Isotropic polynomial invariants of Hall tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.     

两端铰接的细长柔性圆柱体涡激振动响应特性数值研究

目前细长柔性圆柱体涡激振动响应的研究方法主要包括实验方法、计算流体动力学方法以及半经验模型方法. 鉴于实验方法研究成本较高、计算流体动力学方法计算时间较长,本文基于尾流振子模型对线性剪切来流下两端铰接的细长柔性圆柱体涡激振动响应特性进行了半经验模型方法研究. 先建立了柔性圆柱体结构振子以及尾流振子之间的耦合模型,紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解. 对不同剪切参数下柔性圆柱体涡激振动响应的振动波长、振动频率、振动位移以及响应频率随时间的变化特性等参数进行了分析. 分析结果表明:圆柱体的涡激振动响应由驻波和行波混合组成. 当无量纲弯曲刚度较小时,在圆柱体两端附近,驻波占主导;而在圆柱体中间段附近,行波占主导. 当无量纲弯曲刚度较大时,在圆柱体整个长度区间上均为驻波占主导. 随着剪切参数的增大,振动位移以及振动波长均逐渐减小,而振动频率和频率带宽均逐渐增大.      

Bäcklund transformation,rogue wave solutions and interaction phenomena for a $$\varvec{(3+1)}$$ ( 3 + 1 ) -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

Nonlinear Dynamics - Under investigation in this paper is the $$(3+1)$$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq (BKP–Boussinesq) equation, which can display the...     

INSTABILITY OF COUPLED THERMO-SOLUTE CAPILLARY CONVECTION IN LIQUID BRIDGE AND CONTROL BY ROTATING MAGNETIC FIELD

浮区法因具有无坩埚接触污染的生长优点而成为生长高完整性和高均匀性单晶材料的重要技术.但熔体中存在的毛细对流会给浮区法晶体生长带来极大挑战,这是由于对流的不稳定会导致晶体微观瑕疵的产生和宏观条纹等缺陷的形成.为了提高浮区法生长单晶材料的品质,研究浮区法晶体生长中毛细对流特性及如何控制其不稳定性显得尤为重要.本文采用数值模拟的方法对半浮区液桥内Si_xGe_1-x体系中存在的热质毛细对流展开研究并施加旋转磁场对其进行控制.结果表明：纯溶质毛细对流表现为二维轴对称模式,温度场主要由热扩散作用决定,而浓度场则由对流和溶质扩散共同支配;纯热毛细对流呈现三维稳态非轴对称流动,浓度分布与熔体内热毛细对流的流向密切相关,等温线在对流较大的区域发生弯曲;耦合溶质与热毛细对流则为三维周期性旋转振荡流.施加旋转磁场后,熔体周向速度沿径向向外增大,熔体内浓度场和流场均呈现二维轴对称分布.     

纯Cr2O3包覆Li4Ti5O12微球的制备及其储锂性能研究

The pure Cr₂O₃ coated Li₄Ti₅O₁₂ microspheres were prepared by a facile and cheap solutionbased method with basic chromium(III) nitrate solution (pH=11.9). And their Li-storage properties were investigated as anode materials for lithium rechargeable batteries. The pure Cr₂O₃ works as an adhesive interface to strengthen the connections between Li₄Ti₅O₁₂ particles, providing more electric conduction channels, and reduce the inter-particle resistance. Moreover, LixCr₂O₃, formed by the lithiation of Cr₂O₃, can further stabilize Li₇Ti₅O₁₂ with high electric conductivity on the surface of particles. While in the acid chromium solution (pH=3.2) modification, besides Cr₂O₃, Li₂CrO₄ and TiO₂ phases were also found in the final product. Li₂CrO₄ is toxic and the presence of TiO₂ is not welcome to improve the electrochemical performance of Li₄Ti₅O₁₂ microspheres. The reversible capacity of 1% Cr₂O₃-coated sample with the basic chromium solution modification was 180 mAh/g at 0.1 C, and 134 mAh/g at 10 C. Moreover, it was even as high as 127 mAh/g at 5 C after 600 cycles. At-20℃, its reversible specific capacity was still as high as 118 mAh/g.     

Difluoromethylation of 2-Hydroxychalcones Using Sodium 2-Chloro-2,2-difluoroacetate as Difluoromethylating Agent

Difluoromethylation of 2-hydroxychalcones using sodium 2-chloro-2,2-difluoroacetate as the difluoro-methylating agent was developed. Under facile conditions, a wide range of aryl difluoromethyl ethers were obtained in yields of 36%-80%. It is noteworthy that the new addition products, 2,2-difluoro-2H-benzofuran derivatives, were also synthesized in the reactions. The yield of 2,2-difluoro-2H-benzofuran derivative could be up to 35% when 3-methyl-2-hydroxychalcone was used as the reactant. A plausible reaction mechanism was proposed.     

Local trimer orbital ordering in LiNiO2 studied by quantitative convergent beam electron diffraction technique

A local trimer orbital ordering model of LiNiO₂ was studied by means of theoretical calculation and experimental measurement of electron structure factors. Based on the trimer model, the electron structure factors were calculated by using the scattering factor of non-spherical Ni³⁺ ion. From these results, it is found that the effect of local orbital ordering on the electron structure factors of several subtle reflections, such as (202) and (107), is very large. The electron structure factors of these subtle reflections were measured by quantitative convergent beam electron diffraction method. The experimentally measured electron structure factor values of these reflections indicate that the trimer orbital ordering model is more close to the true structure of LiNiO₂.     

多波长级联拉曼光纤激光器的设计

基于稳态条件下描述光纤中受激拉曼散射效应的光功率耦合方程组,提出一种新的多波长级联拉曼光纤激光器的设计算法.结合遗传算法和打靶法的优点,采取对每一代种群中少数优良个体进行几次打靶,使得种群中目标函数最优化值附近的个体加速收敛.以500 m掺磷光纤为增益介质、光纤布拉格光栅构成谐振腔的三波长(1427 nm, 1455 nm, 1480 nm)级联拉曼光纤激光器为例,采用该算法计算了其输出特性.结果表明,总输出功率与抽运功率近似成线性关系,斜率效率约51%;由于谐振腔中三个输出波长相互之间的受激拉曼散射作用产生的能量转移,使得输出的长波长斯托克斯光斜率效率大于短波长斯托克斯光斜率效率.     

Atomistic simulations of mechanical properties of graphene nanoribbons

The mechanical behavior of graphene nanoribbons (GNRs) was investigated by molecular dynamics (MD) simulations. The simulation results showed that GNRs behave nonlinear elastically under tensile loads. When the strain exceeds 18%, the stress stiffening causes an increase in the Young's modulus. The width of a GNR has slight effects on the Young modulus and fracture strength. The maximum strain at which fracture occurs can reach 30.26% with an intrinsic strength of about 0.175 TPa. The excellent flexibility is attributed to the elongation of the CC bonds and the variations of the bond angles.     

Choosing effective controlled nodes for scale-free network synchronization

Previous studies concerning pinning control of complex-network synchronization have very often demonstrated that in an unweighted symmetrical scale-free network, controlling the high-degree nodes is more efficient than controlling randomly chosen ones; due to the heterogeneity of the node-degree or edge-connection distribution of the scale-free network, small-degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network. This raises the question of whether or not controlling the high-degree nodes is always better than controlling the small ones in scale-free networks. Our answer to this is yes and no. In this study, we carry out extensive numerical simulations to show that in an unweighted symmetrical Barabasi-Albert scale-free network, when the portion of controlled nodes is relatively large, controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones. However, we also show that for normalized weighted scale-free networks, controlling the big nodes is in fact always better than controlling the small ones.