the anomalous diffusion behavior of the particle is displayed.
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Anomalous diffusion: exact solution of the generalized Langevin equation for harmonically bounded particle.
Physical Review E, 2006Co-Authors: A D Viñales, M A DespósitoAbstract:We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace Analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
A D Viñales - One of the best experts on this subject based on the ideXlab platform.
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Oscillations and negative velocity autocorrelation emerging from a Brownian particle model with hydrodynamic interactions.
Physical Review E, 2020Co-Authors: A D Viñales, M. Camuyrano, G. H. PaissanAbstract:We study the dynamics of a particle in a fluid from a generalized Langevin equation (GLE) with a frictional exponential memory kernel and hydrodynamic interactions. By using Laplace Analysis we obtain the analytical expressions for the velocity autocorrelation function (VACF) and mean square displacement (MSD) of the particle. Our results show that, in the strictly asymptotic time limit, the dynamics of the particle correspond to a particle ruled by a GLE with a Dirac delta friction memory kernel and hydrodynamic interactions. However, at intermediate times the dynamical behavior is qualitatively different due to the presence of a characteristic time in the frictional exponential memory kernel. Remarkably, the VACF exhibits oscillations and negative correlation regimes which are reminiscent of features already observed in pioneering works of molecular dynamics simulations. Moreover, ripples in the MSD appear as an emerging behavior associated with the mentioned regimes.
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Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.
Physical Review E, 2009Co-Authors: A D Viñales, K. G. Wang, M A DespósitoAbstract:The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace Analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
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Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise
arXiv: Statistical Mechanics, 2009Co-Authors: A D Viñales, K. G. Wang, M A DespósitoAbstract:The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace Analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
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Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation.
Physical Review E, 2008Co-Authors: M A Despósito, A D ViñalesAbstract:We investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized Langevin equation. Using Laplace Analysis together with Tauberian theorems we derive asymptotic expressions for the mean values, variances, and velocity autocorrelation function in terms of the long-time behavior of the memory kernel and the correlation function of the random force. The internal and external noise cases are analyzed. A simple criterion to determine if the diffusion process is normal or anomalous is established.
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Anomalous diffusion induced by a Mittag-Leffler correlated noise.
Physical review. E Statistical nonlinear and soft matter physics, 2007Co-Authors: A D Viñales, M A DespósitoAbstract:We introduce a Mittag-Leffler correlated random force leading to anomalous diffusion. Starting from a generalized Langevin equation, and using Laplace Analysis we derive exact expressions for the mean values, variances and diffusion coefficient for a free particle in terms of generalized Mittag-Leffler functions and its derivatives. The asymptotic behavior of these quantities are obtained, from which the anomalous diffusion behavior of the particle is displayed.
Hong Zhang - One of the best experts on this subject based on the ideXlab platform.
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Fourier-Laplace Analysis of the multigrid waveform relaxation method for hyperbolic equations
BIT Numerical Mathematics, 1996Co-Authors: Shlomo Ta'asan, Hong ZhangAbstract:The multigrid waveform relaxation (WR) algorithm has been fairly studied and implemented for parabolic equations. It has been found that the performance of the multigrid WR method for a parabolic equation is practically the same as that of multigrid iteration for the associated steady state elliptic equation. However, the properties of the multigrid WR method for hyperbolic problems are relatively unknown. This paper studies the multigrid acceleration to the WR iteration for hyperbolic problems, with a focus on the convergence comparison between the multigrid WR iteration and the multigrid iteration for the corresponding steady state equations. Using a Fourier-Laplace Analysis in two case studies, it is found that the multigrid performance on hyperbolic problems no longer shares the close resemblance in convergence factors between the WR iteration for parabolic equations and the iteration for the associated steady state equations.
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On the multigrid waveform relaxation method
SIAM Journal on Scientific Computing, 1995Co-Authors: Shlomo Ta'asan, Hong ZhangAbstract:The multigrid waveform relaxation method is an efficient method for solving certain classes of time-dependent partial differential equations (PDEs). This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier–Laplace Analysis, practical convergence rate estimates of the multigrid waveform relaxation are obtained. Experimental results show that the Analysis yields accurate performance prediction.
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On Waveform Multigrid Method
1993Co-Authors: Shlomo Ta'asan, Hong ZhangAbstract:Abstract : Waveform multigrid method is an efficient method for solving certain classes of time-dependent PDEs. This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace Analysis, practical convergence rate estimates of the waveform multigrid iterations are obtained. Experimental results show that the Analysis yields accurate performance prediction.... Waveform relaxation, Multigrid, Spectral radius, Fourier-Laplace, Steady-state problem.
Brian Rider - One of the best experts on this subject based on the ideXlab platform.
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on the shape of the ground state eigenvalue density of a random hill s equation
Communications on Pure and Applied Mathematics, 2006Co-Authors: Santiago Cambronero, Brian Rider, Jose A RamirezAbstract:Consider the Hill's operator Q = −d2/dx2 + q(x) in which q(x), 0 ≤ x ≤ 1, is a white noise. Denote by f(μ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at μ. We prove the detailed asymptotics as μ + ∞. This result is based on a precise Laplace Analysis of a functional integral representation for f(μ) established by S. Cambronero and H. P. McKean in 5. © 2005 Wiley Periodicals, Inc.
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On the shape of the ground state eigenvalue density of a random Hill's equation
arXiv: Probability, 2004Co-Authors: Santiago Cambronero, Jose A Ramirez, Brian RiderAbstract:Consider the Hill's operator $Q = - d^2/dx^2 + q(x)$ in which $q(x)$, $0 \le x \le 1$, is a White Noise. Denote by $f(\mu)$ the probability density function of $-\lambda_0(q)$, the negative of the ground state eigenvalue, at $\mu$. We describe the detailed asymptotics of this density as $\mu \to +\infty$. This result is based on a precise Laplace Analysis of a functional integral representation for $f(\mu)$ established by S. Cambronero and H.P. McKean.
Jose A Ramirez - One of the best experts on this subject based on the ideXlab platform.
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on the shape of the ground state eigenvalue density of a random hill s equation
Communications on Pure and Applied Mathematics, 2006Co-Authors: Santiago Cambronero, Brian Rider, Jose A RamirezAbstract:Consider the Hill's operator Q = −d2/dx2 + q(x) in which q(x), 0 ≤ x ≤ 1, is a white noise. Denote by f(μ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at μ. We prove the detailed asymptotics as μ + ∞. This result is based on a precise Laplace Analysis of a functional integral representation for f(μ) established by S. Cambronero and H. P. McKean in 5. © 2005 Wiley Periodicals, Inc.
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On the shape of the ground state eigenvalue density of a random Hill's equation
arXiv: Probability, 2004Co-Authors: Santiago Cambronero, Jose A Ramirez, Brian RiderAbstract:Consider the Hill's operator $Q = - d^2/dx^2 + q(x)$ in which $q(x)$, $0 \le x \le 1$, is a White Noise. Denote by $f(\mu)$ the probability density function of $-\lambda_0(q)$, the negative of the ground state eigenvalue, at $\mu$. We describe the detailed asymptotics of this density as $\mu \to +\infty$. This result is based on a precise Laplace Analysis of a functional integral representation for $f(\mu)$ established by S. Cambronero and H.P. McKean.
