Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling

In this paper, we incorporate importance sampling strategy into accelerated framework of stochastic alternating direction method of multipliers for solving a class of stochastic composite problems with linear equality constraint. The rates of convergence for primal residual and feasibility violation are established. Moreover, the estimation of variance of stochastic gradient is improved due to the use of important sampling. The proposed algorithm is capable of dealing with the situation, where the feasible set is unbounded. The experimental results indicate the effectiveness of the proposed method.     

A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses

In this paper, we apply the variational method with Structural Prescribed Boundary Conditions (SPBC) to prove the existence of periodic and quasi-periodic solutions for the planar four-body problem with two pairs of equal masses $m_1=m_3$ and $m_2=m_4$. A path $q(t)$ on $[0,T]$ satisfies the SPBC if the boundaries $q(0)\in \mathbf{A}$ and $q(T)\in \mathbf{B}$, where A and B are two structural configuration spaces in ${({\mathbf{R}}^2)}^4$ and they depend on a rotation angle $\theta \in (0,2\pi )$ and the mass ratio $\mu =\frac{m_2}{m_1}\in {\mathbf{R}}^{+}$.We show that there is a region $\mathrm{\Omega }?(0,2\pi )\times R^{+}$ such that there exists at least one local minimizer of the Lagrangian action functional on the path space satisfying the SPBC $\{q(t)\in H^1([0,T],{({\mathbf{R}}^2)}^4)|q(0)\in \mathbf{A},q(T)\in \mathbf{B}\}$ for any $(\theta ,\mu )\in \mathrm{\Omega }$. The corresponding minimizing path of the minimizer can be extended to a non-homographic periodic solution if θ is commensurable with π or a quasi-periodic solution if θ is not commensurable with π. In the variational method with the SPBC, we only impose constraints on the boundary and we do not impose any symmetry constraint on solutions. Instead, we prove that our solutions that are extended from the initial minimizing paths possess certain symmetries.The periodic solutions can be further classified as simple choreographic solutions, double choreographic solutions and non-choreographic solutions. Among the many stable simple choreographic orbits, the most extraordinary one is the stable star pentagon choreographic solution when $(\theta ,\mu )=(\frac{4\pi }{5},1)$. Remarkably the unequal-mass variants of the stable star pentagon are just as stable as the equal mass choreographies.     

一种基于~4He气闪烁体的裂变中子探测器

研制了一种新中子探测器,它以²³⁵UO₂裂变靶作为转换靶,⁴He气体作为闪烁体.该探测器充分结合了²³⁵U和⁴He两种核素的特点,从而具有中子能量响应平坦、中子灵敏度较高、n/γ分辨本领高等优点,能很好地在混合脉冲裂变辐射场中测量中子.本文对探测器的原理和结构设计进行了介绍,计算了不同能量中子、γ射线在探测器中的能量沉积,并从理论和实验上对探测器的中子灵敏度、γ射线灵敏度、n/γ分辨本领和时间响应进行了研究.结果表明探测器的中子灵敏度约10^-15C·cm²,γ灵敏度约10^-17C·cm²,时间响应约33.1 ns.     

非均匀剪切流场中液晶聚合物微观结构的无网格模拟

基于宏观流场控制方程与微观分子取向扩散方程耦合的微-宏观双尺度模型,率先采用无网格方法对液晶聚合物在非均匀剪切流场中的微观结构进行了模拟研究.无网格方法精度高、稳定性好的特性保证了模拟结果的可靠性.研究了Deborah数对平板Poiseuille流中液晶聚合物微观结构的影响,预测出非均匀剪切流场中液晶聚合物的一种单一结构和五种复合结构.指出在复合结构的过渡区,分子运动具有不稳定性,可能产生瑕疵. 关键词： 液晶 微观结构 双尺度 无网格     

等离子体微带开关特性

 提出一种基于微放电等离子体的微带开关。它是以“时变等离子体”取代微带线射频微机电开关的“金属悬臂”,利用等离子体的导体或介质特性使电磁波沿其表面进行传输或截止,从而实现微带线上电磁波传输的动态控制。等离子体微带开关的基本结构包括用以隔断电磁波的微带间隙和产生片状等离子体的放电装置。放电产生时,电磁波因等离子体导体性通过开关,形成“开”状态;放电停止后,电磁波被微带间隙反射,形成“关”状态。利用CST软件仿真研究了等离子体开关特性,结果表明：这种开关的带宽由等离子体密度决定,隔离度由间隙决定,而工作插损与等离子体密度和电子碰撞频率有关。等离子体位形（宽度、厚度等）对于开关性能也非常重要。     

Theoretical investigation on the threshold value of stimulated Brillouin scattering in terms of laser intensity

The threshold value of stimulated Brillouin scattering (SBS) was investigated theoretically basing on a new concept of real gain length (RGL). It shows that for ideal steady-state SBS or ideal transient SBS, the threshold values are both constants and the later is five orders of magnitude larger than the former. Under general conditions, whether steady-state SBS or transient SBS will occur is determined by RGL. The SBS occurred in a long material may not be steady-state SBS.     

Molecular Dynamics Simulation of Temperature-dependent Flexibility of Thermophilic Xylose Isomerase

构建了嗜热栖热菌木糖异构酶与底物木糖的复合物模型,并运用NAMD2.5软件对其在300 和360 K下进行了10 ns的分子动力学模拟. 对该酶的回旋半径、亚基间相互作用及残基柔性进行了计算与统计分析,确定了该酶在360 K时柔性残基及区域. 研究发现与300 K相比,360 K时木糖异构酶中B-因子增幅较大的残基主要可分为两组：一组位于催化结构域,是由残基55～80组成的helex-loop-helix区域,另一组位于其亚基界面上. 研究表明高温下该酶催化结构域回旋半径增加,可能加速了活性中心的运动从而有利于D-木糖的异构化反应.在360 K时亚基界面上减少了8个氢键和5个离子对,这可能也是高温下其整体结构刚性下降并且活性升高的主要原因,该结果也对文献报道的该酶E372G突变体冷适应的实验现象进行了解释. 研究结果揭示了嗜热栖热菌木糖异构酶温度和结构柔性之间的关系.     

斜入射脉冲X射线产生电流实验

针对斜入射脉冲X射线与金属的几种可能相互作用机制,设计了实验布局,测量了斜入射X射线在金属靶上产生的脉冲电流,建立了相应的理论模型。结果显示,当X射线入射强度低于105 W/cm2时,以光电效应为主,高于此值时,以热电效应为主导。这表明,X射线加载强度较弱时,电子表现出个体行为,而增大X射线入射强度,电子表现出弱关联集体行为。由此可以预测,超强X射线辐照下,金属表面将出现宏观尺度的电荷密度调制,在退激发过程中,这种调制状态可能以较高的效率辐射定向的微波电磁脉冲。     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.     

Synthesis and characterization of core-shell structured SiO2@YVO4:Yb,Er microspheres

In this paper, the core-shell structured SiO₂@YVO₄:Yb³⁺,Er³⁺ microspheres have been successfully prepared via a facile sol-gel process followed by a heat treatment. X-ray diffraction, field emission scanning electron microscopy, energy disperse X-ray spectroscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, and photoluminescence spectra were used to characterize the samples. The results reveal that the SiO₂ spheres have been successfully coated by YVO₄:Yb³⁺,Er³⁺ phosphors to form core-shell structures and the size of obtained microspheres has a uniform distribution. Additionally, the samples exhibit bright green luminescence under the excitation of a 980 nm laser diode. The photoluminescence intensity increases with the number of coatings. These core-shell structured SiO₂@YVO₄:Yb³⁺,Er³⁺ microspheres may have great potential in the fields of infrared detection and display devices.