US-France Cooperative Research: Electrohydrodynamic Convection in Liquid Crystals

该奖项将支持亚利桑那大学的Alan Newell博士和法国巴黎南部大学固体体质实验室的R. Ribotta教授之间的合作研究。提出的工作的目标是一个跨学科的研究电流体动力学不稳定性在向列液晶。向列液晶层中的电流体动力对流（EHC）已引起人们的广泛关注。液晶本身具有理论和实践意义，但在微观层面上，人们对它们如何与电场相互作用知之甚少。对流的开始可以用由流体方程导出的金斯堡-朗道方程来模拟，而液晶的情况使得分析非常容易处理。充分理解所涉及的现象需要理论和实验专业知识；必须使用特定的波解来表示其行为，并且必须在方程中插入实验确定的参数值。研究人员提出了用理论和实验相结合的方法来确定顺序参数的复金斯堡-朗道方程的系数，该方程在接近起始的参数值范围内得到。这些系数的知识将提供关于小振幅波的色散关系的性质以及非线性饱和特性的信息。这个项目的结果可能会导致我们对对流的理解取得重要进展。Newell博士是一位领先的应用数学家，他对金斯堡-朗道方程的主题进行了广泛的研究。Ribotta教授将为先进液晶研究提供必要的实验专业知识。

This award will support collaborative research between Dr. Alan Newell, University of Arizona and Professor R. Ribotta, Laboratoire de Physique des Solides, University of Paris-Sud, France. The objective of the proposed work is an interdisciplinary investigation of electrohydrodynamic instability in nematic liquid crystals. Electrohydrodynamic convection (EHC) in nematic liquid crystal layers is now beginning to attract much attention. Liquid crystals themselves are of theoretical and practical interest, but very little is known about how they interact with electric fields at the microscopic level. The onset of convection can be modelled by the Ginsburg-Landau equations, which are derived from fluid equations, and the case of liquid crystals makes the analysis very tractable. A full understanding of the phenomena involved requires both theoretical and experimental expertise; specific wave solutions must be used to represent the behavior and the parameter values, determined experimentally, must be inserted in the equation. The investigators propose to use a combination of theory and experiment to determine the coefficients of the complex Ginsburg-Landau equation for the order parameter which obtains in a range of parameter values close to onset. The knowledge of these coefficients will provide information on the nature of the dispersion relation for small amplitude waves, as well as nonlinear saturation characteristics. The results of this project could lead to important advances in our understanding of convection. Dr. Newell is a leading applied mathematician, who has worked extensively on the topic of Ginsburg-Landau equations. Professor Ribotta will provide the necessary experimental expertise in advanced liquid crystal research.