Collaborative Research: Symmetry-Breaking Bifurcations in an Oscillating Fluid Layer

合作研究：振荡流体层中的对称破缺分岔

• 批准号: 0604376
• 负责人: Mark Paul
• 金额: --
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2008-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604376&HistoricalAwards=false
• 关键词: Collaborative; Research; Symmetry; Breaking; Bifurcations

PROPOSAL NO.: CTS-0604376/0620872PRINCIPAL INVESTIGATORS: MARK R. PAUL/EDGAR KNOBLOCHINSTITUTION: VPI/ UNIVERSITY OF CAL- BERKELEYSGER: Collaborative Research: Symmetry-Breaking Bifurcations in an Oscillating Fluid Layer This grant will support exploratory research to investigate symmetry-breaking bifurcations in fluid dynamics. The investigation focuses on the numerical exploration of a new class of pattern-forming equations governing the interplay between spontaneous and forced symmetry breaking in a fluid system of direct experimental interest - complex wave dynamics on the surface of a vertically oscillating fluid layer in a gravitational field, also known as the Faraday system. Faraday waves are common in low gravity environments where residual acceleration or g-jitter, due to crew maneuvering and machinery, has a significant impact on both material processing systems and on-board experiments. Also, sensors have been proposed to measure the properties of protein monolayers through measurable effects upon the Faraday wave damping. The coupled amplitude-streaming flow equations are more complex than amplitude equations and more complex than Navier-Stokes hydrodynamics since the boundary conditions are given in terms of the wave amplitudes. However, they are substantially simpler to solve than the governing viscous free-surface problem because all terms are formally of order one and the boundary conditions are applied at the undisturbed surface. A numerical exploration of the coupled amplitude-streaming flow equations for realistic experimental geometries will provide a unique opportunity to probe the fundamental physics governing the Faraday problem. The approach is risky in that there is no guarantee that the coupled amplitude-streaming flow equations capture all of the physics necessary to describe the intriguing experimental results. In particular, there is much uncertainty concerning the role of meniscus dynamics at the lateral walls and, in fact, many experiments do not report the necessary experimental parameter values that would permit detailed modeling. The outcomes of this work are applicable to a variety of technologies, e.g. design and operation of future microgravity vehicles and experiments, the development of large-scale uniform patterning technologies, and molecular sensors. Additionally, the findings of this research will be used to help support the development of a new graduate course at Virginia Tech on the theoretical modeling of spatiotemporal dynamics.

提案编号：CTS-0604376/0620872 主要研究员：MARK R. PAUL/EDGAR KNOBLOCHINSTITUTION：VPI/CALBERKELEYSGER 大学：合作研究：振荡流体层中的对称破缺分岔 这笔赠款将支持探索对称破缺的探索性研究流体动力学中的分岔。 该研究的重点是对一类新型模式形成方程进行数值探索，该方程控制直接实验感兴趣的流体系统中自发对称性和强迫对称性破缺之间的相互作用 - 重力场中垂直振荡流体层表面的复杂波动力学，也称为法拉第系统。 法拉第波在低重力环境中很常见，在这种环境中，由于机组人员的操纵和机械而产生的残余加速度或重力抖动会对材料处理系统和机载实验产生重大影响。此外，还提出了传感器通过可测量对法拉第波阻尼的影响来测量蛋白质单层的特性。 耦合幅度-流动流动方程比幅度方程更复杂，并且比纳维-斯托克斯流体动力学更复杂，因为边界条件是根据波幅给出的。 然而，它们比控制粘性自由表面问题更容易解决，因为所有项在形式上都是一阶的，并且边界条件应用于未受干扰的表面。对现实实验几何形状的耦合振幅流流动方程进行数值探索将为探索控制法拉第问题的基础物理提供独特的机会。 这种方法是有风险的，因为不能保证耦合的振幅流流动方程能够捕获描述有趣的实验结果所需的所有物理原理。特别是，关于侧壁上的弯月面动力学的作用存在很多不确定性，事实上，许多实验没有报告允许详细建模的必要实验参数值。这项工作的成果适用于多种技术，例如未来微重力飞行器和实验的设计和操作、大规模均匀图案技术和分子传感器的开发。此外，这项研究的结果将用于帮助支持弗吉尼亚理工大学关于时空动力学理论模型的新研究生课程的开发。