弱Hopf代数的扭曲理论

本文研究了弱Hopf代数的扭曲理论的对偶问题.利用了弱Hopf代数上的弱Hopf双模的(辫子)张量范畴与扭曲弱Hopf代数上的弱Hopf双模的(辫子)张量范畴等价方法,得到Long模范畴是Yetter-Drinfel'd模范畴的辫子张量子范畴.推广了Oeckl(2000)的结果.     

A Flexible Organic Single Crystal with Plastic-Twisting and Elastic-Bending Capabilities and Polarization-Rotation Function

Flexible organic single crystals capable of plastic or elastic deformations have a variety of potential applications. Although the integration of plasticity and elasticity in a crystal is theoretically possible and it may cause rich and complex deformations which are highly demanded for potential applications, the integration is hard to realize in practice. Here, we show that through utilizing different modes of external forces for influencing molecular packing in different crystallographic directions, plastic helical twisting and elastic bending can both be achieved for a crystal, and they can even be realized simultaneously. Detailed crystallographic analyses and contrast experiments disclose the mechanisms behind these two kinds of distinct deformations and their mutual compatibility. Based on the plastically twistable nature of the crystal, a new application field of flexible organic single crystals, namely polarization rotators, is successfully opened up.     

New Schiff's bases containing 1,3,4-thiadiazole and 1,3,4-oxadiazole units: a study of the effect of the heterocyclic ring and the position of the lateral alkoxy group on liquid crystalline properties

The synthesis of novel Schiff's bases incorporating the five-membered 1,3,4-thiadiazole (series 7, 9) and 1,3,4-oxadiazole (series 8, 10) rings have been prepared and their liquid crystalline properties studied. All compounds of series 7 exhibit an enantiotropic smectic C phase. No liquid crystalline properties were observed for the compounds of series 8-10. A study of the structure/mesomorphic activity relationship is also described.     

受周向剪切载荷的圆轴扭转应力分析

利用分离变量法对受周向剪切载荷作用的圆轴扭转应力问题进行分析,得到了圆轴的切应力分布,并根据分析结果进一步给出了纵截面上沿圆周方向切应力的简单计算方法。     

Creep of plates made of aluminum alloys under bending

Results of experiments dealing with the creep of a V95pchT2 aluminum alloy are presented. Constitutive equations of steady creep are constructed and used to solve the problem of pure twisting of a square plate. Calculated and experimental values of plate curvature are compared. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 156–159, September–October, 2007.     

The morphology of poly(vinylidene fluoride) crystallized from blends of poly(vinylidene fluoride) and poly(ethyl acrylate)

A combined optical and electron microscopical study has been carried out of the crystallization habits of poly(vinylidene fluoride) (PVF₂) when it is crystallized from blends with noncrystallizable poly(ethyl acrylate) (PEA). The PVF₂/PEA weight ratios were 0.5/99.5,5/95, and 15/85. Isothermal crystallization upon cooling the blends from the single-phase liquid region was carried out in the range 135–155°C, in which the polymer crystallizes in the α-orthorhombic unit cell form. The 0.5/99.5 blend yielded multilayered and planar lamellar crystals. The lamellae formed at low undercoolings were lozenge shaped and bounded laterally by {110} faces. This habit is prototypical of the dendritic lateral habits exhibited by the crystals grown from the same blend at high undercoolings as well as by the constituent lamellae in the incipient spherulitic aggregates and banded spherulites that formed from the 5/95 and the 15/85 blends, respectively. In contrast with the planar crystals grown from the 0.5/99.5 blend, the formation of the aggregates grown from the 5/95 blend is governed by a conformationally complex motif of dendritic lamellar growth and proliferation. The development of these aggregates is characterized by the twisting of the orientation of lamellae about their preferential b-axis direction of growth, coupled with a fan-like splaying or spreading of lamellae about that axis. The radial growth in the banded spherulites formed from the 15/85 blend is governed by a radially periodic repetition of a similar lamellar twisting/fan-like spreading growth motif whose recurrence corresponds to the extinction band spacing. This motif differs in its fan-like splaying component from banding due to just a helicoidal twisting of lamellae about the radial direction. © 1993 John Wiley & Sons, Inc.     

一轴模型和横场一轴模型中的量子态保真度

针对一轴模型和横场一轴模型, 研究了自旋压缩演化过程中的量子态的量子保真度, 结果表明：量子态在一轴模型作用下, 保真度呈周期性演化.对于偶粒子数N 个qubit系统, 演化周期为T=2*pi , 在T/4 时刻, 3T/4保真度始终能保持为0.5, 在T/2 时刻,保真度为零,量子态完全失真.对于奇粒子数 N个qubit系统,演化周期为 pi,比较于偶粒子数N 的情况,在T/4,T/2, 3T/4时刻,保真度依赖于粒子数N ;在横场一轴模型中, 横场强度的增加不仅有利于自旋压缩的提高, 还有利于量子保真度的提高.     

三粒子体系中的Wigner-Yanse偏振信息

针对带有衰减机制的一轴模型和二轴模型,在薛定谔图象下, 研究了三粒子体系任意时刻的量子态及最大Wigner- Yanse偏振信息. 体系在非线性相互作用下, 体系的最大偏振信息始终出现在平面 内, 由于衰减的引入, 最大偏振信息能够被调节和存储. 对带有最大偏振信息极值 的GHZ态, 给出了其出现的条件.     

石墨烯纳米带能带结构及透射特性的扭曲效应

利用基于密度泛函理论的第一性原理方法, 系统研究了石墨烯纳米带(GNRs)电学性质的扭曲效应. 结果表明: 锯齿型石墨纳米带(ZGNRs)的带隙对扭曲形变最不敏感, 在扭曲过程中几乎保持金属性不变, 其次是W=3p-1型扶手椅型石墨烯纳米带(AGNRs), 扭曲时带隙也只有较小的变化. W=3p+1型AGNRs的带隙对扭曲最为敏感, 扭曲发生时, 呈现宽带隙半导体、中等带隙半导体、准金属、金属的变化, 其次是W=3p型AGNRs, 扭曲时带隙变化也较为明显. 换言之, GNRs在无扭曲时带隙越大, 扭曲发生后带隙变化(变小)越明显. 对于整个电子结构及透射系数来说, 扭曲对AGNRs影响较大, 而对ZGNRs的影响相对小些. 研究表明: 由于石墨烯容易变形, 其相关电子器件的设计必须适当考虑扭曲对电学性质的影响.