An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

The response of microstructure to processing in a series of poly(siloxaneimide) copolymers

Poly(siloxaneimide) (PSI) segmented copolymers exhibit organized microdomains if the blocks are sufficiently incompatible. As with neat diblock and triblock copolymers, the processing route employed to prepare films of PSI materials is expected to influence the dimensions and/or morphology of the resultant microstructure. In this work, small-angle neutron scattering (SANS) is utilized to characterize the disordered microstructure found in films of a series of PSI copolymers which are subjected to solvent casting and various thermal treatments. Microstructural dimensions such as the periodicity and correlation length are deduced from the Teubner-Strey (TS) model for disordered microemulsions. The scattering intensity of each copolymer up to q = 5.0 nm^?1, where q is the scattering vector, is found to scale as q^?2.8+?0.1. Results indicate that processing the materials as cast films or as melt-pressed films allowed to cool slowly has a small, but discernible, effect on microstructural characteristics. SANS profiles of films quenched from elevated temperatures reveal a clear transition in microdomain periodicity, which correlates well with the glass transition temperature of the imide microphase in these and other materials of similar chemical structure. © 1993 John Wiley & Sons, Inc.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

圆形隧洞周边位移和地层压力预报的简便公式

应用本文所提出的公式可计算地层的初始应力和由开挖引起的洞周位移。预报公式所需要的计算数据是一组相邻测点之间的量测位移,这可通过隧洞的施工监控量测而得到。在推导这些预报公式时,著者先应用一系列的有限元和无限元等数值计算方法来模拟洞室的开挖,从而得到大量的“观测数据”。然后综合应用自动回归和解析方法,建立了实用的计算公式。这些公式使用简便且具有良好的精度。     

粘结平面对称分叉裂纹的奇异积分方程数值解

本文对一个含分叉裂纹的弹性半平面与另一不同材料的半平面粘结的问题用复势方法化为一组三个复Caucby型奇异积分方程。采用修正的Gauss-Legendre和修正的Lobatto-Legendre数值求积法则化成一代数方程组,裂纹尖端的应力强度因子值可从代数方程组的解求得。本文计算得到了弹性半平面、刚体与弹性半平面相粘结、两种不同材料的弹性半平面相粘结的三种问题的几种几何形状的对称分叉裂纹的应力强度因子。本文的结果扩充了“应力强度因子手册”的内容。     

Synthesis of ansa -zirconocenes based on 2-(phenylethynyl)-1 H -indene. The crystal and molecular structure of the complex [μ-CH2CH2(η5-2-PhC≡CInd)2]ZrCl2 (Ind is inden-1-yl)

Alkynyl-substituted indene was first used as a ligand for the synthesis of transition metal complexes. ansa-Zirconocenes containing ethylene and dimethylsilylene bridges were synthesized starting from 2-(phenylethynyl)-1H-indene. The structure of the former compound was established by X-ray diffraction. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 68–73, January, 2007.     

Synthesis,molecular and crystal structures,and characteristic features of electronic structures of salicylamide-based B,Si-containing chelates

The reaction of 4-(2-hydroxybenzoyl)-2,2,6,6-tetramethyl-2,6-disilamorpholine with BF₃Et₂O afforded (O-B)-chelate 4-[2-(difluoroboroxy)benzoyl]-2,2,6,6-tetramethyl-2,6-disilamorpholine. Treatment of the latter with BF₃Et₂O or SOCl₂ gave rise to products of the disilamorpholine ring opening, viz., (O-B) chelate 2-(difluoroboroxy)-N,N-bis(dimethylfluorosilylmethyl)benzamide or 2-(difluoroboroxy)-N, N-bis(dimethylchlorosilylmethyl)benzamide, respectively. The structures of the compounds synthesized were confirmed by X-ray diffraction analysis and ¹H, ¹³C, and ²⁹Si NMR spectroscopy. High-precision X-ray diffraction study and quantum-chemical calculations demonstrated that the coordination OSi bond is absent in the two last-mentioned compounds.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1846–1853, September, 2004.     

A method for selection and use of numerical integration points for molecules with cylindrical symmetry

Boys and Handy [1] have discussed the solution of the bivariational equations with restricted numerical integration. One of the weaknesses of the method was that in the numerical summations over points, some points arose with r _ij= 0 and non-zero weights. This makes the method quite impractical for the Schrodinger Hamiltonian (because of the singularity at r _ij= 0), and it cannot be advantageous for the transcorrelated Hamiltonian C^–1HC because there will be some discontinuous higher derivatives at r _ij=0. Here it is shown how the symmetry of cylindrically symmetric molecules can be used to eliminate such points, without losing any of the advantages of the overall method, such as the convergence of the eigensolutions. It is also shown how the primary numerical integration points (z _i, r_i) may be chosen in any calculation such that each is associated with an equal amount of one-electron density. The choice of the angular coordinates are governed by the removal of the r _ij=0 points and maintaining the natural orthogonality between orbitals of different symmetry types. The method has been programmed and found to be practical, although no new molecular calculations have yet been performed. It is to be hoped that these points will give a basis for new transcorrelated calculations on diatomic molecules.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed.     

哺乳期母婴微量元素含量的干预研究

通过对陕西省西安地区营养正常的母婴进行干预试验,研究了在其饮食习惯下,哺乳期母婴体内锌、铁、钙三种必需元素的代谢情况,以及是否需要补充,给予适当的补充是否有害。     

Synthesis,structure, and magnetic properties of the cobalt(<Emphasis Type="SmallCaps">II</Emphasis>) 1,3,5-benzenetricarboxylate layered coordination polymer

The reaction of Co(NO₃)₂·6H₂O with 1,3,5-benzenetricarboxylic acid (H₃btc, trimesic acid) in DMF at 100 °C afforded the coordination polymer [Co₃(dmf)₆(btc)(Hbtc)(H₂btc)]··9H₂O (1) (dmf is N,N′-dimethylformamide, DMF). According to the X-ray diffraction study, the metal-organic coordination polymer is composed of planar honeycomb (6,3) networks, in which the organic benzenetricarboxylate anions and the inorganic Co²⁺ cations play a role of three-connected nodes. Disordered water molecules are intercalated between the layers. A study of the magnetic properties showed the presence of a weak antiferromagnetic coupling between the Co²⁺ ions (S = 3/2). Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1719–1723, September, 2007.