FRG: Collaborative Research: Dynamics of elastic biostructures in complex fluids

生物流体动力学中的问题通常涉及弹性结构与周围流体的相互作用。纤毛在呼吸道的粘液运输，受精过程中精子穿透卵母细胞，以及输卵管蠕动收缩都是这种相互作用的例子。许多生物流体实际上是复杂的；也就是说，它们不是产生牛顿反应的简单分子结构的液体或混合物，而是具有复杂的非牛顿机械反应，这通常是因为它们具有悬浮的微观结构。虽然在牛顿流体中流体-结构相互作用的数学模型和数值方法的发展已经取得了很大的进展，但在复杂流体的情况下仍需要做大量的工作。这个重点研究小组将使用分析、计算和实验工具的组合来研究与复杂流体耦合的弹性结构的动力学。粘弹性流体耦合到运动和柔性边界的精确和稳健的数值方法将建立在以前为牛顿流体设计的经典浸没边界方法和质点方法的基础上。将实现粘弹性流体的连续描述，以及跟踪流体离散粘弹性微结构的模型。虽然开发的方法将被广泛应用，但该团队将专注于生物流体繁殖机制、线虫在微流体室中的运动以及粘液-纤毛运输。计算模型将与在Courant研究所的应用数学实验室进行的物理和生物实验相协调。数学通过发展牛顿流体流动的理论分析和数值方法，对工程和物理科学产生了巨大的影响。复杂流体的动力学正在成为另一个这样的机会，它从生物物理和工程、医学和生殖健康以及核心生物学的新领域中提取了一些最丰富的问题。数学和计算分析与生物科学的结合给教育带来了挑战和巨大的机遇。这项研究项目接受了这些挑战，并基于四个机构--杜兰大学、纽约大学、华盛顿州立大学和加州大学洛杉矶分校的研究人员的合作。该项目的一个核心组成部分是研究生和博士后研究人员的培训。该FRG项目将赞助两个暑期项目，博士后研究人员和研究生将在库兰特研究所的应用数学实验室度过六周。这将为参与该项目的所有学生和博士后提供机会，让他们并肩工作，全面了解研究的各个方面，并体验和参与工作流体实验室的生活。

Problems in biological fluid dynamics typically involve the interaction of an elastic structure with a surrounding fluid. Mucus transport by cilia in the respiratory tract, sperm penetration of the oocyte in fertilization, and peristaltic contractions of the oviduct are examples of such interactions. Many biological fluids are actually complex; that is they are not liquids or mixtures of a simple molecular structure that yields Newtonian responses, but instead have complicated non-Newtonian mechanical responses that arise, usually, because they have suspended microstructure. While much progress has been made in the development of mathematical models and numerical methods for fluid-structure interactions in a Newtonian fluid, much work needs to be done in the case of complex fluids. This focused research group will use a combination of analytical, computational and experimental tools to investigate the dynamics of elastic structures coupled to a complex fluid. Accurate and robust numerical methods for viscoelastic fluids coupled to moving and flexible boundaries will be developed that build upon classical immersed boundary methods and particle methods previously designed for Newtonian fluids. Continuum descriptions of the viscoelastic fluid will be implemented, as well as models that track discrete viscoelastic microstructure of the fluid. While the methods developed will be widely applicable, the team will focus upon the biofluidmechanics of reproduction, nematode motility in microfluidic chambers, as well as mucus-ciliary transport. Computational models will be coordinated with physical and biological experiments performed at the Applied Mathematics Lab at the Courant Institute.Mathematics has had a huge impact on engineering and the physical sciences through its development of theoretical analyses and numerical methods for Newtonian fluid flows. The dynamics of complex fluids is emerging as another such opportunity, and is one which draws some of its richest problems from new areas in biophysics and engineering, medicine and reproductive health, and from core biology. The integration of mathematical and computational analysis into biological science presents educational challenges and great opportunities. This research project embraces these challenges, and is based upon collaborations of investigators at four institutions - Tulane University, New York University, Washington State University and the University of California, Los Angeles. A central component of this project is the training of graduate students and postdoctoral researchers. This FRG project will sponsor two summer programs, where the postdoctoral researchers and graduate students will spend six weeks at the Applied Mathematics Lab at Courant Institute. This will provide opportunities for all the students and postdocs involved in the project to work together side by side, develop a comprehensive understanding of the various aspects of the research, and experience and participate in the life of a working fluids lab.