Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

白藜芦醇分子的转动惯量和电偶极矩

通过分子轨道理论和杂化轨道理论推断出较稳定的白藜芦醇分子是平面型分子,然后根据白藜芦醇分子结构特点计算了该化合物的一种稳定异构体的转动惯量,用矢量合成法计算了其电偶极矩,为微波辅助白藜芦醇萃取理论研究提供转动惯量和电偶极矩的数据.     

Relationships among Preparative Technique,Phase Composition and Bending Strength of Bauxite Porcelain

1 INTRODUCTION Bauxite porcelain is a novel “K2O–Al2O3–SiO2” system ceramic by using sintered bauxite, clay and potash feldspar and albite as the main raw materials with the Al2O3’s content of 50%～60(massfraction). Compared to the traditional“K2O–Al2O3–SiO2” feldspar porcelain by using quartz, bolus alb and potash feldspar and albite as the main raw materials, the bauxite porcelain possesses such advantages as high mechanical strength, excellent electrical insula- tion prop…     

APPLICATION OF THE MOMENT METHODS TO ANALYSIS OF X-RAY DIFFRACTION LINE PROFILE FOR PA1010-BMI SYSTEM

Pure X-ray diffraction profiles have been analysed for polyamide 1010 and PA1010--BMI system by means of multipeak fitting resolution of X-ray diffraction.The methods ofvariance and fourth moment have been applied to determine the particle size and strainvalues for theparacrystalline materials.The results indicated that both variance and fourthmoment of X-ray diffraction line profile yielded approximately the same values of theparticle size and the strain.The particle sizes of(100)reflection have been found todecrease with increasing BMI content,whereas the strain values increased.     

三级相互作用对聚亚甲基链末端距四次矩的影响

本文用三级相互作用近似理论导出了高分子链末端距的四次矩的计算公式。计算聚亚甲基链的末端距四次矩,并同二级相互作用的结果进行了比较。对于聚亚甲基链,三级相互作用近似的四次矩小于二级相互作用近似的四次矩。     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

Ionic Mobility, Phase Transitions, and Superionic Conduction in Solid Solutions (100 ? x)PbF2-xZrF4 and Crystals K2ZrF6, (NH4)2ZrF6, KSnZrF7, and M(NH4)6Zr4F23 (M = Li, Na)

Methods of (¹⁹F, ¹H) NMR and impedance spectroscopy are used to investigate the internal mobility and ionic conduction in solid solutions arising in the system PbF₂-ZrF₄ and polycrystals KSnZrF₇, Li(Na)(NH₄)₆Zr₄F₂₃, and M₂ZrF₆ (M = K, NH₄). Factors responsible for the form of ionic motions and their energetics at 170–550 K are considered. It is established that the phase transitions in these compounds are connected with the crystal transition to a superionic state and that the high ionic (superionic) conductivity of beta phases is due to the diffusion of fluoride ions, ammonium cations, and possibly alkali metal cations. The obtained data testify to a substantial role of chainlike aggregation of anionic groupings and a variableness of structural mechanisms of formation of such chains in fluorozirconates for the development of translational diffusion in these compounds.__________Translated from Elektrokhimiya, Vol. 41, No. 5, 2005, pp. 573–582.Original Russian Text Copyright © 2005 by Kavun, Uvarov, Slobodyuk, Goncharuk, Kotenkov, Tkachenko, Gerasimenko, Sergienko.     

Molecular Dipole Moment and Interaction Dipole Moment in 2-N-Substituted Amino-3(or 5)-methyl-4-nitropyridines and Their N-Oxides

The dipole moments of 2-alkylaminoand 2-alkylnitramino-3(or 5)-methyl-4-nitropyridines and their N-oxides have been measured, as well as calculated, using vectorial summation of the group moments and by ab initio method. The estimated interaction dipole moments, _int, have been discussed in terms of the electronic and steric effects and intramolecular hydrogen bonding. Introduction of the NHCH₃ group to position 2 in 4-nitropyridine strengthens the conjugation between the nitro group and ring nitrogen. The lack of such strengthening in 4-nitropyridine-N-oxides is explained as being due to formation of intramolecular hydrogen bond between the N-oxide group and the hydrogen of alkylamino group. Introduction of the nitramino group does not lead to marked modification of the charge distribution in a molecule. This fact may be explained by much weaker electron-donating ability of this group in comparison with the alkylamino group.     

Infrared intensities of liquids XXV: Dielectric constants, molar polarizabilities and integrated intensities of liquid toluene at 25 °C between 4800 and 400 cm

The main purpose of this paper is to present accurate infrared integrated intensities of liquid toluene, C₆H₅CH₃, at 25 °C. Also presented are the decadic molar absorption coefficients, E_m, the real and imaginary dielectric constants, ε′ and ε″, and the real and imaginary molar polarizabilities, ^′_m and ^″_m. Integrated intensities were determined as C_j, the area under bands in the spectrum, for all bands between 4800 and 440 cm⁻¹. The contributions from the different bands were separated by fitting the spectrum with classical damped harmonic oscillator bands. The uncertainties in the integrated intensities of most bands are estimated to be 5–10%, with the uncertainties in very weak bands and in shoulders possibly up to 100%. The intensity that should be assigned to the fundamentals is more difficult to estimate due to Fermi resonance with overtone and combination bands, and a best estimate is given. The integrated intensities of the fundamental vibrations and the corresponding transition dipole moments are summarized and are compared with literature values for the gas.     

内含式化合物X@B12P12的结构与稳定性研究

采用B3LYP/6-31G*方法，对内含式化合物X@B₁₂P₁₂(X=Li^0/+、Na^0/+、K^0/+、Be^0/2+、Mg^0/2+、Ca^0/2+、H和He)的不同对称性构型进行了计算，讨论其最稳定构型的几何参数、布居分析、偶极矩、电离势、包含能、振动频率、能隙和自旋密度． 发现在X@B₁₂P₁₂化合物中，客体X=Li、Na^0/+、K^0/+、Mg^0/2+、Ca^0/2+和He处在偏离笼的中心0.006 nm的半径内． Be²⁺沿着C₃轴偏离中心点0.279 nm． 在Be@B₁₂P₁₂和H@B₁₂P₁₂的基态结构中，Be和H与笼上的B原子成键． 除Li@B₁₂P₁₂、 Be²⁺@B₁₂P₁₂和He@ B₁₂P₁₂外， 其余结构为C_s对称稳定构型．