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研究，网络科学本科生研究的指导，以及改进生物本科生数学演示的课程开发。 该项目探讨了流体-固体相互作用的计算建模，从遵守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）技术有效近似关键特征的流动。 在研究悬浮液时，将采用PI开发的“分类和扫描”模拟方法，并将其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，Rayleigh-Taylor重轻不稳定性）和其他似乎是悬浮体特有的（例如，在电泳悬浮和载有颗粒的液滴的分裂中）。 一个主要目标是测试沉积过程的宏观模型。模型DLM计算将扩展到探索重要的流体动力学现象的规模之间的相互作用的小数目的刚性，关节，或可变形的固体，包括自然和人工模式的推进液体在小，但非零雷诺数的调查。 研究和指导活动在这个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，包括调查流体动力学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数学工具集。开发微纳米系统和机器的能力的不断进步导致小尺度流体动力学的设计问题，这些问题必须用不同于大尺度的工具来解决。 在小尺度下，粘度起着更大的作用（空气泵不能很好地泵送更粘稠的枫糖浆），外部边界条件变得更加重要（血管壁）。 同样重要的是固体和它们悬浮在其中的复杂粘弹性流体之间的相互作用，这在生物情况下是常见的。 开发计算工具以更高效和有效地处理这种相互作用是一个目标。 其他基本的流体动力学现象进行了进一步研究，无论是自己的重要性和验证这些制度的拟议计算方法。 例如，对小尺度物体通过液体推进的一般问题的调查导致了可用于研究潜在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.