Dr. Paula Vasquez awarded an NSF CAREER grant for the project "Multi-Scale Modeling of Biological Gels by Coupling Langevin Equations and Fractional Viscoelastic Constitutive Models" from the Division of Mathematics Sciences. Considered one of the National Science Foundation's most prestigious awards, this grant supports early-career faculty in both their research and educational missions.

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.