RUI: Non-linear dynamics in fluid networks

在许多不同的流体流动网络中，无论是人工的还是自然的，在不同的尺度上都观察到或预测了复杂的动态行为。其中一些例子包括血液在微循环中的流动、液滴在微流控装置中的流动、岩浆在熔岩管中的流动、冷却系统中的制冷剂流动以及太阳能蒸汽发生器中的水流。虽然物理上不同，但潜在的现象往往是相似的。在上述所有例子中，很难预测和确定网络中不同相或组分的分布。在一个包含不寻常液体(如微血管中的血液)的许多相互连接的网络中，复杂性似乎并不令人惊讶。然而，即使是使用普通流体的最简单的网络也可以表现出非凡的行为。这一建议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，全面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，将验证理论的关键预测。没有实验数据，就不可能将数学理论映射到具体的物理表现上。网络流体动力学的理论和计算研究已有近20年的历史，但关于网络行为的一般表述却很少。流行的方法是直接模拟，这不允许以系统的方式理解关键参数。此外，关键预测从未在实验中得到检验。这一建议克服了这些局限性，并将发展一种新的网络流体动力学的一般理论，它植根于实验，并将以一般的方式描述网络的平衡和动态行为，从而使结果可以很容易地转化为特定的物理系统。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.