Analytical dynamics of continuous medium and its application

综述了国内和国外学者研究连续介质分析动力学问题的进展,阐明了本文主要论述将Lagrange方程应用于连续介质动力学的问题.论文采用Lagrange-Hamilton体系,分别论述了非保守非线性弹性动力学、不可压缩黏性流体动力学、黏弹性动力学、热弹性动力学、刚--弹耦合动力学和刚--液耦合动力学的Lagrange方程及其应用.论述了应用Lagrange方程建立有限元计算模型的问题. 最后,展望了将Lagrange方程应用于连续介质动力学问题的研究前景.     

非线性动力学常微分方程组高精度数值积分方法

建立了一种求解非线性动力学常微分方程组初值问题的新方法．若非线性函数一阶导数存在，则给出解的积分方程表达式，计算得到按规定误差要求的高精度数值解．引入一般自治或非自治非线性系统的首次近似Jacobi矩阵，不作任何假设重构等价的非线性常微分方程组，简捷而有广泛的适应性，不改变方程的本质，但其主项构成线性化方程组，其它项则代表非线性函数高阶余项而不涉及Taylor级数展开计算，给出该方程组初值问题的Duhamel卷积分解析表达式，在时间步长内进行数值积分选代求解，在指定误差内快速收敛，逐步递推获得非线性常微分方程的瞬态响应和全时域高精度数值解．积分解连续满足微分方程组而不是在离散的步长端点上满足代数方程组，打破了传统用增量法在离散点上建立的代数方程组迭代求解，从而使传统Euler型逐步积分法的各种差分格式算法改变成真正的积分格式算法．数值计算中给出指数矩阵递增展开式，变矩阵乘法为乘积系数的加法，避免了大量矩阵自乘而大大提高计算效率．算法验证为无条件稳定，则保证对线性常微分方程而言，计算中舍入误差的传播不会扩散，不出现计算机字长有限而引起舍入误差导致计算不确定性问题．基于以上理论和数值方法，计算了线性非线性算例并进行了分析，验证了本方法简捷而有广泛的适应性，可以有足够的精确性．     

法向载荷和滑动速度对GCr15钢干滑动摩擦的影响

本文研究了在干滑动摩擦情况下,GCr15钢与YG8硬质合金对磨时的摩擦系数与法向载荷及滑动速度的关系。结果表明,摩擦系数是随着法向载荷和滑动速度的增加而降低。根据磨损表面发生的变化和磨损表面温度计算,作者认为法向载荷和滑动速度的增加使闪温增高,从而导致了摩擦磨损表面的局部熔化,即形成了边界润滑,故此摩擦系数降低,而且在较高的载荷和滑动速度条件下,不同显微组织材料的摩擦系数之差减小。     

有限长圆柱壳中轴对称弹性瞬态波

有限长的计及剪切变形和转动惯性的弹性圆柱壳的轴对称运动方程经过Laplace变换后转化为一组相空间中的方程。对该方程组作了一些适当的处理后,应用广义射线法,得到了相空间中位移和内力的射线法表达式。采用快速Fourier变换作Laplacl逆变换,即可得到圆柱壳受轴对称冲击载荷时的弹性瞬态波解。     

Purely elastic interfacial instabilities in superposed flow of polymeric fluids

Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.     

Shape memory polymer based on chemically cross-linked poly(vinyl alcohol) containing a small number of water molecules

In this paper, shape memory polymers based on poly(vinyl alcohol) (SM-PVA) cross-linked with different contents of glutaraldehyde were prepared. Because PVA is a hydrophilic polymer, all samples prepared always have a small number of water molecules exposed to air, and the water molecules are helpful for shape memory characteristics. The influences of water contents on the prepared materials were investigated. The properties of SM-PVA were investigated by dynamic–mechanical analysis, differential scanning calorimetry, and thermogravimetric analysis. Shape memory behavior of SM-PVA, depending on the switching of chain segments, occurred at around T _g. Thermo-mechanical cycle test was performed to investigate shape memory properties, including the percentage shape recovery, shape recovery ratio, and percentage shape fixity. The studied materials show promising shape memory and cyclic behavior indicative of potential applications of SM-PVA as shape memory materials.     

13顶点金属碳硼烷结构和非线性光学性质的DFT研究

采用量子化学密度泛函理论(DFT)B3LYP/6-31G(d)方法,对4,1,6-MC2B10H1213顶点金属碳硼烷几何构型进行优化,结合有限场(FF)方法计算了它们的极化率和二阶非线性光学(NLO)系数.结果表明,十个13顶点金属碳硼烷分子中1a～6a的二阶NLO系数与其构型纵向扩张呈现相同的规律.分子的前线分子轨道能级差越小,其二阶NLO系数越大.对于不同自旋态的同种金属碳硼烷分子,其偶极矩值为高自旋态大于相应的低自旋态,极化率和二阶NLO系数与自旋多重度没有一致的对应规律,自旋多重度对NLO性质影响不大.     

Spatially controlled SERS patterning using photoinduced disassembly of gelated gold nanoparticle aggregates

Controlling the assembly of the nanoparticles is important because the optical properties of noble metal nanoparticles, such as the surface plasmon resonance (SPR) and surface-enhanced Raman scattering (SERS), are critically dependent on interparticle distances. Among many approaches available, light-induced disassembly is particularly attractive because it enables spatial modification of the optical properties of nanoparticle assemblies. In this study, we prepare gold nanoparticle (AuNP) aggregates in a gel matrix. Irradiation of the gelated AuNP aggregates at 532 nm leads to the disassembly of the aggregates, changing the color (SPR) from dark blue to red and extinguishing the SERS signal along the irradiated pattern, which opens the possibility of facile fabrication of spatially controlled SERS-generating microstructures. The photoinduced disassembly of the AuNP aggregates in solution is also investigated using UV-vis spectroscopy and transmission electron microscopy.     

Self‐Assembly of Discrete Homochiral,Helical, Hydrogen‐Bonded Nanocages: From Vesicles to Microspheres and Tubules Capable of Gelating Solvents

The chiral tris‐monodentate imidazolinyl ligands 1 a – c exhibit a strong tendency to form the discrete, helical [2+3] nanocages 3 ([ 1 ₂ ?2 ₃]) with tartaric acids 2 . Circular dichroism (CD) spectra and theoretical calculations reveal that supramolecular handedness of capsulelike architectures is determined only by the chirality of the imidazolinyl ligands rather than tartaric acids. The chirality of imidazolinyl ligands is transferred to the helicity of the complexes through the directed hydrogen bonds between the N3 atom of imidazoline rings and the carboxyl of tartaric acids. These hydrogen‐bonded nanocages can spontaneously self‐assemble into spherical vesicles, during which the hydrogen bonding that arises from the hydroxyl groups of tartaric acids plays a crucial issue. The vesicles formed by [{(S,S,S)‐ 1 a }₂( 2 ^L)₃] ( 3 a ) may further evolve into microspheres that gelate organic solvents after being aged at ?20 °C for 24 h, and can also be unprecedentedly transformed to tubular assemblies capable of rigidifying the solvents when subjected to ultrasound irradiation.     

Real‐Time Monitoring of Mass‐Transport‐Related Enzymatic Reaction Kinetics in a Nanochannel‐Array Reactor

To understand the fundamentals of enzymatic reactions confined in micro‐/nanosystems, the construction of a small enzyme reactor coupled with an integrated real‐time detection system for monitoring the kinetic information is a significant challenge. Nano‐enzyme array reactors were fabricated by covalently linking enzymes to the inner channels of a porous anodic alumina (PAA) membrane. The mechanical stability of this nanodevice enables us to integrate an electrochemical detector for the real‐time monitoring of the formation of the enzyme reaction product by sputtering a thin Pt film on one side of the PAA membrane. Because the enzymatic reaction is confined in a limited nanospace, the mass transport of the substrate would influence the reaction kinetics considerably. Therefore, the oxidation of glucose by dissolved oxygen catalyzed by immobilized glucose oxidase was used as a model to investigate the mass‐transport‐related enzymatic reaction kinetics in confined nanospaces. The activity and stability of the enzyme immobilized in the nanochannels was enhanced. In this nano‐enzyme reactor, the enzymatic reaction was controlled by mass transport if the flux was low. With an increase in the flux (e.g., >50 μL min^?1), the enzymatic reaction kinetics became the rate‐determining step. This change resulted in the decrease in the conversion efficiency of the nano‐enzyme reactor and the apparent Michaelis–Menten constant with an increase in substrate flux. This nanodevice integrated with an electrochemical detector could help to understand the fundamentals of enzymatic reactions confined in nanospaces and provide a platform for the design of highly efficient enzyme reactors. In addition, we believe that such nanodevices will find widespread applications in biosensing, drug screening, and biochemical synthesis.