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

建议没有。项目：MARK R. PAUL/EDGAR knoblochin机构：VPI/加州大学伯克利分校：合作研究：振荡流体层中的对称性破缺分岔本基金将支持探索流体动力学中对称性破缺分岔的研究。该研究的重点是对一类新的模式形成方程的数值探索，这些方程控制着具有直接实验兴趣的流体系统中自发和强制对称破破之间的相互作用-引力场中垂直振荡流体层表面的复杂波动动力学，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，由于船员操纵和机械的残余加速度或g抖动对材料处理系统和机载实验都有重大影响。此外，已经提出了传感器通过测量对法拉第波阻尼的影响来测量蛋白质单层的特性。由于边界条件是以波幅值的形式给出的，因此幅值流耦合流动方程比幅值方程更复杂，也比Navier-Stokes流体力学方程更复杂。然而，它们比控制的粘性自由曲面问题要简单得多，因为所有项在形式上都是一阶的，并且边界条件是在未扰动的表面上应用的。对实际实验几何的耦合振幅流流动方程的数值探索将提供一个独特的机会来探索控制法拉第问题的基本物理。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捕捉到描述有趣的实验结果所必需的所有物理。特别是，关于侧壁半月板动力学的作用有很多不确定性，事实上，许多实验没有报告必要的实验参数值，这将允许详细的建模。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，大规模均匀图案技术的发展，以及分子传感器。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建模的新研究生课程的发展。

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.