Old and new from SOR

From the long history of Successive Over Relaxation (SOR) between the end of second world war and today three points are considered: (1) Classical results of Young and Varga are described. (2) It is shown how results on semiiterative methods can be used to derive these classical results in a unifying way and to compare SOR with other iterative methods. (3) In the last 15 years the application of SOR to compute the stationary distribution of a homogeneous Markov chain has been discussed. These results are reported, considering especially the term extended convergence introduced by Kontovasilis, Plemmons and Stewart.     

Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

Unconventional chain-growth mode in the assembly of colloidal gold nanoparticles

One-dimensional assembly of gold nanoparticlesis achieved by a sphere-to-cylinder transformation of polymer shells. A large amount of monomers remains after the assembly, which is characteristic of the chain-growth "polymerization". Single-line chains can be converted to double-line chains, thus substantiating the unique role of the polymer shell.     

Improving the impact property and heat‐resistance of PLA/PC blends through coupling molecular chains at the interface

The influences of both the molecular structure and the melt viscosity differences between Poly(lactic acid) (PLA) and polycarbonate (PC) on the interpenetration of molecular chains at the interface were investigated by comparing the dynamic mechanical properties and morphologies of the as‐prepared PLA/PC solution‐casting blends with those of their corresponding annealed (180°C, 8 h) samples or PLA/PC melt blends. Additionally, two chain extenders containing epoxy groups (ADR and TGDDM) were used to improve the interfacial strength. Subsequently, the interpenetration of PLA and PC molecular chains at the interface was also surveyed. Finally, the effects of the morphology formed by after adding ADR or TGDDM on the impact property, and heat resistance were discussed. The results showed that there was no interpenetration of molecular chains at the interface in PLA/PC melt blends because of the serious hindrance of the molecular structure and the melt viscosity differences. Although the interfacial strength achieved significant increase after adding ADR or TGDDM, the increase of the interfacial strength should be caused by the connection of ADR or TGDDM molecules with PLA and PC molecules at the interface through chemical bonds rather than the entanglements of PLA and PC molecular chains because of no interpenetration of PLA and PC molecular chains at the interface. Thus, the morphology formed after adding ADR or TGDDM is still the type of complete phase separation, which may be the most suitable morphology for achieving high impact and heat resistance PLA/PC blends because these two properties strongly depend on the crystallinity of PLA phase. Copyright © 2015 John Wiley & Sons, Ltd.     

Proof of gridlock in a polymer model

It has been suggested that some lattice models of polymers, especially ones that incorporate more realistic excluded volume interactions extending to further neighbors, may be subject to gridlock. A model is defined to have the property of gridlock if it cannot melt at any temperature unless a density decrease is allowed. Classical theories of polymer melting are incompatible with the property of gridlock. This paper proves rigorously that a two-dimensional square-lattice model of polymer chains that have nearest-neighbor excluded volume interactions (called the X1S model) has the gridlock property. The proof uses elementary concepts from graph theory. Also, different interpretations of the X1S model are given in terms of real polymers. This leads to a discussion of a number of different classes of melting depending upon whether the intramolecular rotameric energies and the attractive intermolecular energies are antagonistic to or supportive of the melting transition.     

Mn和Co线性单原子链填充Cu纳米管的稳定性和磁性

基于密度泛函理论框架下的第一性原理计算,系统地研究了过渡金属(TM)Mn和Co线性单原子链填充Cu纳米管所形成复合结构的稳定性和磁性.相对于孤立单原子链,复合结构的结合能大大增加,表明Cu纳米管的包裹使得Mn和Co单原子链的稳定性显著增强.随着管内TM原子间距的增加,Mn@CuNT复合结构表现出由反铁磁向铁磁的磁相变,而Co@CuNT复合结构则表现出由铁磁向反铁磁的磁相变.相对于自由单原子链,复合结构的磁晶各向异性能显著增强,且Cu纳米管的包裹使得Mn原子链的易磁化方向发生了改变.     

利用微悬臂梁表面应力研究聚N-异丙基丙烯酰胺分子的构象转变

提出了一种基于微悬臂梁传感技术研究大分子折叠/构象转变的新方法.通过分子自组装的方法将热敏性的聚N-异丙基丙烯酰胺(PNIPAM)分子链修饰到微悬臂梁的单侧表面，用光杠杆技术检测温度在20—40℃之间变化时由于微悬臂梁上的PNIPAM分子在水中的构象转变所引起的微悬臂梁变形.实验结果显示：在升温过程中，微悬臂梁的表面应力发生了变化并且导致微悬臂梁产生了弯曲变形，这个过程对应着微悬臂梁上的PNIPAM分子从无规线团构象到塌缩小球构象的构象转变.在降温过程中，微悬臂梁发生了反方向的弯曲变形，这对应着PNIPA 关键词： 构象转变 聚N-异丙基丙烯酰胺分子链 表面应力 微悬臂梁     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.