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.     

h.c.p.-f.c.c. phase transition in solid parahydrogen

The difference of free energies for the h.c.p. and f.c.c. parahydrogen is calculated as a function of molar volume. It is shown that the observed transition in solid parahydrogen¹ can be explained by differences in the structure of the cubic and quartic anharmonic terms.     

Diffraction dissociation into high masses at N.A.L.-I.S.R. energies

The triple-pomeron picture of diffraction dissociation into high masses, combined with recent observations about the dominance of short-range correlations in multiparticle production at very high energies, implies that the cross section for diffractive dissociation into high masses rises approximately logarithmically in the NAL-ISR energy range. Predictions are also made about the multiplicity distribution of diffractively-produced particles.     

In memoriam: Prof. Dr. dr.h.c. Rolf Hosemann

Dr. h.c. Rolf Hosemann, the “father of the ideal paracrystal,” passed away in Berlin on September 28, 1994, in his 83rd year. Rolf Hosemann was born in 1912 at Rostock on the Baltic Sea. He studied physics at Marburg and Freiburg, in Germany. In 1939 he obtained qualifications as a university teacher upon a “Habilitationsschrift” about the small-angle x-ray scattering of cellulose. In 1950 he laid the foundation to his theory of ideal paracrystals making wide use of convolution integrals as introduced into x-ray crystallography by P. P. Ewald. M. V. Laue was so much impressed by Hosemann's papers that he asked him to join the Fritz-Haber-Institut at Berlin-Dahlem as a staff member. It was there that Hosemann compiled his extensive work of more than 370 papers. Hosemann taught a large number of students. More than ten among them became university professors.     

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。     

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.     

Hall effect studies in ytterbium through the f.c.c.-h.c.p. transformation

The Hall coefficient (R_H) of polycrystalline Yb showing the f.c.c.-h.c.p. transformation has been determined at 20 koe in the range 1.8–420°K. Both the structural and the associated magnetic transformation would separately be expected to modify R_H, but the evidence suggests that the observed behaviour through the transition arises primarily from the effects of the change in structure. A more detailed interpretation is presently not possible, however, because of the lack of knowledge of the band structure of h.c.p. Yb.     

Relative stability of f.c.c. and b.c.c. structures for model systems at high temperatures

Summary Free-energy, entropy and volume differences between face-centered and body-centered cubic structures have been evaluated for model rare gas and alkali metal crystals by using the method of overlapping distributions. Stable phases are predicted in agreement with the behaviour of real materials in the regions of validity of classical mechanics and in agreement with the results of previous dynamical-simulation studies of crystal nucleation from the melt and of polymorphic transformations. The existence of a stable b.c.c. phase at high pressure and temperatures is predicted in this way for Lennard-Jones solids, while no high-pressure f.c.c. phase is expected for model Rb and Cs systems. We also show the possibility of making calculations of free-energy barriers to displacive crystalline transformations along a prescribed trajectory in configuration space. Work supported by the U.S. Department of Energy, Istituto per la Ricerca Scientifica e Tecnologica, Trento, and Gruppo Nazionale di Struttura della Materia del C.N.R., Italy.     

Linear and Nonlinear Raman Spectroscopy onⅡ-Ⅵ Semiconductor Quantum Wires and Dots

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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.     

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.     

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.     

B.c.c.-f.c.c. allotropy, F-bands,and metallization in xenon and krypton

APW-Xα calculations of a f.c.c.-b.c.c. phase transition in Xe prior to metallization give P ? 950 kbar, contrary to the 820 kbar result of Hama and Matsui; their use of non-touching APW spheres (f.c.c.) may be the crucial difference. Hartree-Fock plus correlation calculations in Kr indicate that f-bands play no role in rare gas crystal metallization.     

Sputtering yield measurements on H. C. P. and F. C. C. cobalt V. S. chernysh

A computer code previously set up to simulate ion penetration in amorphous solids has been extended to handle with recoil phenomena. Preliminary results are compared with existing experimental data.