Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

一般Brown桥的解析解、数值解及仿真

对任意区间[t₀,t₁]任意初值为x₀和终值为x₁的Brown桥,即随机微分方程dx=(x₁-x)/(t₁-t)dt+dB(t) x(t₀)=x₀,给出其解析解(包括随机积分解和Fourier级数解),及Milstein数值解并进行期望和方差分析,求得期望函数、期望±标准差曲线和95%置信区间边界曲线.并对不同Brown运动对应的不同轨线实现进行仿真模拟.对一个非真实的近似解加以辨别.     

融合鲸鱼算法的混合灰狼优化算法

针对灰狼优化(GWO)算法存在容易陷入局部最优、收敛速度慢、求解精度不高等问题,提出一种融合鲸鱼算法的混合灰狼优化(HWGWO)算法.首先在鲸鱼算法的螺旋泡网狩猎行为中融入Levy飞行并将其整体引入灰狼优化算法;然后将动态权重和差分进化思想引入灰狼优化算法;最后利用贪婪选择策略来保留较好的灰狼位置.选取23个测试函数进行数值试验,结果表明,HWGWO算法在收敛速度和求解精度上都有所提升.此外,利用HWGWO算法求解拉伸/压缩弹簧设计问题得到的设计方案更有效.     

三维主体分子的合成及阴离子识别研究进展

生物功能体系的模拟是生物有机化学和超分子化学发展的前沿领域之一。本文简要论述新型大二环．大三环、笼型环番以及其它三维主体分子的合成及对阴离子选择性识别作用的研究新进展。     

三维有序大孔杂化材料SiW11O8-39-SiO2和γ-SiW10O8-36-SiO2的制备与表征

通过溶胶-凝胶和聚苯乙烯模板等方法制备了含缺位Keggin阴离子SiW11O8-39和γ-SiW10O8-36的三维有序大孔杂化氧化硅复合材料, 并通过紫外漫反射光谱(UV/DRS)、傅里叶变换红外光谱(FTIR)、固体核磁共振波谱(MAS NMR)等手段对其结构进行了表征. 结果表明, 杂化材料中的Keggin阴离子仍保留其基本骨架结构, 但其与氧化硅基体之间存在化学作用. 杂化材料的孔道结构用扫描和透射电子显微镜(SEM和TEM)进行表征, 其平均孔径为(335±50) nm. 对杂化材料孔壁的微孔性通过氮气吸附进行了测定. 此类材料对水溶液中羟基丁二酸的降解反应具有活性, 光催化过程中未发现Keggin阴离子自载体中脱落的现象.     

超氧化物岐化酶的模拟: 大环双核铜(II)配合物中咪唑桥的稳定性

以2,6-二乙酰基吡啶与3-氧杂戊烷-1,5-二胺缩合而成的二四元环配体, 合成了以咪唑为桥基的双核铜(II)配合物。用EPR和pH滴定分别研究了在50%DMSO和水溶液中桥基稳定性。实验结果表明: 在混合溶液中桥基稳定的pH范围为5.6-10.3, 在水溶液中pH范围为7.5-10.5, 当pH>10时, 羟基取代了咪唑桥。由于大环效应使配合物的咪唑桥能在较宽的pH范围内稳定存在。     

味觉电化学传感器的研究——Ⅰ.甜、酸、苦、咸物质对模拟生物膜电位振动频率的影响

本文以十六烷基三甲基溴化铵/含苦味酸的硝基苯/蔗糖溶液为研究体系,发现甜、酸、苦、咸物质均能使体系的振动波形和频率发生变化,初步建立了测定有味物质的定性、定量方法,并对该味觉电化学传感器的响应机理进行了探讨。     

对DSC单峰纯度测定法的评述

指出了当前流行的差示扫描量热法DSC单峰法测样品纯度所基于的假定有一些不确切的地方,并用计算机动态摸拟了DSC实验过程,结果证实了本文的论断。     

烯烃聚合数学模拟研究与现状

综述了近年来国内外在烯烃聚合微观形态和宏观反应器数学模拟方面取得的研究成果，指出了烯烃聚合过程数学模拟的发展方向。     

聚苯乙烯乳胶球三维有序体的制备及其显微形貌表征

A three-dimensional (3D) ordered structure was achieved by self-organization of monodisperse polystyrene latex about 250nm in diameter after being ambient dried. The stacked morphology was investigated by scanning electron microscopy(SEM) observation. It is shown that the face-centered cubic(FCC) phase dominantly exists. This finding presents a potential template for preparing an inverse FCC structure as a photonic crystal of full band gap if the index contrast is higher than 2.8.