具有局域E2对称性的推广玻色-哈巴德模型

利用局域的E2生成元构造了一种具有准严格解的推广玻色-哈巴德模型.与原来的玻色-哈巴德模型类似,推广玻色-哈巴德模型可用于描述格点玻色系统从超流相到Mott绝缘相的量子相变.介绍了模型的准严格解及其显著特点,给出了一维推广玻色-哈巴德模型填充数ρ=1时的相图,并计算了N=M=14时体系的基态纠缠度随控制参量的变化特征.     

气液两相流中液相局部速度测量实验

针对气液两相流中液相局部速度测量的问题,设计了一种电导探针和与其相配合的电导检测仪表,并将示踪物质的注入装置和探针合为一体,在气水泡状流流型中进行冷态实验,利用互相关技术对实验数据进行处理,获得液相速度,并进行了实验结果和误差分析。结果表明,通过一定的数据处理技术,此测量系统可以得到满意的测量结果。此外,由于电导探针能够适应多工况的变化,而且可以进行多点测量,因此可用于各种实验并具有广泛的应用前景。     

基于局部对称性及灰度统计特征的人眼定位方法

为了兼顾人眼定位方法的准确率和实时性,提出基于局部对称性和灰度统计特征的人眼定位方法。该方法结合了模板匹配与对称变换的思想,利用了人眼灰度统计信息,取得了较好的效果。通过仿真实验表明:算法在满足算法定位准确率的同时,具有较好的实时性,因为其算法复杂度相对于模板匹配法和基于学习的方法大大降低。     

Observation of shear-induced nematic-isotropic transition in side-chain liquid crystal polymers

Flow-induced phase transitions are a fundamental (but poorly understood) property of non-equilibrium systems, and are also of practical importance for tuning the processing conditions for plastics, petroleum products, and other related materials. Recognition that polymers may exhibit liquid crystal properties has led to the discovery of the first tailored side-chain liquid crystal polymers (SCLCPs), which are formed by inserting a spacer between the main polymer chain and the lateral mesogen liquid-crystalline graftings. Subsequent research has sought to understand the nature of the coupling between the main polymer chain and the mesogens, with a view to obtaining better control of the properties of these tailored structures. We show here that the parallel or perpendicular orientation of the mesogens with respect to the main chain can be reversed by the application of an external field produced by a shear flow, demonstrating the existence of an isotropic nematic phase transition in SCLCPs. Such a transition, which was theoretically predicted for low-molecular-weight liquid crystals but never observed, is shown to be a general property of SCLCPs too. We expect that these SCLCPs will prove to be good candidate systems for the experimental study of these non-equilibrium phenomena.     

铅离子的液膜分离法研究

采用内耦合大块液膜分离技术,通过考察料液相pH值、温度、载体浓度对Pb2 迁移率的影响,研究了在以烷基膦酸为载体的液膜中Pb2 的液膜迁移行为,测定了不同载体浓度下的半迁移pH1/2值。结果表明:Pb2 的迁移率随温度和载体浓度的升高而逐渐增大;当外水相pH值及温度分别控制在2.75～3.75和278～298K范围内,载体浓度为5.00%时,Pb2 的迁移率可达99%以上。     

Observation of surface and bulk phase transitions in nematic liquid crystals

The behaviour of liquid crystal (LC) molecules near a surface is of both fundamental and technological interest: it gives rise to various surface phase-transition and wetting phenomena, and surface-induced ordering of the LC molecules is integral to the operation of LC displays. Here we report the observation of a pure isotropic-nematic (IN) surface phase transition-clearly separated from the bulk IN transition-in a nematic LC on a substrate. Differences in phase behaviour between surface and bulk are expected, but have hitherto proved difficult to distinguish, owing in part to the close proximity of their transition temperatures. We have overcome these difficulties by using a mixture of nematic LCs: small, surface-induced composition variations lead to complete separation of the surface and bulk transitions, which we then study independently as a function of substrate and applied magnetic field. We find the surface IN transition to be of first order on surfaces with a weak anchoring energy and continuous on surfaces with a strong anchoring. We show that the presence of high magnetic fields does not change the surface IN transition temperature, whereas the bulk IN transition temperature increases with field. We attribute this to the interaction energy between the surface and bulk phases, which is tuned by magnetic-field-induced order in the surface-wetting layer.     

Observation of a roton collective mode in a two-dimensional Fermi liquid

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, (4)He (bosons) and (3)He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon-roton mode in liquid (4)He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as 'zero-sound' in (3)He, and 'plasmons' in charged systems) and incoherent particle-hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle-hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid (3)He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.     

二次回归正交法碱性蚀刻废液除铅剂配方设计及除铅方程

利用工业品CaCl2和Na2CO3生成的CaCO3与工业品FeCl3.6H2O的协同作用,制得除铅效率高而成本低的碱性蚀刻废液除铅剂。利用二次回归正交设计得到脱铅率的二元二次方程,最佳配比是CaCl210.66 g/L(相应的Na2CO310.18 g/L),FeCl3.6H2O 1.38 g/L。绘出了脱铅率的等高线图,为设计除铅剂的配比提供了直观有效的方法。     

二次回归正交法碱性蚀刻废液除铅剂配方设计及除铅方程

利用工业品CaCl2和Na2CO3生成的CaCO3与工业品FeCl3·6H2O的协同作用,制得除铅效率高而成本低的碱性蚀刻废液除铅剂.利用二次回归正交设计得到脱铅率的二元二次方程,最佳配比是CaCl210.66 g/L(相应的Na2CO3 10.18 g/L),FeCl3·6H2O 1.38 g/L.绘出了脱铅率的等高线图,为设计除铅剂的配比提供了直观有效的方法.     

Inhomogeneity,dynamical symmetry,and complexity in high-temperature superconductors:Reconciling a universal phase diagram with rich local disorder

A model for high-temperature superconductors incorporating antiferromagnetism,d-wave superconductivity,and no double lattice-site occupancy can give energy surfaces delicately balanced between antiferromagnetic and superconducting order for specific ranges of doping and temperature. The resulting properties can reconcile a universal cuprate phase diagram with rich inhomogeneity,relate that inhomogeneity to pseudogaps,give a fundamental rationale for giant proximity eects and other emergent behavior,and provide an objective framework to separate essential from peripheral in the superconducting mechanism.     

Inhomogeneity, dynamical symmetry, and complexity in high-temperature superconductors: Reconciling a universal phase diagram with rich local disorder

A model for high-temperature superconductors incorporating antiferromagnetism, d-wave superconductivity, and no double latticesite occupancy can give energy surfaces delicately balanced between antiferromagnetic and superconducting order for specific ranges of doping and temperature. The resulting properties can reconcile a universal cuprate phase diagram with rich inhomogeneity, relate that inhomogeneity to pseudogaps, give a fundamental rationale for giant proximity effects and other emergent behavior, and provide an objective framework to separate essential from peripheral in the superconducting mechanism. high-temperature superconductivity, pseudogap, critical dynamical symmetry, inhomogeneity, complexity, emergent behavior     

对称在积分中的应用

在多元函数的积分计算中正确地运用对称性,达到简化某些积分计算的目的．     

液体粘度对三相流化床局部相含率径向分布的影响

应用开发的微电导探针测试技术,以粒径分别为0．48mm、0．80mm、12．5mm的玻璃珠和1．45mm的苯乙烯树脂为固相,空气为气相,水和0．05％（wt％）、0．20％（wt％）的羧甲基纤维素钠（SCMC）为液相,对三相流化床的各相局部相含率进行了同时测定。在不同液体粘度下,局部固含率在r／R=0．75-0．85范围内有一个极大值;局部气合率呈现出塔中心处最大,塔壁处最小的分布规律。表明液体粘度对局部相含率径向分布均有不同程度的影响。     

Tetraradial symmetry in early poriferans

Here is currently little consensus on the branching order and phyletic status of the oldest metazoan groups, but sponges are widely believed to be the earliest- branching living metazoans. Porifera are thought to have diverged before the emergence of developmental charac- ters typical of Eumetazoa, such as well-defined symmetry; extant sponges show radial symmetry of indeterminate high order, or none, combined with polarisation along the axis. In contrast, other early-branching phyla include bilateral and tetraradial （Cnidaria） and biradial （Cte- nophora） symmetry, or none （Placozoa）. A variety of prismatic early fossil sponges had shown here where the shared symmetry has been overlooked, and also describe structural tetraradial symmetry in Cambrian sponges from South China. Based on this study, this symmetry is likely to have been a primitive feature of sponges, and that the earliest-known fossil sponges were highly organised, cel- lularly integrated individuals whose body form was under strict genetic control.     

有向图的弱对称性

讨论有向图的弱顶点传递和弱边传递性,得到了弱传递的有向图的刻画,确定了一些具体图类的弱传递性,给出了有向图各种传递性关系之间的区别和联系。     

图的弱对称性

主要研究弱1-弧传递图,即弱对称图的结构与性质,考虑弱对称图的核以及自同态像图等,给出了弱对称图的一些充分和必要条件．此外,还考察顶点个数小于7的所有连通无向图的弱对称性。     

对称性原理在数学物理中的应用

对称性和对称性原理是现代物理学中的重要概念和基本原则。对称性分析是研究现代物理学的典型方法,而对称性原理给出了探索未知科学规律的一项重要途径,它们在科学研究的过程中有着广泛的应用。通过对称性原理及其在数学物理问题中的一些典型应用案例的介绍,可以看到利用问题的对称性能够极大地简化数学物理定解问题的处理。     

对称特征值问题扰动的探讨

利用矩阵函数微分学理论，描述了对称矩阵被对称扰动以后特征值的变化规律，并给出了Wielandt-Hoffman定理的另一个证明方法．     

In search of symmetry lost

Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).