Pattern Formation and Spatiotemporal Complex Dynamics in Extended Anisotropic Systems

扩展各向异性系统中的图案形成和时空复杂动力学

• 批准号: 1615909
• 负责人: Iuliana Oprea
• 金额: $ 41万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1615909&HistoricalAwards=false
• 关键词: Pattern; Formation; Spatiotemporal; Complex; Dynamics

This project studies the mathematics behind the intriguing features of patterns observed in examples such as nematic liquid crystals, nanostructures imprinted on surfaces through ion-beam erosion, the propagation of chemical waves in catalytic surface reactions, epitaxial growth, and ordered patterns in the solidification from a melt. These patterns are formed through a phenomenon described as anisotropic media being driven out of equilibrium through external forces and have motivated a wide range of experimental studies to find the physical mechanisms generating them. The feedback from the research findings on electroconvection in nematic liquid crystals will guide researchers of an experimental liquid crystal group at Kent State University in their experiments and will advance the understanding of pattern formation in complex fluids and their technological applications. Understanding the spatiotemporal changes in the snow surface - the interface between the atmosphere and the Earth - can improve the knowledge of hydrologic processes within the snowpack and their impact on melt dynamics as well as on the climatology of the environment. Roughness methods developed in the project will be useful for earth scientists, especially those working in the realm of climate studies, in visualizing variables over space and time. Mapping and interpretation of dynamic physical surfaces, such as the snow surface, will help inform sampling and monitoring strategies, including adequate ground-truthing of remotely sensed information.The goal of the project is to develop a comprehensive and systematic theoretical approach, through the study of amplitude and phase equations, for the analysis of specific mechanisms and features of the formation and dynamics of complex spatiotemporal patterns in anisotropic systems. Key questions to be addressed are the role of symmetry breaking of a chaotic attractor in the creation of spatiotemporal chaos and the routes to it and the role of nonlinear interactions of waves in the creation of spatiotemporal complexity and which anisotropies are involved in their occurrence. The novelty of this research lies in a combination of qualitative theoretical predictions resulting from a bifurcation analysis of amplitude and phase equations with traditional quantitative diagnostic methods used to study complex dynamics. Moreover, new and innovative tools such as topological data analysis and roughness measures are proposed for the quantitative characterization of anisotropic patterns. The results will provide a firm foundation for the intuition required to make sense of physical experiments and may suggest interesting further questions to test experimentally.

该项目研究了在诸如液晶、通过离子束侵蚀压印在表面上的纳米结构、催化表面反应中化学波的传播、外延生长以及熔体凝固中的有序图案等例子中观察到的图案的有趣特征背后的数学。这些图案是通过被描述为各向异性介质通过外力被驱离平衡的现象形成的，并且已经激发了广泛的实验研究来找到产生它们的物理机制。对液晶电对流研究结果的反馈将指导肯特州立大学实验液晶组的研究人员进行实验，并将促进对复杂流体中图案形成及其技术应用的理解。了解雪面-大气与地球之间的界面-的时空变化，可以增进对积雪内水文过程及其对融化动力学和环境气候学影响的了解。 该项目开发的粗糙度方法将有助于地球科学家，特别是那些在气候研究领域工作的科学家，在空间和时间上可视化变量。对雪面等动态物理表面的测绘和解释将有助于为采样和监测战略提供信息，包括对遥感信息进行适当的地面实况调查，该项目的目标是通过研究振幅和相位方程，用于分析各向异性系统中复杂时空模式的形成和动力学的特定机制和特征。要解决的关键问题是对称性破缺的混沌吸引子的时空混沌的创建和路线，它和波的非线性相互作用的时空复杂性的创建中的作用，其中各向异性参与其发生的作用。这项研究的新奇在于定性理论预测的结合，从分叉分析的振幅和相位方程与传统的定量诊断方法，用于研究复杂的动态。此外，新的和创新的工具，如拓扑数据分析和粗糙度的措施，提出了各向异性图案的定量表征。这些结果将为理解物理实验所需的直觉提供坚实的基础，并可能提出有趣的进一步问题进行实验测试。