US-France Cooperative Research: Electrohydrodynamic Convection in Liquid Crystals

该奖项将支持亚利桑那大学的艾伦·纽威尔博士和法国巴黎-南大学物理实验室的R.Ribotta教授之间的合作研究。这项工作的目标是对向列相液晶的电流体动力学不稳定性进行跨学科的研究。向列相液晶层中的电流体动力对流(EHC)现在开始引起人们的广泛关注。液晶本身具有理论和实践意义，但人们对它们如何在微观水平上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Ginsburg-Landau方程来模拟，而液晶的情况使分析变得非常容易。充分理解所涉及的现象需要理论和实验两方面的专业知识；必须使用特定的波解来表示行为，并且必须在方程中插入由实验确定的参数值。研究人员建议使用理论和实验相结合的方法来确定复数Ginsburg-Landau方程的系数，以确定在接近起始的参数值范围内获得的序参数的系数。这些系数的知识将提供关于小幅度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大进展。纽威尔博士是一位著名的应用数学家，他在金斯伯格-朗道方程方面做了大量的工作。里博塔教授将在高级液晶研究方面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.