Collaborative Research: Pattern Formation and Dynamics in Electroconvection of Nematic Liquid Crystals - A Theoretical and Experimental Study of the Weak Electrolyte Model

题目：向列液晶电对流中的模式形成和动力学——弱电解质模型的理论和实验研究【摘要】本文提出的研究是科罗拉多州立大学应用数学家和肯特州立大学实验凝聚态物理学家之间的合作。这个跨学科团队将密切合作，研究非线性非平衡动力学的范例系统：向列液晶的电对流。所开发的分析技术，以严格和定量的实验结果为支持，将阐明与模式形成和动力学相关的重要但不完全理解的现象，包括爆发，间歇性和时空混沌。研究时空动力学的一个富有成效的方法是使用典型方程，如复金兹堡-朗道方程。在这个项目中，金兹堡-朗道方程系统与向列液晶电对流的最先进模型：弱电解质模型紧密相关。该技术使研究小组能够研究非线性各向异性系统中丰富多样的复杂行为，并为实验人员提供对向列电对流模式形成过程的全面定性和定量见解。特别是，实验和理论之间的反馈使这个项目与众不同，并确保了一种独特的方法来深入探索液晶中极其困难但重要的电荷传输过程及其后果。提出的研究是一项跨学科的努力，旨在深入了解向列液晶的基本物理机制及其数学描述。由于液晶显示设备继续以这些材料为主导，因此该项目与信息技术以及材料科学相关。从更广泛的角度来看，我们提出的研究应用强大的、创新的数学和计算技术来阐明远离平衡的系统中规则和复杂模式自发形成的基本机制。时空复杂行为在生态、金融、气象、人口统计、地震等诸多重要领域都得到了观察。在向列电对流等易于控制的模型系统中，从理论上和实验上更好地理解这种行为，是在更广阔的世界中展开这些动力学工作方式的必要前提。从教育的角度来看，受资助的学生将有机会亲自了解多学科研究，并有机会通过在科罗拉多州立大学和堪萨斯州立大学联合研究研讨会上的正式演讲来练习他们的科学沟通技巧。此外，这项研究的结果将通过两所大学的课程和俄亥俄州肯特市液晶研究与教育中心的现有项目直接融入本科和研究生教育中。

Proposal: DMS-0407418PI: Iuliana OpreaInstitution: Colorado State UniversityTitle: Pattern Formation and Dynamics in Electroconvection of Nematic Liquid Crystals - A Theoretical and Experimental Study of the Weak Electrolyte ModelABSTRACTThe research proposed here is a collaboration between applied mathematicians at Colorado State University and experimental condensed matter physicists at Kent State University. This interdisciplinary team will work together closely to study a paradigm system in nonlinear, non-equilibrium dynamics: electroconvection of nematic liquid crystals. The analytical techniques developed, backed up with stringent and quantitative experimental results, will elucidate important but incompletely understood phenomena related to pattern formation and dynamics, including bursts, intermittency, and spatio-temporal chaos. One fruitful approach to the study of spatio-temporal dynamics is to employ canonical equations such as the complex Ginzburg-Landau equation. In this project systems of Ginzburg-Landau equations are rigorously related to the most advanced model for electroconvection of nematic liquid crystals: the weak electrolyte model. This technique allows the research team to study a rich variety of complex behavior in nonlinear anisotropic systems in general, as well as to provide comprehensive qualitative and quantitative insights into the process of pattern formation in nematic electroconvection of interest for experimentalists. In particular, the feedback between experiment and theory sets this project apart and insures a unique approach to profoundly probing the extremely difficult, yet important process of charge transport in liquid crystals and its consequences.The proposed research is an interdisciplinary effort directed towards a profound understanding of fundamental physical mechanisms in nematic liquid crystals and their mathematical description. Since liquid crystal display devices continue to be dominated by these materials, the project is relevant for information technology, as well as for material science. From a broader perspective, the proposed research applies powerful, innovative mathematical and computational techniques to elucidate the basic mechanisms underlying the spontaneous formation of regular and complex patterns in systems far from equilibrium. Spatio-temporally complex behavior has been observed in a wide variety of important fields including ecology, finance, weather, demographics, earthquakes etc. Developing a better understanding of this behavior, both theoretically and experimentally, in an easily controllable model system such as nematic electroconvection, is a necessary precursor to unfolding the way these dynamics work in the wider world. From an educational perspective, students supported by this grant get a hands-on introduction into multidisciplinary research and have the opportunity to practice their scientific communication skills through formal presentations to joint CSU/KSU research seminars. Moreover, the results of this research will be directly integrated into undergraduate and graduate education through courses taught at both universities and within the existing programs of the Center for Liquid Crystal Research and Education, Kent, OH.