Diagonal Bases in Orlik-Solomon Type Algebras

To encode an important property of the no broken circuit bases of the Orlik- Solomon-Terao algebras, Szenes has introduced a particular type of bases, the so called diagonal basis. We prove that this definition extends naturally to a large class of algebras, the so called - algebras. Our definitions make also use of an iterative residue formula based on the matroidal operation of contraction. This formula can be seen as the combinatorial analogue of an iterative residue formula introduced by Szenes. As an application we deduce nice formulas to express a pure element in a diagonal basis.AMS Subject Classification: 52C35, 05B35, 14F40.     

水坝崩溃的计算机模拟

本文用求解化学流体力学基本方程组的方法研究了不可压自由表面问题,着重引入了流体体积分数技术,建立了水坝倒塌问题的物理模型,运用该技术和模型,计算得到了水流的速度和压力在空间的分布及其随时间的变化,与实验观测一致.     

由运动内热源引起的磁热黏弹性问题的研究

在具有两个热松弛时间的广义热弹性理论下, 研究了处于定常磁场中的均布各向同性黏弹性半空间中, 由以均匀速度运动的线热源引起的瞬态波问题. 通过引入黏弹性向量势和热黏弹性标量势,问题退化为求解3个偏微分方程. 运用Laplace变换(对时间变量)和Fourier变换(对一个空间变量), 得到了变换域内应力和位移的解析表达式. 采用级数展开法, 得到了边界位移在小时间范围内的近似解, 给出了解的近似范围, 同时还研究了两种特例：(1)热源静止不动, (2)不考虑热松弛时间的影响. 最后对于丙烯酸塑料介质给出了数值结果.     

O(N)模型破缺相的红外重正化群计算

利用一个与质量有关的重正化方案,研究了O(N)模型破缺相的红外重正化群性质.得到了与质量有关的一圈重正化群系数以及在红外极限下的二圈重正化群系数.利用标准的微扰场论计算方法,发现特殊的抵消效应,该效应使得二圈的重正化群系数与一圈重正化群系数在红外极限下相同.     

对称性、对称性破缺和相变

本文将扼要介绍物理学中对称性的分类及其特征,说明对称性破缺与一物理系统从无序到有序的相变过程间的关系,并讨论了对称性破缺出现的前提     

Mechanical Deformation–Assisted Fabrication of Plasmonic Nanobowties with Broken Symmetry and Tunable Gaps

A symmetry broken and gap tunable gold nanobowtie array is demonstrated by nanosphere lithography performed on a mechanically uniaxially prestretched elastomeric substrate. Due to symmetry breaking of each nanotriangle with its three neighboring nanotriangles once the uniaxial prestretch is released, the structure exhibits polarization-dependent optical properties. In addition, the decrease in the gap between adjacent triangles provided by mechanical relaxation of the substrate enhances the electric field enhancement between adjacent triangles, which in turn results in enhanced Raman scattering from molecules present in the gap. Triangle apex-to-apex gaps as small as 20 nm are generated using a colloidal crystal formed from 500 nm colloids on at 30% prestretched substrate (gaps formed when an unstretched substrate is used are ≈115 nm).     

基于ISOMAP-DE-SVM的Cz单晶硅等径阶段掉苞预测

针对目测法无法及时发现直拉单晶硅在等径生长阶段发生的掉苞问题,本文提出一种基于ISOMAP-DE-SVM的掉苞预测模型,可以在掉苞现象发生之前发出警告。首先剔除方差较小的参数,采用斯皮尔曼相关系数法剔除冗余参数,采用最大互信息法检验剩余参数的非线性相关性;然后将关键参数的均值和标准差作为等度量映射和多维放缩的输入,得到两份样本数据;最后将这两份样本数据分别输入到经过差分算法、遗传算法优化的支持向量机预测模型,得到4份预测结果。预测结果表明：基于ISOMAP-DE-SVM的预测模型具有收敛速度快、准确度高的特点,平均预测准确率可以达到96%;同时,所使用的方法揭示了单晶硅等径阶段的数据具有非线性特点。通过实际应用验证表明模型具有一定的工程实用价值。     

由压力引起的破裂问题研究

通过力学分析,说明了水结冰后导致水管、水缸等破裂的现象和力学本质,并应用该结果讨论了拱形建筑的拱顶破坏.     

多波段高功率激光扩束系统设计

 对透射式和反射式扩束系统应用于高功率激光扩束的优缺点进行了对比研究。采用次镜为凸抛物面,主镜为凹抛物面的无焦卡塞格林系统,运用ZEMAX光学设计软件,按激光扩束系统的扩束倍率和系统的波像差要求,设计出多波段高功率激光扩束系统。对用于高功率激光反射镜的基底材料进行分析,选用无氧铜作为基底材料;采用金增强的膜系设计,膜系从近红外到远红外宽光谱波段激光的反射率均在98%以上。面形精度均方根值优于λ/40(λ=0.632 8 μm)的平面镜作为基准镜,采用光学干涉方法对设计的激光扩束系统进行检测实验,结果表明：该扩束系统的扩束倍率为3.53,波像差为0.206λ,满足多波段高功率激光光束发射要求。     

Fast generation of broken‐symmetry states in a large system including multiple iron–sulfur assemblies: Investigation of QM/MM energies,clusters charges,and spin populations

A density functional theory study is presented regarding the energetics and the Mulliken population analyses of a quantum mechanical/molecular mechanical (QM/MM) system including multiple iron–sulfur clusters in the QM region. The [FeFe]‐hydrogenase from Desulfovibrio desulfuricans was studied, and both the active site (an Fe₆S₆ assembly generally referred to as the H‐cluster) and an ancillary Fe₄S₄ site were treated at the BP86‐RI/TZVP level. The antiferromagnetic coupling that characterizes both sites was modeled using the broken‐symmetry (BS) approach. For such a QM system, 36 different BS couplings can be defined, depending on the localization of spin excess on the various spin centers. All the BS states were obtained by means of an effective and simple method for spin localization, that is here described and compared with more sophisticated approaches already available in literature. The variation of the QM/MM energy among the various geometry‐optimized protein models was found to be less than 25 kJ mol^–1. This energy variation almost doubles if no geometry optimization is performed. A detailed analysis of the additive nature of these variations in QM/MM energy is reported. The Mulliken charges show very small variations among the 36 BS states, whereas the Mulliken spin populations were found to be somewhat more variable. The relevance of such variations is discussed in light of the available Mössbauer and Electron Paramagnetic Resonance (EPR) spectroscopic data for the enzyme. Finally, the influence of the basis set on the spin populations, charges, and structural parameters of the models was investigated, by means of QM/MM computations on the same system at the BP86‐RI/SVP level. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011