Learn Quasi-Stationary Distributions of Finite State Markov Chain

We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path distributions induced by candidate distribution and true target distribution. To solve this challenging minimization problem by gradient descent, we apply a reinforcement learning technique by introducing the reward and value functions. We derive the corresponding policy gradient theorem and design an actor-critic algorithm to learn the optimal solution and the value function. The numerical examples of finite state Markov chain are tested to demonstrate the new method.     

基于仿射近似从序列图像重建目标三维结构

从序列图像重建目标三维结构是摄影测量学和计算机视觉的研究热点。针对传统算法中精度与计算量的矛盾,提出一种基于仿射近似的新算法,首先用仿射三线性张量合成序列图像中的缺失图像点,重新建立图像测量矩阵,然后用仿射矩阵分解从图像特征直接获得目标三维结构的初始值,最后用基于“R-T”模式的光束法平差进行优化。仿真数据和真实图像实验表明,新算法精度高、稳定性好,有效解决了传统算法中精度、算法复杂性与结果数值稳定性的矛盾,为序列图像三维解析中的关键技术问题提供了解决方案。算法可广泛应用于航空测绘、工业检测、虚拟现实、动画制作以及军事侦察等领域。     

含氟苯乙炔苯胺封端聚酰亚胺的合成与性能研究

设计并合成了一种含氟苯乙炔苯胺封端剂4-苯乙炔基-3-三氟甲基苯胺(3FPA),使用3FPA与4,4′-(六氟异丙基)双邻苯二甲酸二酐(6FDA)和对苯二胺(p-PDA)制备了计算分子量为5000的聚酰亚胺树脂3FPA-PI-50,并对树脂溶液、树脂模塑粉和树脂模压件的制备与性能进行了研究,实验结果表明3FPA-PI-50树脂溶液具有良好的储存稳定性,成型后树脂具有优异的热性能和热氧化稳定性,后固化后树脂玻璃化转变温度为404℃,5%热失重温度大于530℃.此外树脂具有低的介电常数和吸水率.     

Nonsmooth dynamic analysis of rigid-flexible interaction collision

This paper aims to explore the deformation of the collided bodies in multibody systems and to effectively simulate the motion path of colliding bodies. First, we describe the geometrically nonlinear problems of materials by the total Lagrangian formulation. Second, a first-order integration scheme is used to solve the dynamics equations. An algorithm combining the bi-potential method with the node-to-point contact identification is proposed to solve the interface problems of rigid-flexible interaction collision. To observe the collision process more intuitively, the internal software FER/VIEW is introduced to visualize the results. The accuracy is proved by comparing the proposed method with the analytical solution or another numerical solution. Moreover, the proposed method has more numerical robustness, such as occupying less computer storage, saving the computational cost, and broadening the application range of the bi-potential method.     

Synthesis, structure and dielectric properties of Ba1-xSrxMyTi1-yO3 (M = Zr, Sn)

A series of Ba_1-xSr_xM_yTi_1-yO₃ (M = Zr, Sn, 0⩽x⩽0.4, 0⩽y⩽0.3) solid solutions were synthesized with the soft chemical method below 100 °C. XRD pattern and cell parameters-composition figures of the prepared powder demonstrate that they are completely miscible solid solutions based on BaTiO₃. Furthermore, TEM shows that they have a shape of uniform, substantially spherical particles with an average particle size of 70 nm in diameter. The sintered ceramics of the powder doped with Sr²+and Zr⁴⁺ or Sn⁴⁺ have dielectric constant eight times higher and dielectric loss thirty per cent lower than those of pure BaTiO₃ phase at room temperature.     

Coulomb expansion of a van der Waals C60 solid film

Scanning tunneling microscopy study revealed a van der Waals C60 solid film with 13% room-temperature lattice expansion on the GaAs(001) 2×4 surface. The mechanism involves fundamental Coulomb interaction due to charge transfer from the GaAs substrate. Theoretical calculation determines the charge transfer to be 1.76 electrons per C60 molecule. Oriented at its (110) crystallographic axis this film also distinguishes itself from those formed on all other semiconductor and metal substrates where only the low-energy (111) hexagonal packing of C60 molecules was developed. It is shown that this is due to the one-dimensional confinement effect of the anisotropic substrate, which may have the prospect of controlling crystal growth.     

rac-Me_2Si(Ind)_2ZrCl_2负载型催化剂催化丙烯等规聚合的研究

将rac Me2 Si(Ind) 2 ZrCl2 与甲基铝氧烷 (MAO)预络合后负载于SiO2 上得到了高活性的负载型茂金属催化剂 ,并用于丙烯等规聚合 ,研究了 [Al]/ [Zr]比、聚合温度对聚合活性、产物分子量、聚合动力学的影响 ,同时与相应的均相体系进行比较 .结果表明 ,负载化后 ,活性中心的稳定性提高 ,所得聚合物的分子量也明显高于均相体系 .同时用13 C NMR测定了两种催化体系所制备的等规聚丙烯的微结构 .结果发现 ,负载型茂金属催化剂制得的聚丙烯立构选择性高于均相体系 ,其五元组立构序列 [mmmm]从均相的 82 0 %提高到负载的 86 3 % .同时区域选择性也有所改进 ,2 ,1 插入、1 ,3 插入分别从均相体系的 4 4‰和 1 9‰降到负载体系的 3 7‰和 0 5‰ .     

比例边界等几何分析方法Ⅰ:波导本征问题

提出比例边界等几何方法 (scaled boundary isogeometric analysis, SBIGA), 并用以求解波导本征值问题. 在比例边界等几何坐标变换的基础上, 利用加权余量法将控制偏微分方程进行离散处理, 半弱化为关于边界控制点变量的二阶常微分方程, 即 TE 波或 TM 波波导的比例边界等几何分析的频域方程以及波导动刚度方程, 同时利用连分式求解波导动刚度矩阵. 通过引入辅助变量进一步得出波导本征方程. 该方法只需在求解域的边界上进行等几何离散, 使问题降低一维, 计算工作量大为节约, 并且由于边界的等几何离散, 使得解的精度更高, 进一步节省求解自由度. 以矩形和 L 形波导的本征问题分析为例, 通过与解析解和其他数值方法比较, 结果表明该方法具有精度高、计算工作量小的优点.     

波导本征问题的等几何分析方法

利用等几何分析思想通过加权余量法并结合亥姆霍兹方程推导出波导本征问题的等几何分析方程,提出了一种分析波导本征问题低自由度消耗、高精度的方法。该方法消除了传统数值方法中求解域的模型非一致性,从而实现了将问题的分析计算构架于精确的模型之上。以矩形和圆形波导的本征问题分析为例,通过与解析解和其他数值方法比较表明:在同等较细网格下,等几何分析模型仅花费1156个自由度,最大误差为0.003%,相比有限元的2245个自由度和0.03%的最大误差,此方法具有自由度少、精度高、收敛速度快等优点。     

应力和位移约束下连续结构的有效拓扑优化方法

为了解决在拥有位移与应力多个约束条件下,以减少结构重量为目标函数的拓扑优化中多约束难处理的问题,本文研究了以位移约束、应力约束、应变能约束重量最小化为目标的拓扑优化关系.通过对目标函数与约束函数的解析敏度推导,证明了它们之间的等价性.得到的准则方程表明:在最优结构中,单元质量与该单元应变能之比等于结构总质量与结构总应变能之比.由于迭代准则方程中的各项都可以在 ANSYS 有限元分析中直接提取,也不必计算乘子,从而减少了优化过程中的函数调用次数,加快了优化速度.两个算例说明了该方法的简单、高效与适用性.