RUI: Non-linear dynamics in fluid networks

复杂的动态行为已经在许多不同的流体流动网络中被观察或预测，包括人工的和自然的，在各种尺度上。一些例子包括血液在微循环中的流动、水滴在微流体装置中的流动、岩浆在熔岩管中的流动、冷却系统中的制冷剂流动和太阳能蒸汽发生器中的水流。虽然物理上有所不同，但潜在的现象往往是相似的。在以上所有的例子中，很难预测和确定网络中不同相或成分的分布。复杂的网络包含许多不寻常的流体（如微血管中的血液），这似乎不足为奇。然而，即使是普通流体中最简单的网络也能表现出非凡的行为。本提案旨在发展和验证一种新的通用理论，用于描述流体网络中的相分布和动力学行为。建议的工作采用构建块方法，充分描述简单网络元素的行为，然后以系统的方式增加复杂性。理论研究与实验轨道紧密结合，实验轨道将验证理论的关键预测。没有实验数据，就不可能把数学理论映射到具体的物理表现。网络流体动力学的理论和计算研究已经进行了大约20年，但关于网络行为的一般陈述很少。普遍的方法是直接模拟，但不能系统地理解关键参数。此外，关键的预测从未在实验中得到验证。这一建议克服了这些限制，并将发展一个新的网络流体动力学的一般理论，该理论植根于实验，并将以一般的方式描述网络的平衡和动态行为，使结果可以很容易地转化为具体的物理系统。最后，这项工作将在一所本科学院进行，本科生在研究中发挥核心作用。

Complex dynamic behavior has been observed or predicted in a number of different fluid flow networks, both man-made and natural, at a variety of scales. Some examples include the flow of blood through the microcirculation, the flow of droplets through microfluidic devices, the flow of magma through lava tubes, refrigerant flow in cooling systems and water flow in solar steam generators. While the physics differ, the underlying phenomena are often similar. In all of the examples above it is difficult to predict and determine the distribution of different phases or constituents within the network. Complexity in a network with many inter-connections containing unusual fluids (such as blood in the microvasculature) may seem unsurprising. However, even the simplest networks with ordinary fluids can demonstrate extraordinary behavior. This proposal seeks to develop and verify a new general theory for describing phase distribution within and the dynamical behavior of fluid networks. The proposed work takes a building block approach, fully describing the behavior of simple network elements and then adding complexity in a systematic manner. The theoretical study is closely integrated with an experimental track which will verify the key predictions of the theory. Without the experimental data, it would be impossible to map the mathematical theory to specific physical manifestations.Network fluid dynamics have been studied theoretically and computationally for approximately 20 years, yet few general statements about network behavior exist. The prevalent approach has been direct simulation which does not allow for the key parameters to be understood in a systematic way. Further, key predictions have never been tested in experiment. This proposal overcomes these limitations and will develop a new general theory for network fluid dynamics which is rooted in experiment and will describe the equilibrium and dynamic behavior of the network in a general manner such that results can be easily translated to specific physical systems. Finally, the work will be conducted at an undergraduate college with undergraduate students playing a central role in the research.