悬链线竖向集中力作用下的构形分析和张力计算

目前,悬链线在竖向集中力和均布荷载共同作用下的构形分析和受力计算的理论仍不完善。针对这一问题,通过引入悬链线的几何约束方程、力平衡方程和超越方程,建立了竖向集中力与均布荷载共同作用下的非线性方程组。采用牛顿迭代法求解方程组,得到了悬链线的构形和受力情况。为了验证理论计算的正确性,进行了算例和试验验证。结果表明,算例的计算结果与文献结论保持一致,试验测得的构形和水平张力大小与理论计算的构形和水平张力大小吻合较好。本文的理论计算可以更加简单精确地计算出悬链线在竖向集中力和均布荷载共同作用下的构形和受力情况,为实际工程提供重要的理论指导。     

A giant enhancement of magnetic moment in a ternary three-shell icosahedral cluster: Fe@Mn12@Au20

ABSTRACT

The average magnetic moment per atom of Mn₁₃ cluster is expected to be enhanced by doping or coating with a shell. Several ternary core–shell icosahedral clusters TM@Mn₁₂@Au₂₀ were constructed by combining substituting the central Mn with VIII elements (Fe, Co, Ni, Ru, Rh, Pd and Pt) and coating with a icosahedral Au₂₀ shell, and systematically studied by using the first-principles density functional method. Compared to Mn₁₃, Fe@Mn₁₂@Au₂₀ cluster shows a giant enhancement on total magnetic moment (52?µ_B) which can be greatly attributed to the ferromagnetic coupling between spin moments of atoms. Coating with Au₂₀ shell enlarged the average distances of TM-Mn and Mn-Mn and is a useful way to change the magnetic coupling style. By analysis of density of states and electron localisation functional, we can conclude that the weak hybridisation between Fe and Mn in Fe@Mn₁₂@Au₂₀ is propitious to maintain their original direction of spin moments of atoms and then form ferromagnetic coupling.     

The structural,electronic and magnetic properties of Ag4M and Ag4MCO (M = Sc–Zn) clusters

The structures, spectra and electronic and magnetic properties of Ag₄M and Ag₄MCO (M?=?Sc–Zn) clusters have been studied using density functional theory and CALYPSO structure searching method. Structural searches show that M atoms except Zn tend to occupy the highest coordination position in the ground state Ag₄M and Ag₄MCO clusters. Carbon monoxide is most easily adsorbed on Ag atom of Ag₄Zn and M atom of other Ag₄M. Infrared and Raman spectra, photoabsorption spectra and photoelectron spectra of Ag₄M and Ag₄MCO clusters are forecasted and can be used to identify these clusters from experiment. Analysis of electronic properties indicates that the adsorption of CO on Ag₄M clusters changes the zero vibrational energy (ZPVE) and increases stability of the host clusters. Dopant atoms except for Zn improve the stability of silver cluster. The Ag₄Ni cluster shows high chemical activity and maximum adsorption energy for carbon monoxide. Magnetism calculations reveal that the magnetic moment of Ag₄M (M?=?Mn–Ni) cluster adsorbed by carbon monoxide is decreased by 2 μ_B. The change of magnetic moment makes it possible to be used as a nanomaterial for carbon monoxide detection. Simultaneously, it is found that the adsorption of CO on Ag₄Cu cluster is a physical adsorption.     

环化顺1，4－聚丁二烯浓溶液的流动行为

大多数线型高聚物浓溶液的流动行为呈现非牛顿性，线型顺１，４－聚丁二烯（ＬＢＲ）亦然，而环化顺１，４－聚丁烯（ＣＢＲ）的浓溶液在浓度达１７．８％时仍表现为牛顿流体。ＣＢＲ溶液的临界缠结浓度明显地高于ＬＢＲ，ＣＢＲ分子链间的缠结效应比ＬＢＲ弱得多，这是ＣＢＲ的分子链结构特征所致。     

Microwave spectrum,centrifugal perturbation,dipole moment,and conformation of 4-methyl-1,3-dioxane

The microwave spectrum of 4-methyl-1,3-dioxane is studied in a frequency range from 16 GHz to 40 GHz. The rotational transitions of a-, b-, and c-types with J ≤ 57 are identified. The rotational constants (MHz) A = 4802.335(2), B = 2376.163(1), C = 1738.852(1) and the quartic constants of the centrifugal distortion are found for the ground vibrational state of the molecule. The components of the dipole moment (D) μ _a = 0.73(1), μ_b = 1.32(1), μ_c = 1.36(1) and the total dipole moment μ = 2.03(1) are determined. The experimental data obtained correspond to the chair conformation of the molecule with the equatorial orientation of the methyl group.     

几种纤锌矿相半金属铁磁体磁学性能的第一原理研究

通过基于密度泛函理论的第一原理计算,优化了纤锌矿结构的化合物TmZn15S16(Tm=V,Cr,Mn)的几何结构,并研究了它们的磁学性能.结果表明:TmZn15S16均为典型的半金属铁磁体,它们的超胞磁矩分别为3.0099μB,3.9977μB和5.0092μB;这些磁矩主要来源于被掺入的过渡元素;CrZn15S16的半金属特性比VZn15S16和MnZn15S16更稳定;这些半金属铁磁体的半金属带隙均比较宽,表明它们可能具有较高的居里温度;TmZn15S16中杂质过渡离子的电子结构分别为V:eg2↑t12g↑,Cr:eg2↑t22g↑和Mn:eg2↑t32g↑.     

Polarity and steric effect of the lateral substituent on the mesophase behaviour of some newly prepared liquid crystals

Eight homologous series of 2- (or 3-) substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_a–h) were prepared in which, within each homologous series, the length of the terminal alkoxy group varies between 6, 8, 10 and 12 carbons, while the other substituent, X, is a laterally attached polar group that alternatively changed from CH₃, H, F, Br and CN. Compounds prepared were characterised by infrared and ¹H-NMR spectroscopy, and their mesophase behaviour investigated by differential scanning calorimetry and identified by polarised light microscopy. The results were discussed in terms of polarity and steric effects. The stability of the mesophase was correlated once with the dipolar anisotropy of the whole molecule and another with the dipolar anisotropy of the substituent, X. A comparative study was made between the investigated compounds and their previously prepared linear 4-substituted isomers, namely 4-substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_i–k).     

New solution system for circular sector plate bending and its application

Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solutions for the circular sector plate. The results show that the new method is effective. Project supported by National Natural Science Foundation (No. 19732020) and the Doctoral Research Foundation of China.     

A Characterization of Maximally Entangled Two-Qubit States

As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [−12,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are −12. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is −12 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.     

关于非负随机变量的几个矩不等式

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