硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料，是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一，有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布，纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Energy spectrum of multi-radiation of X-rays in a low energy Mather-type plasma focus device

The multi-radiation of X-rays was investigated with special attention to their energy spectrum in a Mather-type plasma focus device （operated with argon gas）. The analysis is based on the effect of anomalous resistances. To study the energy spectrum, a four-channel diode X-ray spectrometer was used along with a special set of filters. The filters were suitable for detection of medium range X-rays as well as hard X-rays with energy exceeding 30 keV. The results indicate that the anomalous resistivity effect during the post pinch phase may cause multi-radiation of X-rays with a total duration of 300 ± 50 ns. The significant contribution of Cu-Kα was due to the medium range X-rays, nonetheless, hard X-rays with energies greater than 15 keV also participate in the process. The total emitted X-ray energy in the forms of Cu-K and Cu-K/3 was around 0.14 ± 0.02 （J/Sr） and 0.04 ±0.01 （J/Sr）, respectively. The total energy of the emitted hard X-ray （〉 15 keV） was around 0.12± 0.02 （J/Sr）.     

数字全息视频成像技术及其在肝吸虫尾蚴观测中的应用

由于传统的显微镜成像需要精确的光学聚焦过程,很难检测到在水体中运动的肝吸虫尾蚴,更难以对其进行连续的动态观测.针对此问题,提出了利用单光束同轴数字全息视频技术对在水体中运动的肝吸虫尾蚴进行连续动态观测的方法,研究了其中的动态跟踪聚焦算法和视频处理算法.利用上一帧再现像中尾蚴的中心位置作为下一帧全息再现中聚焦窗口的中心位置,使聚焦窗口始终跟随观测的尾蚴移动,从而保证处理全息视频时每一帧再现像都能准确自动聚焦,使再现视频中肝吸虫尾蚴始终处于清晰状态.进行了肝吸虫尾蚴观测实验,得到肝吸虫尾蚴在水体中运动的全息再现视频,并对其运动轨迹进行了跟踪,总结了肝吸虫尾蚴在水体中的运动规律.实验结果表明,利用数字全息技术拍摄一张数字全息图即可观察到水体中不同位置的肝吸虫尾蚴,检测更加方便高效;本文提出的数字全息视频成像技术能实现对水体中的肝吸虫尾蚴或其它浮游生物进行连续动态观测.     

Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: Pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.     

Electronic properties of α-graphyne nanoribbons under the electric field effect

In this paper, we investigate the electronic structure of both armchair and zigzag α-graphyne nanoribbons. We use a simple tight binding model to study the variation of the electronic band gap in α-graphyne nanoribbon. The effects of ribbon width, transverse electric field and edge shape on the electronic structure have been studied. Our results show that in the absence of external electric field, zigzag α-graphyne nanoribbons are semimetal and the electronic band gap in armchair α-graphyne nanoribbon oscillates and decreases with ribbon's width. By applying an external electric field the band gap in the electronic structure of zigzag α-graphyne nanoribbon opens and oscillates with ribbon width and electric field magnitude. Also the band gap of armchair α-graphyne nanoribbon decreases in low electric field, but it has an oscillatory growth behavior for high strength of external electric field.