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

建议：DMS-0407418 PI：Iuliana Oprea机构：科罗拉多州立大学题目：向列相液晶电对流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研究是科罗拉多州立大学的应用数学家和肯特州立大学的实验凝聚态物理学家之间的合作。这个跨学科的团队将密切合作，研究非线性，非平衡动力学的范例系统：液晶的电对流。 开发的分析技术，支持严格和定量的实验结果，将阐明重要的，但不完全理解的现象有关的图案形成和动力学，包括突发，不稳定性，时空混沌。 时空动力学研究的一个富有成效的方法是采用正则方程，如复杂的Ginzburg-Landau方程。 在这个项目中，Ginzburg-Landau方程组与最先进的液晶电对流模型：弱电解质模型严格相关。 这种技术使研究小组能够研究非线性各向异性系统中的各种复杂行为，并为实验人员感兴趣的电对流模式形成过程提供全面的定性和定量见解。 特别是，实验和理论之间的反馈使该项目与众不同，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。拟议的研究是一项跨学科的努力，旨在深刻理解液晶中的基本物理机制及其数学描述。 由于液晶显示器件继续由这些材料主导，因此该项目与信息技术以及材料科学有关。 从更广泛的角度来看，拟议的研究应用强大的，创新的数学和计算技术来阐明在远离平衡的系统中自发形成规则和复杂模式的基本机制。 时空复杂的行为已被观察到在各种各样的重要领域，包括生态学，金融，天气，人口统计，地震等发展更好地了解这种行为，无论是理论上和实验上，在一个容易控制的模型系统，如电对流，是一个必要的先驱，展开这些动态的工作方式在更广阔的世界。从教育的角度来看，由该补助金支持的学生获得了动手介绍多学科研究，并有机会通过正式演讲来实践他们的科学沟通技巧，以联合CSU/KSU研究研讨会。此外，这项研究的结果将直接融入本科和研究生教育，通过在两所大学和液晶研究和教育中心，肯特，OH现有的计划内教授的课程。

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.