Fluctuating hydrodynamics and principal oscillation pattern analysis |
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Authors: | Alejandro García Cécile Penland |
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Institution: | (1) Department of Physics, San Jose State University, 95192-0106 San Jose, California;(2) Cooperative Institute for Research in the Environmental Sciences, University of Colorado, 80309-2016 Boulder, Colorado |
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Abstract: | Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series xi(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t)
j
(t*Q
ij
(t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection. |
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Keywords: | Fluctuating hydrodynamics Rayleigh-Bé nard convection Langevin equation principal oscillation pattern analysis |
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