The 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.
