On the Stability of Travelling Waves Arising in Nematic Liquid Crystals

Abstract

The stability of travelling waves which occur when a nematic liquid crystal is subjected to crossed electric and magnetic fields has been studied previously where conditions on a control parameter q for stability to occur have been given. This article is concerned with the behaviour of the stable perturbations as time increases. For each of the three travelling wave solutions we can determine the long-term monotonic or oscillatory behaviour of the perturbations using knowledge of the spectrum of the operator governing the perturbation equation.     

求解Burgers方程的一种交替分段隐式算法

首先提出一个新的求解Burgers方程的差分格式,然后在此差分格式的基础上构造了便于并行计算的交替分段隐格式,并作了线性化稳定性分析.数值结果表明,本方法具有较高的精度,尤适于扩散项系数较小时的计算,且有效避免了数值结果的非物理振荡.     

Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)──Theory

ＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＳＬＯＷＬＹＤＩＶＥＲＧＥＮＴＳＷＩＲＬＩＮＧＦＬＯＷ（Ｉ）──ＴＨＥＯＲＹ＇ＸｉａＮａｎ（夏南）;ＹｉｎＸｉｅｙｕａｎ（尹协远）（ＲｅｃｅｉｖｅｄＪｕｌｙ１９．１９９３．ＣｏｍｍｕｎｉｃａｔｅｄｂｙＴｓａｉＳｈ...     

准三维旋转流体模型及其在部分充液转子稳定性分析中的应用

提了了一种简单的无粘旋转流体准三维模型,并给出了旋转流体对转子作用力的详细表达式,然后用该模型分析了部分充液刚性悬臂转子系统的稳定性,并与实验结果进行了比较,两者在定性上符合较好,准三维无粘流体模型与其它的无粘膜型一样也仅能用来分析无外阻尼或外阻尼较小的部分充液转子系统的稳定性问题。     

Relevance of High Temperature Oxidative Stability Testing to Long Term Polymer Durability

In polymer degradation and durability studies, as well as predicting shelf-life for medical devices, one is confronted with the need for accurate prediction and difficulties of long term real-time evaluation. Various ways to accelerate the degradation process have met with mixed success. However, recently, in our own studies, a ‘master curve’ like behavior was found to be valid for polypropylene samples studied. Evidently, for samples obeying the master curve, very few data points at high temperatures can be scaled to obtain reasonably accurate estimates on long term durability. Nevertheless, in a reference medium density polyethylene (MDPE) film material, the high temperature oxidative induction time data appear to diverge when run under air atmosphere compared with oxygen environments. In this article, we will present data on many of the polymer systems studied with an emphasis on extrapolation schemes for high temperature accelerated data to lower temperature very long-term durability. In this context, polymer and antioxidant reactivity toward oxygen, morphology, and mechanical property dependence on extent of degradation all need to be considered. And the potential and limitations of this approach will be discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

一类四阶非线性微分方程的周期解

本运用Liapunov函数方法，研究了一类四阶非线性微分方程的周期解，得到了存在唯一渐近稳定的周期解的充分条件。