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91.
Gregorio Falqui 《Reports on Mathematical Physics》2002,50(3):395
We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem. 相似文献
92.
We study the order reduction method of the rotational relativistic Birkhoffian equations.For a rotational relativistic autonomous Birkhoffian system,if the conservative law of the Birkhoffian holds,the conservative quantity can be called the generalized energy integral.Through the eneralized energy integral,the order of the system can be reduced.If the rotational realtivistic Birkhoffian system has a generalized energy integral,then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the result. 相似文献
93.
94.
Hirohisa Yokota Kenji Kamoto Jun-ichi Igarashi Norihiko Mouri Yutaka Sasaki 《Optical Review》2002,9(1):9-12
A new configuration for an ASE reduction filter in EDFA repeaters for WDM optical transmission systems using optical fiber grating couplers (FGCs) was proposed and first demonstrated. The filtering characteristics of the proposed filter for amplified single wavelength signal and 2-channel WDM signals using EDFA were identified. It was found that the filter was effective to improve SNR in optical domain by reducing ASE noise. The required FGC characteristics for the filter were theoretically predicted under the condition that the total filter loss did not exceed 3 dB. More than 70% of drop efficiency was required in each FGC for the application of the proposed filter to an 8-channel WDM system using EDFA repeaters. 相似文献
95.
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
96.
Letters in Mathematical Physics - Suppose we are given a compact Riemannian manifold (Q,g) with a completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by... 相似文献
97.
Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance. 相似文献
98.
Hans C. Fogedby 《Journal of statistical physics》1992,69(1-2):411-425
We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang. 相似文献
99.
Ling Guocan 《Acta Mechanica Sinica》1988,4(3):211-222
In the present paper the mechanism involved in vortex shedding flows is investigated in detail. In the early stage of the
unsteady separated flow the interaction between secondary vortices and primary vortices is quite strong. In the later stage
of the flow, corresponding to the vortex shedding the recirculating flow region on each side of the aft body goes through
such a cycle: growth-contraction-growth, the secondary separation occurs periodically rather than continuously. The reduction
of circulation is taken into account in three cases with different decay factors to study its influence on the prediction
of main flow characteristics. Results show that to simulate vortex shedding flow it is necessary to include the reduction
of circulation to bring the calculated results into good agreement with experiments. An improved discrete vortex model is
suggested in which both the secondary separation and the reduction are incorporated. The processes of vortex shedding, the
forces prediction and other flow characteristics are given and some discussions are made.
Porject is supported by National Natural Science Foundation of China. 相似文献
100.
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions. 相似文献