Kirchhoff方程的相对常值特解及其Lyapunov稳定性

对于超细长弹性杆静力学的Kirchhoff方程，用动力学的概念和方法研究其常值特解 和稳定性问题.计算了Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet 坐标系的常值特解，进行了Kirchhoff动力学比拟，用一次近似理论分别讨论了它们的Lyapu nov稳定性，导出了若干稳定性判据，并在参数平面上绘出了稳定域. 关键词： 超细长弹性杆 Kirchhoff方程 常值特解 Lyapunov稳定性     

梯度棒折射率分布系数的计算和验证

本文推导了用离子交换法制作的径向折射率梯度棒的g,h_4和h_6与材料特性相联系的计算公式。根据测定的材料参数,并用本文公式算出的g值与用成像法测得的g值相比较,其结果基本相符。     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.     

Mineral–water interfacial structures revealed by synchrotron X-ray scattering

Chemical reactions occurring at the mineral–water interface are controlled by an interfacial layer, nanometers thick, whose properties may deviate from those of the respective bulk mineral and water phases. The molecular-scale structure of this interfacial layer, however, is poorly constrained, and correlations between macroscopic phenomena and molecular-scale processes remain speculative. The application of high-resolution X-ray scattering techniques has begun to provide substantial new insights into the molecular-scale structure of the mineral–water interface. In this review, we describe the characteristics of synchrotron-based X-ray scattering techniques that make them uniquely powerful probes of mineral–water interfacial structures and discuss the new insights that have been derived from their application. In particular, we focus on efforts to understand the structure and distribution of interfacial water as well as their dependence on substrate properties for major mineral classes including oxides, carbonates, sulfates, phosphates, silicates, halides and chromates. We compare these X-ray scattering results with those from other structural and spectroscopic techniques and integrate these to provide a conceptual framework upon which to base an understanding of the systematic variation of mineral–water interfacial structures.     

Growth of ramification-like ZnO rods in the presence of polyaniline

To obtain new materials with synergetic or complementary behaviors, polyaniline composite filled with ZnO rods in ramification-like structure was prepared by a hydrothermal approach. Comparative experiments of ZnO preparation in the presence of some metal ions were also carried out. The results indicated that the morphology of ZnO was strongly affected by the preparation condition. The method to grow ZnO rods in the presence of polyaniline offers a simple approach to obtain polyaniline composite filled with linear ZnO structure. The results of X-ray photoelectron spectroscopy show that the strong interaction between ZnO and polyaniline possibly exists to cause the charge transfer.     

邻苯二甲酸二烯丙酯和甲基丙烯酸甲酯共聚物梯度折射率棒制备过程的研究

<正> 梯度折射率棒是折射率沿径向或轴向连续变化的透明圆棒,具有光自聚焦性能。可用于制作自聚焦型光纤维和自焦聚透镜。用玻璃制得的梯度棒直径和折射率差都很小。近年来,开始研究高分子梯度棒,据估计其直径可望达到100mm,折射率差也可达0.1。本文采用二元掖体扩散共聚法,制得梯度棒,其径向折射率分布接近于抛物线型。     

On the Rigidity of Polynorbornenes with Dipolar Pendant Groups

A range of polynorbornenes (PNBs) with fused dipolar pendant groups at C‐5,6 positions was synthesized by ring‐opening metathesis polymerization catalyzed by a ruthenium carbene complex (Grubbs I). Photophysical studies, EFISH measurements, and atomic force microscopy images have been used to investigate the structures and morphology of these polymers. These results suggest that the polymers may adopt rigid rod‐like structures. The presence of the double bonds in PNBs appeared to be indispensable for the rigidity of the polymers. Interaction between unsaturated pendant groups may result in coherent alignment leading to a rod‐like structure.     

Molecular composites in thermosets

The synthesis of molecular composites where rigid polymer molecules are reinforcing elements in a thermoset bisimide matrix has been investigated. The approach has been designed to avoid phase separation by selecting systems where reaction of amine-terminated rigid and semiflexible oligomers with maleimide unsaturation occurs prior to crosslinking of the thermoset. This objective has been met for some compositions. The concentration and molecular weight of the rigid oligomers have been varied. The structure of the reinforcing polymer, the reactivity of the maleimide and the conditions for composite synthesis are variables of critical importance, and further work must determine the promise and limitations of this approach.     

Korn inequality for a thin rod with rounded ends

We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd.