Nonequilibrium statistical mechanics. I. Mathematical formalism. Theorem of N. S. Krylov

Based on an algebraic formulation of quantum mechanics we introduce concepts playing a fundamental role in the constructionof the statistical mechanics of systems having direct classical analogs. We give the definition of a macrostate, mixing in the quantum version, and also demonstrate the existence of an upper bound to the relaxation time for an isolated system. It is shown that the theory constructed here contains both quantum and classical mechanics as limiting cases, but these two cases are not reducible to each other. The existence of a transition range not describable by the Schrodinger equation is noted.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 11, pp. 42–45, November, 1981.     

Analysis of R. P. Smith's and D. C. Parris-R. B. Mclellan's carbon diffusivity data

A phenomenological model is proposed to account for the variation of carbon diffusivityD(N₁) with composition in austenite. This model is based on Parris-McLellan's statement that the increase ofD(N₁) with carbon concentrationN ₁ is due to the increase in chemical driving force. The gradient of the carbon activity in Wagner's and in Zupp-Stevenson's interpretation is presumed to be the intrinsic driving force. The predictions of the model are compared with carbonD(N₁) values both with [1] and without [5] a chemical concentration gradient. TheD(0) values and the carbon-carbon interaction coefficients ₁ are calculated by the use of the least squares method from the experimental data. The application of Zupp-Stevenson's definition of the activity coefficient ₁ results in a better fit of the theory to the experimental data.     

N.M.R. spectra of oriented molecules

The phosphorescence spectra of anthracene-h₁₀ and -d₁₀ have been studied in a number of glasses and crystalline matrices. The line widths are very matrix dependent and they range from about 150 cm^-1 to 1 cm^-1 in n-heptane. There is a correlation between the line width and the wavenumber position of the origin. A study of the relative intensities of fluorescence and phosphorescence from various sites in Shpolskii matrices has shown that the intersystem crossing rate is site dependent. It is postulated that this involves the relative energies of the singlet state and a triplet state, nearly degenerate with it, which are site dependent.     

N.M.R. study of solid perfluorocyclobutane

spin-lattice relaxation times and linewidth measurements for fluorine nuclei in solid perfluorocyclobutane are presented. The results are discussed in terms of D _2d molecular species performing fast internal motion. The relaxation measurements corroborate the existance of four solid-solid phase transitions and give some insight into their nature. The activation energies for molecular reorientation and self-diffusion processes are found to be 28·0 and 32·2 kJ mol^-1, respectively.     

N.M.R. spectra of oriented molecules

By analysis of the high resolution N.M.R. spectrum of 1,2,2,3-tetrachloro-propane partially oriented in a liquid-crystal solvent, it has been shown that this molecule takes up predominantly the G′G′ type of conformation.     

E.S.R. spectroscopy of non-cyclic enones

The π-bond model is applied to the calculation of the proton chemical shifts of a range of benzenoid hydrocarbons. The simple calculations give results which compare well with experiment and with calculations based on the ring current model. Least squares fitting of the predicted chemical shifts to the observed values can give an indication of the occurrence of local aromatic groups in larger molecules. This procedure also yields an empirically adjusted estimate of the anisotropy in the molar magnetic susceptibility from the experimental proton chemical shifts. A simple criterion for aromaticity is also given. The overall results suggest that there is no need to associate a special ring current attribute to π conjugation in aromatic molecules.     

On the mathematical structure of the B.C.S.-model. II

It is shown for the degenerate B.C.S.-model how in the limit of an infinite system the exact thermal Greens-functions approach a gauge invariant average of the one's calculated with the Bogoliubov-Haag method.Work performed as consultant to General Atomic Europe.     

N.M.R. relaxation study of crystalline quinuclidine

Transient signals in the fluorescence intensity induced by microwaves can be used to acquire quantitative information on the molecular rates of populating and depopulating of the lowest triplet state of organic molecules. This method seems especially promising when the molecule emits no detectable phosphorescence.

Part of this paper concerns the introduction of an appropriate mathematical model for describing the fluorescence transients. The model is formulated in conjunction with a specific series of experiments from which one may evaluate the molecular quantities in a systematic way. The kinetics of the lowest triplet state of free base porphin (H₂P) are determined explicitly by this method.

In the discussion the results for H₂P are compared with those for Zn porphin. A satisfactory qualitative explanation based on the theory of radiationless transitions can be given for the great difference in behaviour of these two porphyrin molecules.

Short attention is given to effects due to the photochemical shift of the two H atoms in the centre of H₂P, which is proven to occur even at a temperature as low as 1·3 K.     

Orbital pair theory of N.M.R. shielding

A simple correction accounting for the effect of truncating the atomic orbital basis on the calculation of N.M.R. shielding is proposed. This correction is obtained from the expression for the magnetic shielding as a sum of orbital pair contributions: a spurious term that vanishes only if a complete basis is used appears in this expression. It is demonstrated both theoretically and numerically (using the example of PH₃) that removing this term from the results obtained with a truncated basis improves significantly the agreement with the experimental values. As a by-product the gauge dependence of the numerical results is much reduced. The additional computing time is negligible.     

N.M.R. studies of liquid boron trifluoride

Previous ¹⁹F N.M.R. studies of liquid BF₃ have been extended by obtaining the ¹¹B spectrum of BF₃ and the ¹⁹F spectrum of ¹⁰BF₃ at various temperatures. Values for the B-F coupling constant and the boron relaxation times have been obtained by computer matching and visual matching of observed and calculated spectra. Relaxation times have the Arrhenius temperature dependence found previously. The temperature dependence of the B-F coupling constant is discussed. Some of the possible advantages of ‘high spin spectra’ are discussed.     

75As N.Q.R. and 19F N.M.R. study of solid AsF3

The temperature dependence of the ⁷⁵As pure quadrupole resonance frequency in AsF₃ has been studied from 77 K to a temperature very close to the melting point. It is found that the effective electric field gradient at the As site does not shift much from the gas-phase value and that the temperature dependence of the ⁷⁵As N.Q.R. frequency seems to follow the Bayer-Kushida model. The occurrence of a line-width transition in the ¹⁹F N.M.R. spectrum between 200 and 150 K demonstrates the presence of low-frequency, large-amplitude molecular motions which are too slow to average out the ⁷⁵As quadrupole coupling.     

FAAS法测定丰城鸡血藤中锶含量的方法探讨

探索建立空气-乙炔火焰原子吸收测定丰城鸡血藤中微量元素锶含量的方法。以丰城鸡血藤为研究对象,HNO3-HCLO4(4+1)为消解液,采用压力主控微波消解样品,EDTA-2Na溶液为抑制剂,用火焰原子吸收光谱法(FAAS)测定丰城鸡血藤中微量元素锶的含量。微波消解药材消化完全,测定线性良好,范围0~1.6μg.mL-1,回归方程为Y=0.036 5X-0.001 1,r=0.999 4,方法学检出限为0.008 2μg.mL-1(n=21),平均回收率101.5%,RSD=2.04%。该方法灵敏度高,操作简单,结果准确,适用于该药材中锶元素的含量测定。     

Modified independent modal space control of m.d.o.f. systems

The performance of the independent modal space control (IMSC) algorithm for structural vibration control is examined in this paper. Both the theoretical analysis and numerical simulation show that, for a multi-degree-of-freedom system, the modal control forces may increase the contributions of the vibration of higher modes (uncontrolled modes) to the system response if the IMSC algorithm is used to design a structural control system. Therefore, the responses of the controlled structure may be underestimated if the effects of control forces on the higher modes are not considered in the response analysis. A new control algorithm—modified independent modal space control (MIMSC) algorithm is proposed in this paper for eliminating the effect of modal control force on the uncontrolled modes. Numerical example shows that the structural responses can be effectively reduced when control system design is carried out based on the proposed algorithm. By comparing the simulated results obtained by the IMSC and MIMSC algorithms, it is found that, in order to achieve the same control objective, the proposed algorithm is more effective than IMSC since the modal control forces do not have any effect on the uncontrolled modes. In order to verify the effectiveness of the proposed algorithm, a practical example—active control design of UCLA Math-Science Building is presented and discussed.     

Interpretation of S-state ion E.P.R. spectra

Although a considerable body of data exists on the parametrization of the ground-state splittings of S-state ions in crystals, relatively little progress has been made in obtaining a quantitative understanding of the mechanisms which determine these parameters. In the course of summarizing our present understanding, we emphasize the need for making planned experiments explicitly aimed at testing theoretical models, such as those proposed in this article. The variable frequency E.P.R. technique is described in some detail, as it has proved to be particularly useful in this respect.