Crystal structures and electronic properties of solid fluorine under high pressure

As the previously proposed structures of C2/m and C2/c possess similar enthalpies and x-ray diffraction patterns, the space group of fluorine at ambient pressure is in controversy. We successfully obtain its thermodynamically stable lowpressure phase, which shares the same structure as the earlier known C2/c. Further investigations on phonon spectra reveal the instability of the C2/m structure with imaginary frequency in the Brillouin zone and confirm the dynamically stable property of the C2/c structure at the same time. Compressing fluorine up to 8 GPa, the C2/c phase is found to undergo a phase transition to a new structure with a space group of Cmca. Electronic energy band structures indicate the insulating feature of C2/c and Cmca with no bands across the Fermi level. The infrared(IR) and Raman spectra of C2/c and Cmca at selected pressures are calculated to provide useful information to future experiments.     

光热显微术:基于光吸收的单分子成像技术

光热显微术是近年来获得广泛关注和长足发展的一种新型光学显微成像技术,能够实现单个纳米粒子甚至单分子的免标记光学成像。其成像原理是利用先进的光学方法探测单分子或单纳米粒子吸收特定波长激发光后所产生的局域温度和介质折射率的微小变化,从而定量研究观测对象的光热特性。由于无辐射弛豫是激发态分子回到基态的优势过程,分子的光热特性相比于荧光特性更具有普遍意义。凭借无需标记、高灵敏度和信号稳定等优点,近十年来,关于单分子和单纳米粒子的光热显微成像研究不断取得突破,并在纳米科学和生命科学等领域获得越来越多的发展和应用,展现出了蓬勃的生命力和良好的发展前景。本文重点综述了光热显微技术的成像原理、发展历程、技术特色以及系统优化方法,列举了光热成像在活细胞研究和生物学领域的应用,最后总结了光热成像的优缺点并分析其主要面临的挑战以及未来的发展趋势,希望吸引更多的研究人员加入到这一新技术的研究队伍中来。     

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.     

用离散均值—水平集求全局最优算法

全局最优理论和方法,由于全局性的要求,比局部最优理论和方法更为困难,特别是,至今还没有很好的全局最优性的判别准则,故多数算法法缺少好的终止准则.西文提出了一个只需计算函数值的离散均值—水平集求全局最优的方法,给出了算法的终止准则,证明了算法的收敛性,并给出了某些数值例子.     

基于当地笛卡尔架构的无网格方法

提出了一种新的无网格方法,该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点,然后运用全导数公式构造该样点的所有导数,它不需要任何网格单元,所以是彻底的无网格方法．数值算例表明,该方法具有很高的精度．     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.     

让学生在"数学交流"中学习

近日听一位教授谈到斯坦福校长办学经验之一是鼓励创新,并且提到学生的自学能力50%是从其他学生身上学到的.对孩子来说最好的老师不是大人而是比他大一点或同龄的孩子.而数学教学过程必然伴随着数学交流过程,如师生交流、学生与学生的交流、教学媒体(如计算机)的交流.全美数学教师协会(NCTM)发表的<中小学数学课程与评估标准>中明确地把数学交流作为课程目标之一.把学生培养成有素养的社会成员的一个重要标志是他们会数学交流.但在我国由于受长期应试教育的影响,无论在实践中还是理论上都对此重视不够,课堂教学往往围绕"高考会考的问题"满堂灌而忽视了学生主体地位,忽视了问题的开放性、学生学习的合作性.本文拟结合平时课堂教学中的一些实例,谈一谈如何在数学课堂教学中进行"数学交流"教学.     

S_2流面正命题适用于纯物质流体的变分原理族及实际蒸汽跨声流动的变分有限元解

一、前言 自从叶轮机械基于两类流面迭代的三元流动通用理论提出以来,国内外在对叶轮机械的各种气动命题的求解方面已作大量工作,并得到令人满意的计算结果。但在流动工质的物性对流动的影响方面开展工作尚少,尤其在变分有限元计算方面,几乎还是空白。其主要原因是由于变分有限元的计算需要构造一套对各种流动工质普遍适用的变分     

影响反相微乳液导电性能的因素

分别以聚乙二醇辛基苯基醚(Triton X-100)或十六烷基三甲基溴化铵(CTAB)为表面活性剂, 与正己烷、正己醇和水构成反相微乳液. 研究了水相H+浓度、表面活性剂、助表面活性剂等对微乳液导电性能的影响. 结果表明, 增加水相H+浓度可大幅度提高反相微乳液的导电能力, 当H+浓度由1.0 mol•L-1增加到10 mol•L-1时, 微乳液的电导率可提高1~2个数量级. 当水相H+浓度为10 mol•L-1时, 微乳液的电导率随溶水量的增大而增大, 水油体积比为3:10时, 两种体系的电导率均达到3200 μS•cm-1. Triton X-100浓度对微乳液的电导率影响较大, 电导率随其浓度增加而增大；而CTAB浓度对微乳液电导率的影响较小, 电导率随其浓度增加略有减小；助表面活性剂正己醇使非离子型反相微乳液的电导率下降, 而使阳离子型反相微乳液的电导率先增大, 然后减小, 呈骆峰状变化.     

炭化条件和铁系添加剂对炭分子筛性能影响的研究

炭分子筛(ＣａｒｂｏｎＭｏｌｅｃｕｌａｒＳｉｅｖｅ,以下简称ＣＭＳ)是具有特别发达的微孔结构的特种活性炭,在气体分离方面有广阔的应用前景[1]。目前作为变压吸附空气分离技术的首选吸附剂,在国内外被广泛用于中小规模的空气分离以制取富Ｎ2气体,制取ＣＭＳ的原料多是椰子壳、果核、植物、石油沥青及各种煤等[2,3]。煤是一种具有较为发达的孔隙结构的物质,且价格低廉,来源广泛,是制取ＣＭＳ的一种较为理想的原料。鸡西地区拥有丰富的煤炭资源,开发煤炭的深加工及高附加值产品具有十分重要的意义。本文以鸡西地区的烟煤为原料,制备空…