Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

Simulation of pedestrian counter flow through bottlenecks by using an agent-based model

Considerable research has been conducted on the topic of unidirectional evacuations from exits. However, few studies aim at simulating counter flow through a bottleneck with complex conflict. This paper proposes an agent-based model to investigate bidirectional flow evacuation. Pedestrian speed is determined by the speed of the leading agent and the surrounding agents. The moving direction of pedestrian originates from four forces, namely, gradient force, repulsive force, resistance force, and random force. These four forces dominate the main stream of the pedestrian moving trajectory, the interaction between pedestrians and their local environment, the resistance or disinclination to movement, and the random variations and chaotic nature of pedestrian dynamics. The novelty of this research is in the agent-based model that combines the agent and forces while providing insights for the simulation of the pedestrian dynamic on the cognitive level. The experiment results show that the behavior that arises from this model is consistent with the observations from Guangzhou Metro and that this model could help capture the essence of pedestrian behavior near egresses.     

稳恒磁场对Fe-Fe50 wt.%Si扩散偶中间相生长的影响

本文考察了Fe-Fe50 wt.%Si扩散偶在1200℃ 无磁场以及稳恒磁场下扩散层生长规律. 利用真空浇注强制冷却技术制备Fe-Fe50 wt.%Si扩散偶, 将制备的扩散偶进行1200℃不同磁感应强度下的热处理. 对获得热处理后试样进行SEM与EDS线扫描分析, 结果表明, 无论无磁场还是稳恒磁场下Fe-Fe50 wt.%Si扩散偶均生成两个扩散层, 即FeSi相层和Fe-Si固溶体层, 并且发现0.8 T下的两个扩散层宽度均小于0 T磁场下试样. 按照抛物线规律, 计算了扩散偶中间扩散层的互扩散系数, 发现0.8 T磁场下FeSi相层和Fe-Si固溶体层的互扩散系数较无磁场下 分别降低了26.7%与34.1%. 通过对磁吉布斯自由能的计算, 发现0.8 T磁场对扩散激活能Q的影响不足以影响扩散过程. 但扩散过程中原子振动频率ν会受到磁场的影响, 进而影响扩散常数D₀, 磁场对原子振动频率的影响可以用拉莫尔旋进理论进行解释. 关键词： Fe-Fe50wt.%Si扩散偶 稳恒磁场 FeSi相 Fe-Si固溶体     

Photocatalytic degradation efficacy of Bi4Ti3O12 micro-scale platelets over methylene blue under visible light

〈001〉 textured Bi₄Ti₃O₁₂ platelets with micro scale size were synthesized by a facile molten salt method. The photocatalytic activities of the as-prepared samples were measured with the photodegradation of methylene blue at room temperature under visible light irradiation. The Bi₄Ti₃O₁₂ with the aspect ratio of 35 exhibited good absorption in the visible light region and the photodegradation against methylene blue was higher than that of anatase TiO₂ reference, showing that the high degree of preferred {001} facets on the plate surface benefits the electronic transmission. In addition, the layer-pervoskite structure facilitates the mobility of the photogenerated carriers and hampers their recombination. The above results indicated that the large specific surface area of the as-prepared samples could attribute to the presence of a number of oxygen vacancies and then lead to the good photo-electric property. This work proposed an alternative way to tailor the structure of micro-sized platelets to get excellent properties comparable to the nano materials.     

On C1-class local diffeomorphisms whose periodic points are nonuniformly expanding

Using a sifting-shadowing combination, we prove in this paper that an arbitrary C¹-class local diffeomorphism f of a closed manifold M ⁿ is uniformly expanding on the closure ${\mathrm{Cl}_{M^n}(\mathrm{Per}(f))}$ of its periodic point set Per(f), if it is nonuniformly expanding on Per(f).     

On σ(·, W)-Holomorphic Functions and Theorems of Vitali-Type

The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved.     

“韩信点兵”问题新解

对"韩信点兵"问题的解法进行新解,给出了较孙子定理简便的求同余式组最小正整数解的一种递推公式解法.     

The Existence and Multiplicity of Solutions for Second-order Impulsive Differential Equations on the Half-line

In this paper, we consider the existence and multiplicity of solutions for a class of nonlinear impulsive problem on the half-line. By using a variational method and a variant fountain theorem, we obtain some new criteria to guarantee that the impulsive problem has at least one solution and infinitely many solutions respectively. We extend and improve some recent results.