CAREER: Model Fluid-Solid Interactions, Networks REUs, and BioCalculus

该项目包括一系列活动，包括低雷诺数流体动力学的研究、网络科学本科生研究的指导，以及为提高生物学本科生的数学表达而开发的课程。该项目探索了流体-固体相互作用的计算模型，从遵循相互作用固体之间简单规则的悬浮现象，到可以通过分布式拉格朗日乘子（DLM）技术有效地近似关键特征的流动。在研究悬浮液时，PI开发的“排序-扫描”模拟方法将被应用并扩展到研究沉降不稳定性，包括一些类似于经典流体不稳定性（例如，瑞利-泰勒重轻不稳定性）和其他似乎是悬浮液特有的（例如，电泳悬浮和颗粒负载滴的破碎）。主要目标是测试沉积过程的宏观模型。模型DLM计算将扩展到在少量刚性、节理或可变形固体之间相互作用的尺度上探索重要的流体动力学现象，包括在小但非零雷诺数下研究液体中的自然和人工推进模式。研究和指导活动在本项目中通过网络科学本科生的研究经验，包括用于识别分层社区结构的工具和将这些工具应用于新数据集的工具，包括研究水动力相互作用组件的有效网络的潜力。该项目还包括广泛的课程开发，旨在优化生物学和健康科学专业本科生课程中涵盖的一套数学工具。开发微纳米系统和机器的能力不断进步，导致了小尺度流体动力学的设计问题，必须使用不同于大尺度工具的工具来解决。在小尺度上，粘度起着越来越重要的作用（气泵不能很好地泵出更粘稠的枫糖浆），外部边界条件变得更重要（血管壁）。同样重要的是固体与它们悬浮其中的复杂粘弹性流体之间的相互作用，这在生物环境中很常见。开发计算工具以更有效地处理此类交互是一个目标。其他基本的流体动力学现象，由于其本身的重要性和对这些制度提出的计算方法的验证，进一步研究。例如，对小型物体在液体中推进的一般问题的研究导致了可用于研究潜在的生物和医学重要性的计算技术。

This project includes a collection of activities spanning research in low Reynolds number fluid dynamics, mentoring of undergraduate research in networks science, and curriculum development for improved presentation of mathematics to biology undergraduates. The project explores the computational modeling of fluid-solid interactions from suspensions phenomena obeying simple rules between interacting solids, to flows where key features can be effectively approximated by distributed Lagrange multiplier (DLM) techniques. In studying suspensions, the "sort-and-sweep" simulation method developed by the PI will be employed and extended to investigate sedimentation instabilities, including some analogous to classic fluid instabilities (e.g., the Rayleigh-Taylor heavy-over-light instability) and others that appear to be special to suspensions (e.g., in electrophoretic levitation and breakup of particle-laden drops). A main goal is testing macroscopic models of sedimentation processes. Model DLM calculations will be extended to explore important hydrodynamic phenomena at the scale of interaction between small numbers of rigid, jointed, or deformable solids, including investigation of natural and artificial modes of propulsion in liquids at small but non-zero Reynolds numbers. Research and mentoring activities are bridged in this project through Research Experiences for Undergraduates in networks science, including tools for identifying hierarchical community structures and the application of such tools to novel datasets, including the potential of investigating effective networks of hydrodynamically-interacting components. The project also includes extensive curriculum development aimed at optimizing the set of mathematical tools covered in courses for undergraduate students majoring in biology and the health sciences.Continuing advances in capabilities for developing micro- and nano-systems and machines lead to design questions about fluid dynamics at small scales that must be addressed with different tools than those used at large scales. At small scales viscosity plays an increased role (an air pump doesn't do a good job pumping more viscous maple syrup), and external boundary conditions become more important (the walls of blood vessels). Also important are interactions between solids and the complex viscoelastic fluids in which they are suspended, a common occurrence in biological situations. Developing computational tools for more efficiently and effectively handling such interactions is a goal. Other fundamental fluid-dynamic phenomena are further investigated, both for their own importance and for the validation of the proposed computational approaches to these regimes. For instance, the investigation of general questions about propulsion of small-scale objects through liquids leads to computational techniques that can be used to study scenarios of potential biological and medical importance.