RUI Collaborative Research: Characterization and Control of Spatio-Temporally Chaotic Pattern Dynamics in Taylor Vortex Flow

技术摘要：本项目的目的是定量表征从局部混沌到时空混沌（STC）的转变作为系统大小的函数。这是一项新颖的研究，将有助于更好地理解动态空间模式是如何变得无序的。实验研究了长单腰沙漏和多腰沙漏两种形状的泰勒涡流。pi先前的实验表明，具有短单沙漏几何形状的TVF具有空间局域化的低维混沌模式动力学，该模式由靠近漩涡模式中心的持续相位滑移组成。延长这个系统，或者引入多个沙漏腰，有望产生更复杂的动态，不再是空间局部化的。数值上，将探讨一个空间斜坡反应扩散模型和扩散耦合非线性振子模型。已知反应扩散模型在短系统中表现出局部混沌，在长系统中表现出STC，但这些状态之间的转换尚未得到检验。在他们之前成功控制局部混沌模式动力学的基础上，pi将尝试在实验几何中对STC进行反馈控制，并根据数值模型控制算法的发展进行反馈控制。该项目将为本科生提供学习混沌、非线性动力学、模式形成、控制理论和流体力学的机会。摘要本项目的目的是更好地理解和表征动态空间模式是如何变得无序的，以及开发足以抑制这种无序的最小干预措施。不断变化但可识别的空间模式存在于整个自然和人为系统中——例如，云的形成模式，哺乳动物心脏的导电模式，以及高功率激光器的光输出模式。动态模式经常表现出所谓的“时空混沌”（STC），这是一种有序和无序的组合状态，在这种状态下，模式的变化在时间和空间上都是不可预测的。随着系统规模的增加，模式是如何从局部混沌过渡到STC的，目前还不清楚。这个项目将在一个旋转流体系统中研究这种转变，在这个系统中产生了一种漩涡模式，并在计算机模型中模拟了类似的动态模式。流体系统的几何结构是这样设计的，在这些区域中，漩涡无序地产生和破坏。pi还将尝试通过创建一个反馈回路来控制STC（即抑制紊乱），该反馈回路对旋转速度进行非常小的改变。控制STC的能力具有重要的技术和医学意义（例如控制不稳定的激光、心律失常的心脏以及化学和制药工业中的混合过程）。该项目将为本科生提供学习混沌、非线性动力学、模式形成、控制理论和流体力学的机会。

Technical AbstractThe objective of this project is to quantitatively characterize the transition from localized chaos to spatiotemporal chaos (STC) as a function of system size. This is a novel study that will lead to a better understanding of how dynamic spatial patterns become disordered. Experimentally, Taylor vortex flow (TVF), with both long single and multiple-waist hourglass geometries will be studied. Previous experiments by the PIs demonstrate that TVF with a short single hourglass geometry exhibits spatially-localized, low-dimensional chaotic pattern dynamics consisting of persistent phase slips near the center of the vortex pattern. Lengthening this system, or introducing multiple hourglass waists, is expected to generate more complex dynamics that are no longer spatially localized. Numerically, a spatially-ramped reaction-diffusion model and models of diffusively coupled nonlinear oscillators will be explored. The reaction-diffusion model is already known to exhibit localized chaos in a short system and STC in a long system, but the transition between these states has not been examined yet. Building on their previous success controlling localized chaotic pattern dynamics, the PIs will attempt feedback control of STC in the experimental geometries, informed by the development of control algorithms for the numerical models. The project will offer highly accessible opportunities for undergraduate students to learn about chaos, nonlinear dynamics, pattern formation, control theory, and fluid mechanics.Non-technical AbstractThe objective of this project is a better understanding and characterization of how dynamic spatial patterns become disordered, and the development of minimal interventions sufficient to suppress this disorder. Constantly changing but recognizable spatial patterns occur throughout natural and human-made systems-for example, patterns of cloud formation, of electrical conduction in mammalian hearts, and of light output from high-powered lasers. Dynamic patterns often display what is referred to as "spatiotemporal chaos" (STC), a combined state of order and disorder in which the changes in the pattern are unpredictable over both time and space. How patterns make a transition from localized chaos to STC as the size of a system is increased is not yet understood. This project will investigate this transition in a rotating fluid system in which a pattern of vortices is created and in computer models that simulate analogous dynamic patterns. The geometry of the fluid system is designed so that there are regions in which vortices are chaotically created and destroyed. The PIs will also attempt to control STC (i.e. suppress the disorder) by creating a feedback loop that makes very small changes to the speed of rotation. The ability to control STC has important technological and medical implications (e.g. control of erratic lasers, arrhythmic hearts, and mixing processes in the chemical and pharmaceutical industries). The project will offer highly accessible opportunities for undergraduate students to learn about chaos, nonlinear dynamics, pattern formation, control theory, and fluid mechanics.