运用欧拉动力学方程解决力学竞赛两道理论力学试题1)

针对两道力学竞赛试题,从欧拉动力学方程出发分别给出了更加简化的固连系选取方法,分别命名为"Serret-Andoyer近似固连系"和"虚固连系",在此基础上对第1届全国青年力学竞赛理论力学试题第9题,拓展讨论了大球同步旋转时,小球的稳 定性条件,结果表明后者的稳定临界转速要求更低,这将更有利于提高旋转结构的稳定性;对第12届全国周培源大学生力学 竞赛第3题,剖析了任一纬度的运动规律,发现当体系初始角动量为零时会出现一种简洁又优美的运动模式。     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

密度泛函理论研究闪锌矿结构CrTe和VTe半金属铁磁性的稳定性

采用基于密度泛函理论的全势能线性缀加平面波方法对闪锌矿结构CrTe和VTe的电子结构进行自旋极化计算.闪锌矿相CrTe和VTe处于平衡晶格常数时都是半金属性的,它们自旋向下子能带的带隙分别是2.82 eV和2.70 eV,半金属隙分别是0.89 eV和0.33 eV.使晶体相对于平衡晶格在±10%的范围内发生各向同性形变,对闪锌矿相CrTe和VTe的电子结构进行计算,计算结果表明相对于平衡晶格的各向同性形变分别为-6%～10%和-3%～10%时它们仍然具有半金属性质;与此同时,在以上相同的形变范围内闪锌矿相CrTe和VTe的总磁矩分别稳定于4.00μB/formula和3.00μs/formula.在晶体相对于平衡晶格发生各向同性形变分别为-6%～10%和-3%～10%时,闪锌矿相CrTe和VTe能保持半金属铁磁性.     

机械结构因素对光电跟踪伺服系统性能的影响

为克服机械结构因素对光电跟踪伺服系统性能的不良影响,分析了转动惯量、结构谐振频率、摩擦力矩等伺服机械结构因素与伺服系统性能的关系,包括分析转动惯量与伺服系统性能的关系、结构谐振频率与伺服系统性能的关系、摩擦力矩与伺服系统性能的关系,探讨了消除或减小机械谐振的措施.该分析方法可应用于设计和制造响应速度快、跟踪精度高的光电跟踪伺服系统.     

The complete multi-ζ electric dipole moment matrix of π-(C6H6) Cr(CO)3 and tests of semi-empirical MO models

First, we evaluated the complete electric dipole moment matrixeZ using a multi- AO basis on Cr, C, and O centers fortheimportant, parent organometallic molecule -C₆H₆Cr(CO)₃. Second, we generated ground state LCAO-MO eigenvectors employing five commonly used semi-empirical procedures for molecules of this size which contain transition metals. Transformation of operator matrixeZ into the MO space of each of the five methods then leads us to conclude that the empirical input of Basch, Viste and Gray is most suitable. Finally, we compare the merits of several single- basis orbitals with the multi- metal orbitals.[/p]     

Liquid chromatography of benzene derivatives on a porous methacrylate copolymer containing epoxy groups

Summary The retention of benzene derivatives with nonpolar and polar substituents on a porous methacrylate copolymer containing epoxy groups using both nonpolar and polar eluents was investigated. When n-hexane is used as the eluent, the retention of n-alkylbenzenes and polymethylbenzenes is weaker than that of benzene. In the case of benzene derivatives containing polar functional groups their capacity ratios (k) on this porous polymer increases approximately linearly with the increase of the adsorbate molecules dipole moment. The retention characteristics of the methacrylate copolymer were compared with that of a styrene-divinylbenzene copolymer and silica gels with a hydroxylated surface and with a surface modified by chemically bonded alkylsilyl groups.     

吡啶基团的对称性和离子化对分子双光子吸收截面的影响

采用超快速激光光谱方法研究了含吡啶基团的四个联苯乙烯衍生物及两个杂环分子(A: 4,4’-二(2-(4-吡啶基)乙烯)联苯; B: 4,4’-二(2-(2-吡啶基)乙烯)联苯; C: 1-甲基-4-(2-(4’-(2-(4-吡啶基)乙烯基)-4-联苯)乙烯基)吡啶碘盐; D: 1-甲基-2-(2-(4’-(2-(2-吡啶基)乙烯基)-4-联苯)乙烯基)吡啶碘盐; E: 4-(2-(9-丁基-9氢-3-咔唑)乙烯基)-1-甲基吡啶碘盐; F: 4-(2-(9-丁基-9氢-3-咔唑)乙烯基)-1-甲基喹啉碘盐)的结构-性能关系. 实验结果显示双光子吸收截面最大的是分子E, 高达617.3 GM; 最小的是分子B, 为19.3 GM(1 GM=10^-50 cm⁴·s·photon^-1). 实验研究结果表明, 分子中吡啶基团的对称性及其离子化对分子双光子吸收截面起很重要的作用; 进一步用理论计算证实了以上实验结论并对其机制进行了分析讨论.     

大港常压渣油临氮与临氢热反应过程中胶体稳定性变化研究

对比了大港常压渣油临氮和临氢热反应过程中的胶体稳定性变化。结果表明,随着反应时间的延长,在热反应生焦诱导期内,渣油样品的胶体稳定性迅速下降;开始生焦后,胶体稳定性缓慢下降。从组分组成和组分性质角度,对大港常压渣油样品在热反应过程中胶体稳定性变化原因进行了分析。结果表明,随着反应时间的延长,沥青质含量先上升、后下降,在生焦诱导期结束时达到最大值,与体系胶体稳定性的变化特征相一致。随着热反应的进行,饱和分和轻芳烃组分的含量在上升,重芳烃、轻胶质、中胶质、重胶质含量下降,临氮热反应过程中轻胶质、中胶质、重胶质含量的下降更为显著。对渣油样品各组分的数均相对分子质量和平均偶极矩进行了研究。结果表明,随着热反应的进行,轻、中、重胶质组分的数均相对分子质量和平均偶极矩呈下降趋势,而沥青质的数均相对分子质量和偶极矩先增大后减小,从而使沥青质和胶质的分子性质差别先增加后减小,与体系胶体稳定性的变化趋势一致;同时沥青质的偶极矩变化表明,强极性的沥青质优先聚集生焦、临氢热反应过程中,氢与催化剂的作用有助于抑制沥青质分子量增大和极性增强,从而有助于抑制生焦。     

Determination of the ground- and excited-state dipole moments of 4’-(hexyloxy)-4-biphenylcarbonitrile and 4-isothiocyanatophenyl 4-pentylbicyclo [2,2,2] octane-1-carboxylate nematic liquid crystals and their mixtures

The dipole moments of the ground and excited states of 4′-(hexyloxy)-4-biphenylcarbonitrile and 4-isothiocyanatophenyl 4-pentylbicyclo [2.2.2] octane-1-carboxylate nematic liquid crystals and their mixtures prepared in chloroform and dichloromethane were studied at room temperature. The dipole moments of the ground states of the all samples were calculated according to the Guggenheim–Smith method. The dipole moments of their excited states were determined with the help of the Lippert equation by measuring the absorption and fluorescence spectra, solvent polarity and refractive index values. It was determined that dipole moments of the excited states were higher than those of the ground states. Moreover, the dipole moments of the ground and excited states of two nematic liquid crystals were also estimated by using molecular mechanic method (Gaussian09 program (DFT/B3LYP 6-31G(dp)). The results obtained are interpreted in detail.     

Structures of the reduced niobium oxides Nb12O29 and Nb22O54

The crystal structure of Nb₂₂O₅₄ is reported for the first time, and the structure of orthorhombic Nb₁₂O₂₉ is reexamined, resolving previous ambiguities. Single crystal X-ray and electron diffraction were employed. These compounds were found to crystallize in the space groups P2/m (, , , β=102.029(3)^°) and Cmcm (, , ), respectively and share a common structural unit, a 4×3 block of corner sharing NbO₆ octahedra. Despite different constraints imposed by symmetry these blocks are very similar in both compounds. Within a block, it is found that the niobium atoms are not located in the centers of the oxygen octahedra, but rather are displaced inward toward the center of the block forming an apparent antiferroelectric state. Bond valence sums and bond lengths do not show the presence of charge ordering, suggesting that all 4d electrons are delocalized in these compounds at the temperature studied, T=200 K.