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

建议编号：CTS-0604376/0620872研究人员：Mark R.Paul/Edgar KNOBLOCHINSTUTION：VPI/加州大学伯克利分校：合作研究：振荡流体层中的对称破坏分叉这笔赠款将支持探索性研究，以研究流体动力学中的对称破坏分叉。这项研究的重点是数值探索一类新的图案形成方程，该方程控制着直接实验感兴趣的流体系统中自发对称破缺和强制对称破缺之间的相互作用--引力场中垂直振荡流体层表面上的复波动力学，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操作，剩余加速度或g抖动对材料处理系统和机载实验都有重大影响。此外，还提出了通过对法拉第波衰减的可测量影响来测量蛋白质单分子层的性质的传感器。由于边界条件是以波幅形式给出的，因此耦合波幅流方程比波幅方程更复杂，也比Navier-Stokes流体力学更复杂。然而，它们比控制粘性自由面问题要简单得多，因为所有项形式上都是一阶的，边界条件应用于未扰动的表面。对于实际实验几何形状的耦合振幅-流动方程的数值探索将为探索支配法拉第问题的基本物理提供一个独特的机会。这种方法是有风险的，因为不能保证耦合的振幅-流动方程能够捕捉描述有趣的实验结果所需的所有物理信息。特别是，关于半月板动力学在侧壁上的作用有很大的不确定性，事实上，许多实验没有报告必要的实验参数值，以便进行详细的建模。这项工作的成果适用于各种技术，如未来微重力飞行器和实验的设计和操作、大规模均匀图案化技术的开发和分子传感器。此外，这项研究的发现将被用来帮助支持弗吉尼亚理工大学关于时空动力学理论建模的新研究生课程的开发。

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.