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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
23.
直流稳压电源可以将交流电压变换为直流电压,并使之稳定,在我们现实生活中应用很广泛,在实验中我们利用的电学知识,设计制造了一种直流稳压电源。本文简要介绍了这种直流稳压电源波形演示器的设计目的和电路原理,重点阐述了它的制作流程、滤波和稳压原理以及性能测试输出波形。 相似文献
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25.
Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates
The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination. 相似文献
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An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss 总被引:3,自引:0,他引:3
Mohammad Jafari Jozani Nader Nematollahi Khalil Shafie 《Statistics & probability letters》2002,60(4):437-444
A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given. 相似文献
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应用TGT法生长了直径为75mm的U:CaF2晶体,宏观上透明完整.应用公式K0=Cs/Cl计算了U在CaF2晶体中的分凝系数等于0.53.应用溶质分布一般公式Cs=K0C0(1-g)K0-1,计算U的浓度分布与测量值,数值符合说明晶体生长过程接近平衡状态.分析不同条件下生长的U: CaF2晶体的晶胞参数和吸收光谱,结果表明生长气氛决定U的价态及电荷补偿机理:无PbF2存在的条件下,U为+4价,晶体呈绿色;PbF2的加入起到氟化去氧作用,U倾向于以离子半径最接近于Ca2+的U3+存在,晶体呈红色.从晶体生长开始到结束的部位,U3+:CaF2晶体吸收光谱的峰位不变,峰强呈现与U浓度相同的增加趋势.U3+:CaF2晶体外层厚约5mm处呈黄色,含有U3+和U2+的混合价态离子,其原理是石墨坩埚的还原作用通过单质铅,使部分的U3+进一步还原成了U2+.
关键词:
铀
氟化钙晶体
分凝系数
晶胞参数 相似文献
30.
Noboru Nakatani 《Optical Review》2003,10(4):206-210
This paper describes a compulsorily phase locked differential interferometer using an orthogonally polarized light source of a modulated LD with high extinction ratio to reduce non-linearity of the interferometer caused by polarization cross-talk. The current modulated LD is used as a light source to make the interferometer compact and for the scanning phase of the interferometer. The interferometer is operated compulsorily at the maximum inclination point of the fringe intensity curve by fringe scanning and an electric system. A Wollaston prism of high extinction ratio (50 dB) is used to combine the polarizing beams and to make the polarization cross-talk very small. In one light source the polarized output beams are on the same propagation axis; in the other they have a small crossing angle (2.5 mrad ∼ 10 mrad) to completely exclude non-linearity of the interferometer causded by polarization cross-talk. Using jets of a gas mixture of nitrogen and ethylene, this interferometer was demonstrated to be useful in detecting the photothermal effect of a photothermal velocimeter under phase fluctuation in a turbulent flow. 相似文献