CAREER: Multi-Scale Modeling of Biological Gels by Coupling Langevin Equations and Fractional Viscoelastic Constitutive Models

这项研究将确定重要的生物流体的数学性质，这些流体影响着气道粘液的清除和细胞分裂过程中细胞核中DNA的组织等不同过程。 日常生活中遇到的许多流体，如水，汽油和蜂蜜，都是众所周知的（牛顿）流体，但许多与工业和生物应用有关的流体却不是。非牛顿流体的常见例子包括油漆、多级发动机油、洗衣粉、儿科液体药物、肺粘液和细胞膜。非牛顿流体的一个显着特征是微观结构，可以在流动过程中显着重新排列，从而随着时间的推移和环境之间改变行为。本研究的目的是建立数学关系的微观结构的过程和流动特性的软生物物质。目前在显微镜、流动测量、理论和计算方面的进展将导致新的模型，使科学家能够设计和测试下一代生物材料并研究生物流动。本科生和研究生不仅能够学习如何设计和执行湿实验室实验，制定数学模型和执行高性能计算模拟，而且还有机会与来自数学，生物学，物理学和生物医学科学的研究人员密切互动。来自南卡罗来纳州少数民族参与计划联盟的STEM学生将被招募为新生，参加该项目支持的各种研究和教育活动。 第二个项目是SC妇女科学午餐会，将汇集女本科生和研究生进行纵向综合研究报告、讨论和指导。 这些教育工作将对教育下一代STEM科学家产生广泛的影响，为他们跨越不同领域的职业生涯做好准备。许多非牛顿流体的一个显著特征是它们具有微观或分子水平的结构，这些结构可以在流动中显着重排，从而改变材料的宏观行为或性能。这个项目将集中在幂律流变学，这是在许多生物和工业领域普遍存在。新的数学关系将建立调查软物质平衡，其中热波动占主导地位，并远离平衡的反应。这些关系将密切告知实验结果，并基于随机，积分微分方程和确定性，分数偏微分方程的耦合。这些项目的成果包括对幂律材料中宏观和微观尺度动力学之间关系的新理解，新的线性和非线性本构方程，使用分数微积分描述非局部量的分析结果，生理条件下分数模型的数值模拟，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值进行评估来支持和更广泛的影响审查标准。

This research will determine the mathematical properties of important biological fluids which influence processes as diverse as clearance of mucus from airways and the organization of DNA in the nucleus of cells during cell division. Many of the fluids encountered in everyday life, such as water, gasoline, and honey, are well-understood (Newtonian) fluids, but many of the fluids related to industrial and biological applications are not. Common examples of non-Newtonian fluids include paint, multi-grade engine oils, laundry detergent, pediatric liquid medicines, pulmonary mucus, and cell membranes. A distinguishing feature of non-Newtonian fluids is microscopic structures that can be rearranged significantly during flow and consequently alter behavior over time and between circumstances. The goal of this research is to establish mathematical relationships between microstructural processes and flow properties in soft biological matter. Current advances in microscopy, flow measurement, theory and computation will lead to new models, allowing scientists to design and test next-generation biomaterials and investigate biological flows. Undergraduate and graduate students will not only be able to learn how to design and perform wet-lab experiments, formulate mathematical models and perform high-performance computational simulations, but also have opportunities to closely interact with researchers from mathematics, biology, physics and biomedical sciences. STEM students from the South Carolina Alliance for Minority Participation program will be recruited as incoming freshmen to participate in a variety of research and educational activities supported by this project. A second program, the SC Women in Science Luncheon, will bring together female undergraduate and graduate students for vertically-integrated research presentation, discussion and mentoring. These educational efforts will have a broad impact on educating the next generation of STEM scientists, preparing them for careers that span the boundaries between different fields. A distinguishing feature of many non-Newtonian fluids is that they have microscopic or molecular-level structures that can be rearranged significantly in flow and as a consequence alter the macroscopic behavior or performance of the material. This project will focus on power-law rheology, which is ubiquitous in many biological and industrial fields. New mathematical relationships will be established by investigating soft matter both in equilibrium, where thermal fluctuations dominate, and for far-from-equilibrium responses. These relationships will be closely informed by experimental findings and are based on the coupling of stochastic, integro-differential equations and deterministic, fractional partial differential equations. The outcomes of these projects include a new understanding of the relation between macro- and micro-scale dynamics in power-law materials, new classes of linear and nonlinear constitutive equations, analytical results describing non-local quantities using fractional calculus, numerical simulations of fractional models under physiological conditions, and new experimental insights into the microstructure of soft matter.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.