Studies of Pattern Formation using Electroconvection

这项工作主要研究各向异性系统中的图案形成。模式形成是指在被驱离平衡的系统中发生规则的空间变化。本研究中使用的具体系统是向列相液晶中的电对流。我们将研究模式形成中的一系列开放问题，包括局域模式、离散数量的简并模式的相互作用，以及自发对称性破缺的作用。一个重要的努力将致力于研究时空混沌的例子。电对流为解决非线性动力学中的这一主要问题提供了一个独特的系统。由于系统是电驱动的，因此很容易产生控制参数的空间和时间调制。这为探索时空混沌的稳健性和探索时空混沌的控制问题提供了一种手段。此外，电极的像素化阵列将用于在小空间尺度上探测系统，并研究空间自由度和时间动力学之间的联系。最后，这项研究将包括理论和实验之间的定量比较，这在大多数时空混沌的例子中是不可能的，这将为揭示时空混沌的本质提供重要的见解。%本工作主要研究各向异性系统中的图案形成。模式形成是指在被驱离平衡的系统中发生规则的空间变化。模式在自然界中无处不在，出现在广泛的系统中，包括交通流量、天气、心脏上的化学信号、疾病传播和种群动态。一类特别重要的模式是那些表现出时空混沌的模式。时空混沌是指在空间和时间上具有不规则行为的模式。例如，常见的心脏衰竭模式涉及控制心率的化学信号的时空混乱。这个项目使用向列相液晶中的电对流的精确实验来探索时空混沌本质的基本方面。特别是，电对流特别适合于解决时空混沌的控制问题。这项研究的结果将为其他表现出类似行为的系统提供控制技术的洞察。这项研究还将为研究生提供重要的培训，使他们能够继续在行业或学术界的职业生涯。

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.***