基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Bottom‐Up Construction and Reversible Structural Transformation of Supramolecular Isomers based on Large Truncated Tetrahedra

A rational synthetic strategy to construct two supramolecular isomers based on polyoxovanadate organic polyhedra with tetrahedral symmetries is presented. VMOP‐α , a low‐temperature product, has an extremely large cell volume (470 842 ų), which is one of the top three for well‐defined MOPs. The corner‐to‐corner packing of tetrahedra leads to a quite low density of 0.174 g cm^?3 with 1D channels (ca. 5.4 nm). The effective pore volume is up to 93.6 % of cell volume, nearly the largest found in MOPs. For the high‐temperature outcome, VMOP‐β , the cell volume is only 15 513 ų. The packing mode of tetrahedra is corner‐to‐face, giving rise to a high‐density architecture (1.324 g cm^?3; channel 0.8 nm). Supramolecular structural transformation between VMOP‐α and VMOP‐β can be reversibly achieved by temperature‐induced solvent‐mediated transformation. These findings give a good opportunity for understanding 3D supramolecular aggregation and crystal growth based on large molecular tectonics.     

间氨基水杨酸修饰超高交联吸附树脂对酚类化合物的吸附行为

合成间氨基水杨酸修饰的超高交联吸附树脂LZ-01,比较LZ-01树脂与NJ-8树脂对对甲基苯酚和对硝基苯酚的吸附能力,研究LZ-01树脂在不同温度(288K,313K,318K)下吸附水溶液中对甲基苯酚和对硝基苯酚的静态吸附热力学和动力学行为。结果表明,由于LZ-01树脂具有更大的比表面积、更多的微孔且含有氨基、羟基和羧基等基团,使其对对甲基苯酚和对硝基苯酚的吸附量明显高于NJ-8树脂。Freundlich方程对等温吸附数据能够很好地拟合,吸附焓变绝对值小于40kJ/mol,表明吸附是焓驱动的物理吸附过程。LZ-01树脂对对甲基苯酚和对硝基苯酚吸附动力学均符合准一级动力学方程,吸附速率随温度升高而增大,颗粒内扩散是该吸附过程的速控步骤。     

没食子酸修饰树脂对对氯苯胺和对硝基苯胺的吸附行为

通过Friedel-Crafts后交联及化学修饰反应,制备了没食子酸修饰的超高交联吸附树脂(GAMR),并通过傅里叶变换红外光谱仪、元素分析仪和比表面及孔径分析仪对其理化性质进行了表征。通过等温吸附实验和吸附动力学实验,研究了GAMR树脂对不同温度下水溶液中的对氯苯胺和对硝基苯胺的吸附行为。结果表明,GAMR树脂具有较高的比表面积(1227.1m2/g)和较丰富的微孔(888.5m2/g),树脂表面修饰了较丰富的羟基和羰基。GAMR树脂对对氯苯胺和对硝基苯胺均具有良好的吸附性能,吸附量随着温度的升高而下降。Freundlich等温吸附方程能够更好地拟合吸附等温线数据,GAMR树脂对对氯苯胺和对硝基苯胺的吸附机理较复杂。吸附焓变ΔH0,表示吸附过程为放热反应,且以物理吸附为主;吸附自由能变ΔG0,说明吸附过程可自发进行;吸附熵变ΔS0,表明吸附质分子在树脂表面上的运动受到了限制。动力学实验结果表明,吸附过程符合一级动力学方程,颗粒内扩散是吸附过程的主要控制步骤。     

用自行设计的自动分析系统测定高含量SO3--对硫酸钡浊度测定法的改进

为了解决湿法磷酸生产中高含量SO3的测定,对硫酸钡浊度测定法的反应条件进行了改进,并自行设计制造了自动化的分析系统。测定时样品由蠕动泵(P)推入酸化盘管(AC)中进行酸化和稀释,由定量环(Sv)取样25μL,注入反应系统。在第一反应盘管(RC1)中,SO3与第一混合试剂中的BaCl2溶液反应生成BaSO4悬浊液,该溶液中的聚乙二醇-4000(PEG-4000)和乙醇通过协同作用避免了BaSO4颗粒的团聚,降低粒子间的相互作用,使BaSO4的生成减少,降低了测定的灵敏度,提高了稳定性。在第二反应盘管(RC2)中,BaSO4与第二混合试剂中的NH3·H2O/乙二胺四乙酸二钠(Na2EDTA)溶液发生络合反应同时被Na2EDTA包裹,进一步降低其灵敏度。最后反应溶液进入流通式光度检测器,在680.0nm波长处测试BaSO4悬浊液的吸光度。经优化试验条件,上述第一混合试剂中3种组分的质量分数或体积分数为:BaCl24%,PEG-4000 3%和乙醇2%;第二混合试剂中Na2EDTA的质量分数为6%,NH3·H2O的体积分数为6%。对实际按本方法及重量法分析进行测定,两种方法所得结果的相对偏差在±2%以内,且不受共存的高含量PO43-和F-的干扰。     

非对称铺层复合材料层合板质量优化设计

复合材料广泛应用于航空航天等领域,追求轻量化设计已经成为研究重点.对复合材料层合板质量优化设计,可以减少层合板的纤维用量,减小层合板的质量,降低成本.首先研究复合材料层合板在承受轴向载荷时,产生的形变量、应力示意图,分析容易发生失效部位;以层合板铺层厚度为设计变量,最大应变、铺层比例等为约束条件,最小化层合板质量为优化...     

Giant Asymmetric Transmission and Circular Dichroism with Angular Tunability in Chiral Terahertz Metamaterials

Inspired by the chiral structure from mode interaction, a chiral terahertz metamaterial and its complementary structure with the coexistence of asymmetric transmission and circular dichroism response are designed. The asymmetric transmission happens in the presence of electric and magnetic modes perpendicular to each other, resulting from intrinsic chirality under normal incidence. Circular dichroism exists in the presence of electric and magnetic modes parallel to each other under oblique incidence because of extrinsic chirality. Both asymmetric transmission and circular dichroism are enhanced by complementary structures, benefitting from the coupling between adjacent units. The maximum of chiral parameter κ can achieve 450, which is one hundred times higher than previously reported. The chiral response can be tuned by the incident angle and is sensitive to the environmental refractive index. The results highlight the potential applications of these metamaterials in chiral sensing and polarization transformation devices.     

45钢柱壳爆炸膨胀断裂的SPH模拟分析

金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式,目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟,探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程,模拟结果与实验结果一致。SPH数值模拟结果表明:在爆炸加载阶段,随着冲击波在柱壳内、外壁间来回反射形成二次塑性区,沿柱壳壁厚等效塑性应变演化呈凸形分布,壁厚中部区域等效塑性应变较内、外壁大;在较高爆炸压力（JOB-9003）作用下,柱壳断裂发生在爆轰波加载阶段,损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展,形成剪切型断裂模式;而在RHT-901空心炸药加载下,虽然裂纹仍从壁厚中部开始沿剪切方向扩展,但随后柱壳进入自由膨胀阶段,未断区域处于拉伸应力状态,柱壳局部发生结构失稳,形成类似“颈缩”现象,裂纹从剪切方向转向沿颈缩区向外扩展,呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见,柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程,不能简单将其作为一系列膨胀拉伸环处理。     

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.