基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

声学超表面的非对称声分束特性研究

非对称声分束超表面是由人工微单元结构按照特定序列构建的二维平面结构,可将垂直入射的声波分成两束传播方向和分束比自由调控的透射波,在声功能器件设计及声通信领域具有广泛的应用前景。本文系统研究了一种实现非对称声分束的设计理论和实现方法,基于局域声功率守恒条件研究了声分束器的设计理论、阻抗矩阵分布、法向声强分布、声压场分布等。利用遗传算法对四串联共振腔结构进行参数优化实现了声分束器所需的阻抗矩阵分布,声压场分布表明声波入射到声分束器后在入射侧激发出两列传播方向相反且幅值和衰减系数均相同的表面波,实现了入射侧与透射侧的局域声功率相互匹配。声波经过声分束器后被分为两束透射波,两束透射波的折射角和透射系数与理论值十分吻合,证明了设计理论及实现方法的正确性和可行性。本文的研究工作可以为新型非对称声分束结构设计提供理论参考、设计方法和技术支持,并促进其在工程领域的实际应用。     

A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

Metamorphic InAs(Sb)/InGaAs/InAlAs nanoheterostructures grown on GaAs for efficient mid-IR emitters

High-efficiency semiconductor lasers and light-emitting diodes operating in the 3–5?μm mid-infrared (mid-IR) spectral range are currently of great demand for a wide variety of applications, in particular, gas sensing, noninvasive medical tests, IR spectroscopy etc. III-V compounds with a lattice constant of about 6.1?Å are traditionally used for this spectral range. The attractive idea to fabricate such emitters on GaAs substrates by using In(Ga,Al)As compounds is restricted by either the minimum operating wavelength of ～8?μm in case of pseudomorphic AlGaAs-based quantum cascade lasers or requires utilization of thick metamorphic In_xAl_1-xAs buffer layers (MBLs) playing a key role in reducing the density of threading dislocations (TDs) in an active region, which otherwise result in a strong decay of the quantum efficiency of such mid-IR emitters. In this review we present the results of careful investigations of employing the convex-graded In_xAl_1-xAs MBLs for fabrication by molecular beam epitaxy on GaAs (001) substrates of In(Ga,Al)As heterostructures with a combined type-II/type-I InSb/InAs/InGaAs quantum well (QW) for efficient mid-IR emitters (3–3.6?μm). The issues of strain relaxation, elastic stress balance, efficiency of radiative and non-radiative recombination at T?=?10–300?K are discussed in relation to molecular beam epitaxy (MBE) growth conditions and designs of the structures. A wide complex of techniques including in-situ reflection high-energy electron diffraction, atomic force microscopy (AFM), scanning and transmission electron microscopies, X-ray diffractometry, reciprocal space mapping, selective area electron diffraction, as well as photoluminescence (PL) and Fourier-transformed infrared spectroscopy was used to study in detail structural and optical properties of the metamorphic QW structures. Optimization of the growth conditions (the substrate temperature, the As₄/III ratio) and elastic strain profiles governed by variation of an inverse step in the In content profile between the MBL and the InAlAs virtual substrate results in decrease in the TD density (down to 3?×?10⁷ cm^?2), increase of the thickness of the low-TD-density near-surface MBL region to 250–300?nm, the extremely low surface roughness with the RMS value of 1.6–2.4?nm, measured by AFM, as well as rather high 3.5?μm-PL intensity at temperatures up to 300?K in such structures. The obtained results indicate that the metamorphic InSb/In(Ga,Al)As QW heterostructures of proper design, grown under the optimum MBE conditions, are very promising for fabricating the efficient mid-IR emitters on a GaAs platform.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

均匀磁场下碳离子笔形束的剂量变化分析及位置修正方法

分析外加均匀磁场对于碳离子笔形束剂量分布的影响,并考虑修正这种影响,为磁共振成像引导碳离子放射治疗的临床应用提供指导。本文利用蒙特卡罗方法模拟计算了不同能量碳离子笔形束在不同强度磁场下的剂量分布情况,发现垂直于碳离子束入射方向的均匀磁场对于碳离子笔形束射程缩短的影响很小,磁场对碳离子束的主要影响是引起束流横向偏转,特别是碳离子束布拉格峰位置的横向侧移。横向侧移程度与碳离子束的能量和磁场强度相关,根据模拟结果,得到了一个计算碳离子束布拉格峰在磁场中相对横向偏转的方程,并提出一种校正外加磁场引起的碳离子束布拉格峰横移的角度修正方法。这些结果可用于指导磁共振图像引导碳离子放射治疗计划系统的研发。     

Recent Advances in Spatial Self-Phase Modulation with 2D Materials and its Applications

In recent years, spatial self-phase modulation (SSPM) with two-dimensional (2D) materials has attracted the attention of many researchers as an emerging and ubiquitous nonlinear optical effect. In this review, the state of the art of 2D material-based SSPM is summarized. SSPM measures or tunes the nonlinearity of 2D materials, and it is also an effective approach to study the band structure of 2D materials. Several modified forms of SSPM, such as high-order, white-light-excited, vector field excited, and optically nonlinearly enhanced SSPM are also presented. Subsequently, the physical origin of the SSPM formation mechanism is compared and analyzed. Furthermore, the applications of SSPM with 2D materials, including passive photonic devices, generation of Bessel beams, and identifying the mode of the orbital angular momentum, are listed. Finally, several urgent problems of the SSPM with 2D materials, potential applications, and prospects for future development are presented.