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-0407418PI：Iuliana Oprea研究所：科罗拉多州立大学标题：向列相液晶电对流中的图案形成和动力学-弱电解质模型的理论和实验研究本文提出的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、非平衡动力学中的一个范例系统：向列相液晶的电对流。开发的分析技术，加上严格和定量的实验结果，将阐明与图案形成和动力学相关的重要但尚未完全理解的现象，包括爆发、间歇和时空混沌。研究时空动力学的一种卓有成效的方法是使用正则方程，如复Ginzburg-Landau方程。在这个项目中，Ginzburg-Landau方程组与向列相液晶电对流的最先进模型：弱电解质模型严格相关。这项技术使研究小组能够在总体上研究非线性各向异性系统中丰富多样的复杂行为，并对向列相电对流中感兴趣的图案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这一项目与众不同，并确保了一种独特的方法来深入探讨液晶中极其困难但重要的电荷传输过程及其结果。拟议的研究是一项跨学科的努力，旨在深刻理解向列相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由这些材料主导，该项目与信息技术和材料科学有关。从更广泛的角度来看，这项拟议的研究应用了强大的、创新的数学和计算技术，以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。在生态、金融、天气、人口统计学、地震等广泛的重要领域都观察到了时空复杂的行为。在向列相电对流等易于控制的模式系统中，从理论和实验上更好地理解这种行为，是揭示这些动力学在更广泛的世界中工作方式的必要先导。从教育的角度来看，这笔助学金资助的学生将获得多学科研究的实践介绍，并有机会通过在CSU/KSU联合研究研讨会上的正式演讲来练习他们的科学交流技能。此外，这项研究的结果将通过两所大学教授的课程和俄亥俄州肯特市液晶研究和教育中心的现有计划直接整合到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.