Studies of Pattern Formation using Electroconvection

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This work focuses on the study of pattern formation in anisotropic systems. Pattern formation refers to the occurrence of regular spatial variations in systems that are driven out of equilibrium. The specific system used in this research is electroconvection in nematic liquid crystals. A range of open questions in patterns formation will be studied including localized patterns, the interaction of a discrete number of degenerate modes, and the role of spontaneous symmetry breaking. A significant effort will be dedicated to studying examples of spatio-temporal chaos. Electroconvection provides a unique system for addressing this major problem in nonlinear dynamics. Because the system is driven electrically, spatial and temporal modulations of the control parameters are easily produced. This provides a means of probing the robustness of the spatio-temporal chaos and exploring issues of control of spatio-temporal chaos. Also, pixelated arrays of electrodes will be used to probe the system on small spatial scales and to study the connection between the spatial degrees of freedom and the temporal dynamics. Finally, this research will include quantitative comparison between theory and experiment, something that is not possible in most examples of spatio-temporal chaos, that will provide important insights into the nature of spatio-temporal chaos.%%%This work focuses on the study of pattern formation in anisotropic systems. Pattern formation refers to the occurrence of regular spatial variations in systems that are driven out of equilibrium. Patterns are ubiquitous in nature, occurring in a wide range of systems including traffic flow, the weather, chemical signals on the heart, spread of disease, and population dynamics. A particularly important class of patterns are those that exhibit spatio-temporal chaos. Spatio-temporal chaos refers to patterns that have irregular behavior in space and time. For example, common failure modes of the heart involve spatio-temporal chaos of the chemical signals that control the heart rate. This project uses precision experiments in electroconvection in nematic liquid crystals to probe fundamental aspects of the nature of spatio-temporal chaos. In particular, electroconvection is uniquely suited for addressing the issue of control of spatio-temporal chaos. The results of this study will provide insight into control techniques for other systems that exhibit similar behavior. The research will also provide important training for graduate students that will enable them to go on to careers in either industry or academics.***