Landau常数的逼近公式

对于所有的整数n≥0,Landau常数定义为Gn=nΣk=01/16k(2kk)2.该文建立了Landau常数新的逼近公式.指出了获得的结果与先前已有结果之间的相关联系     

Phase transition at 233 K in [(CH3)4N]2cdI4

Abstract

[(CH₃)₄N]₂cdI₄ exhibits a phase transition at 233 K from Pnma to P2 1/c as shown by single-crystal X-ray measurements and differential scanning calorimetry. The observed entropy change amounts to approximately 8.4 J.mole^?1 K^?1 and the spontaneous strain is about – 18.10^?3. The symmetry change can be interpreted in the framework of the Landau theory.     

Well-posedness of the fractional Ginzburg–Landau equation

In this paper, we investigate the well-posedness of the real fractional Ginzburg–Landau equation in several different function spaces, which have been used to deal with the Burgers’ equation, the semilinear heat equation, the Navier–Stokes equations, etc. The long time asymptotic behavior of the nonnegative global solutions is also studied in details.     

Some new results on planar harmonic mappings

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.     

Elliptic theta functions and the fractional quantum Hall effect

Algebro-geometric methods are applied to the theoretical understanding of the fractionary quantum Hall effect on a periodic lattice. The fermionic Fock space of the many-electron system is precisely identified, and as a consequence, the variational Haldane-Rezayi ground state is decomposed in terms of one-particle wave functions at the first Landau level; the filling factor is thus analytically computed. Quasi-hole and quasi-particle excitations are also analyzed. The center of mass dynamics is described in terms of a section in a very subtle stable vector bundle. The Hall conductance arises as a topological invariant; namely, the slope of the vector bundle previously mentioned.     

合肥光源储存环上八极磁铁的动力学效应分析

 为达到合肥光源二期工程通用模式的设计流强，在储存环上选择垂直方向β函数比较大的位置增加一组八极磁铁。该组八极磁铁对水平方向动力学孔径影响很小，虽然垂直方向动力学孔径明显减小，但仍然大于物理孔径，不会影响束流的注入积累过程。该组八极磁铁产生的垂直方向振荡频率分散可以提供ms量级的Landau阻尼时间，将明显增强抑制垂直方向束流集体不稳定性的能力。该组八极磁铁投入运行后，合肥光源注入积累过程明显改善，注入流强从无八极磁铁时的约100 mA提高到330 mA左右。     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

流动稳定性弱非线性理论中的问题及其改进

流动稳定性弱非线性理论存在三个主要问题:(1)其摄动参数收敛半径太小且无具体估值;(2)其解有特定结构,一般不能满足很多实际问题的初始条件;(3)当其线性部分不是中性时,Landau系数的确定法不唯一,不知何者应是最好的方法。本文以平面Poiseuille流为例,从理论上解决了问题(1)和(2),并提出了改进办法。又通过将理论和数值模拟结果相比较的方法,澄清了问题(3)。改进了的理论,将可解决许多实际问题。     

硅烯中受电场调控的体能隙和朗道能级

近年来, 硅烯(单层硅)由于其独特的结构和电子性质以及在量子霍尔效应等领域的潜在应用而成为理论和实验研究的一个热点. 借助于四带次近邻紧束缚模型, 详细计算和研究了硅烯中受电场调制的体能隙和电子能级. 结果表明: 硅烯原胞中的两个子格处于不同的平面上, 可以通过外电场区分和控制这两个子格, 这将破坏在纯石墨烯中无法被破坏的K-K'对称性, 并消除由这一对称性导致的电子能级的二重简并; 外加电场还会引起硅烯中次近邻格点之间的Rashba自旋轨道耦合, 这一作用会在不同狄拉克点有选择地消除电子能级在部分电场点的简并, 相邻能级从交叉状态变为反交叉状态; 电子能级中除一些孤立的交叉点外, 每个能级都具有确定的自旋取向, 石墨烯中电子能级的四重简并在硅烯中被完全消除, 从而导致填充因子ν=0, ±1, ±2, ±3,…的量子霍尔平台.     

Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

This paper is devoted to the well‐posedness for time‐space fractional Ginzburg‐Landau equation and time‐space fractional Navier‐Stokes equations by α‐stable noise. The spatial regularity and the temporal regularity of the nonlocal stochastic convolution are firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag‐Leffler functions, respectively. Numerical simulations for time‐space fractional Ginzburg‐Landau equation are provided to verify the analysis results.