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The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility. 相似文献
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Warren WM. McGovern 《代数通讯》2013,41(4):1636-1646
The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero. 相似文献
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Horst G. Adolph Judah M. Goldwasser William M. Koppes 《Journal of polymer science. Part A, Polymer chemistry》1987,25(3):805-822
A series of primary and secondary diols carrying nitroalkyl, nitro, and fluoro substituents was reacted with formaldehyde under conditions of acid catalysis. Short-chain primary diols gave cyclic formals while predominantly linear polymers were obtained beginning with pentane-1,5-diols and hexane-1,6-diols, depending upon the nature of the substituents. No polymers were formed from secondary diols with 1-nitroalkyl substituents. The effect of monomer structure on polymer formation is discussed. The polymers obtained were characterized by GPC and end group analysis. 相似文献
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Synthetic mixtures of aliphatic and aromatic ethers, satmated fatty acids, and substituted benzenes and naphthalenes were separated by elution through columns of ion-exchange resins with aqueous solutions of acetic acid as eluent An attempt was made to use a resin of low capacity for the separation of such mixtures, and the results of this attempt are used to help elucidate the theory of solubilization chromatography 相似文献
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A new approach to on-line oxygen isotope analysis has been developed which utilises existing elemental analyser and mass spectrometry technology to produce a sample of carbon dioxide gas for oxygen isotople analysis. The method relies on on-line high temperature pyrolysis of the sample over a carbon source followed by a rapid, non-contributive partial catalytic oxidation over nickel powder at between 550 and 600 degrees C. Initial results demonstrate both good precision (better than 0.2 per thousand) and accuracy for both cellulose and silver nitrate samples. Copyright 1999 John Wiley & Sons, Ltd. 相似文献
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Hydrogenation of azo bonds with hydrazine, mono-substituted hydrazine, and hydrazobenzene was studied with selected diazene compounds under oxygen-free conditions. The reactions proceed rapidly and in high yield in several solvents, utilizing all N-H protons. While the reduction process is accompanied by the evolution of nitrogen gas in the case of N2H4, the intermediacy of diimide could not be confirmed by standard trapping experiments. 相似文献
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WM.B. Peatman Gerald B. Kasting David J. Wilson 《Journal of Electron Spectroscopy and Related Phenomena》1975,7(3):233-246
Autoionization electrons in threshold photoionization spectra are known to occur. The effect of such electrons on the interpretation of threshold electron spectra is discussed and a new method is described which enables one to discriminate between zero kinetic energy electrons and energetic electrons in photoionization experiments with little ambiguity. The method largely overcomes the main problem present in some previously described threshold electron studies; namely, the line-of-sight transmission of energetic electrons which gives rise to non-threshold electron peaks. A rejection ratio of 25 is readily obtained for 0.038 eV electrons compared with threshold (zero kinetic energy) electrons and the (small) transition probability for energetic electrons falls off more rapidly than for analysers previously described. Design parameters based on electron trajectory calculations are given for the analyser used, and photoionization results on argon are presented. 相似文献
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Richard T Libby Gareth R Howell Iok-Hou Pang Olga V Savinova Adrienne K Mehalow Joseph W Barter Richard S Smith Abbot F Clark Simon WM John 《BMC neuroscience》2007,8(1):108