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Title: Data-driven non-Markovian closure models

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Grant/Contract Number:
DOE-DE-F0A-0000411; 14.Z50.31.0033
Resource Type:
Journal Article: Published Article
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 297; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-06-21 21:27:56; Journal ID: ISSN 0167-2789
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Citation Formats

Kondrashov, Dmitri, Chekroun, Mickaël D., and Ghil, Michael. Data-driven non-Markovian closure models. Netherlands: N. p., 2015. Web. doi:10.1016/j.physd.2014.12.005.
Kondrashov, Dmitri, Chekroun, Mickaël D., & Ghil, Michael. Data-driven non-Markovian closure models. Netherlands. doi:10.1016/j.physd.2014.12.005.
Kondrashov, Dmitri, Chekroun, Mickaël D., and Ghil, Michael. 2015. "Data-driven non-Markovian closure models". Netherlands. doi:10.1016/j.physd.2014.12.005.
title = {Data-driven non-Markovian closure models},
author = {Kondrashov, Dmitri and Chekroun, Mickaël D. and Ghil, Michael},
abstractNote = {},
doi = {10.1016/j.physd.2014.12.005},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 297,
place = {Netherlands},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.physd.2014.12.005

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Cited by: 16works
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  • Mode-selective excitation of adsorbates by shaped infrared laser pulses is investigated here theoretically, for the example of a H atom on a hydrogen-covered Si(100)-2x1 surface. The mode-selective excitation is perturbed by the intermode coupling within the system (bending and stretching modes) and by system-bath coupling to substrate phonons. Using a force-field based model, vibration-phonon coupling was found and predicted to lead to vibrational relaxation of the H-Si stretching mode on a ns timescale, and of the Si-Si-H bending mode on a ps timescale [I. Andrianov and P. Saalfrank, J. Chem. Phys. 124, 034710 (2006)]. To address the question as tomore » whether in such a dissipative situation mode-selective control of adsorbate vibrational dynamics is still possible, a system-bath ansatz is used to derive an open-system density matrix theory in which the H vibrations are driven either by sin{sup 2}, or by freely optimized infrared ps laser pulses. Both for the Si-H stretching and Si-Si-H bending vibrations mode-selective excitation is predicted to be possible. It is also found that the Markov approximation works well in most of the applications, and that simple sin{sup 2} are nearly as effective as pulses which were freely optimized by optimal control theory.« less
  • The test-field model is shown to be potentially {ital nonrealizable} in the presence of linear waves such as those frequently encountered in models of plasma and geophysical turbulence. A new statistical closure, the realizable test-field model (RTFM), is proposed as a remedy. Both the damping rate and frequency are renormalized to account for nonlinear damping and frequency shifts. Like the realizable Markovian closure (RMC), the RTFM is based on a modified fluctuation-dissipation ansatz. Numerical solutions of the RTFM, RMC, and direct-interaction approximation for the Hasegawa{endash}Mima equation are presented; rough agreement with direct numerical solution is found. The number of retainedmore » Fourier modes is dramatically reduced with an anisotropic generalization of a recently developed wave-number partitioning scheme. {copyright} {ital 1997 American Institute of Physics.}« less
  • A type of eddy-damped quasinormal Markovian (EDQNM) closure is shown to be potentially [ital nonrealizable] in the presence of linear wave phenomena. This statistical closure results from the application of a fluctuation--dissipation (FD) ansatz to the direct-interaction approximation (DIA); unlike in phenomenological formulations of the EDQNM, both the frequency and the damping rate are renormalized. A violation of realizability can have serious physical consequences, including the prediction of negative or even divergent energies. A new statistical approximation, the realizable Markovian closure (RMC), is proposed as a remedy. An underlying Langevin equation that makes no assumption of white-noise statistics is exhibited.more » Even in the wave-free case the RMC, which is based on a nonstationary version of the FD ansatz, provides a better representation of the true dynamics than does the EDQNM closure. The closure solutions are compared numerically against the exact ensemble dynamics of three interacting waves.« less
  • Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain themore » periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a nonunitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures. {copyright} {ital 1997} {ital The American Physical Society}« less
  • The dynamics of a driven spin-boson model is studied by means of the perturbation approach based on a unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained. The results show that for weak driving, the population difference displays damping coherent oscillation and/or damping quantum beat, depending on the initial preparation. The coherence exhibits damped oscillation with Rabi frequency. When driving is strong enough, the population difference exhibits undamped large-amplitude coherent oscillation. In addition, our theory leads to correct results in two limiting cases: without dissipation and without driving field.