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Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example. 相似文献
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Abazov AI Anosov OL Faizov EL Gavrin VN Kalikhov AV Knodel TV Knyshenko II Kornoukhov VN Mezentseva SA Mirmov IN Ostrinsky AV Pshukov AM Revzin NE Shikhin AA Timofeyev PV Veretenkin EP Vermul VM Zatsepin GT Bowles TJ Cleveland BT Elliott SR O'Brien HA Wark DL Wilkerson JF Davis R Lande K Cherry ML Kouzes RT 《Physical review letters》1991,67(24):3332-3335
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Problems of controllability and methods of stabilizing programmed motions of a large class of mechanical and electromechanical systems which are reversible with respect to the control are considered. Criteria of the controllability and stabilizability of reversible systems are obtained. Programmed motions and algorithms of programmed control are designed in analytical form and algorithms of programmed motions for non-linear reversible systems are synthesized. 相似文献
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KM Varier AM Vinodkumar NVSV Prasad PV Madhusudhana Rao DL Sastry Lagy T Baby MC Radhakrishna NG Puttaswamy JJ Das P Sugathan N Madhavan AK Sinha DO Kataria 《Pramana》1999,53(3):529-533
Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies.
Coupled channel calculations incorporating couplings to 2+ and 3− states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements
had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer
were carried out for 46,48Ti+61Ni systems. The present paper gives the results of these studies. 相似文献
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S. I. Dolaptchiev U. Achatz I. Timofeyev 《Theoretical and Computational Fluid Dynamics》2013,27(3-4):297-317
We present a new approach for the construction of stochastic subgrid scale parameterizations. Starting from a high-resolution finite-difference discretization of some model equations, the new approach is based on splitting the model variables into fast, small-scale and slow, large-scale modes by averaging the model discretization over neighboring grid cells. After that, the fast modes are eliminated by applying a stochastic mode reduction procedure. This procedure is a generalization of the mode reduction strategy proposed by Majda, Timofeyev & Vanden-Eijnden, in that it allows for oscillations in the closure assumption. The new parameterization is applied to the forced Burgers equation and is compared with a Smagorinsky-type subgrid scale closure. 相似文献
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This paper is devoted to estimation of parameters for a noisy sum of two real exponential functions. Singular Spectrum Analysis is used to extract the signal subspace and then the ESPRIT method exploiting signal subspace features is applied to obtain estimates of the desired exponential rates. Dependence of estimation quality on signal eigenvalues is investigated. The special design to test this relation is elaborated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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