Fluid-structure interactions have drawn intense attention due to their biological applications. In this talk, two types of problems will be discussed. The first is fluid-structure interactions between fluid flow and structures such as cilia, helical flagella, micro-fluidic tweezers in the low Reynolds number regime. We utilize the singularity method to explore flow fields induced by 'carpets' of rotating flagella, processing nodal cilia and micro-fluidic tweezers. Using our model system, we are able to capture the phenomena observed in experimental studies. The second problem is about simulating and modeling the dynamics of spider ballooning. The detailed physics driving this ballooning process remains little understood. We develop a mathematical model to identify the crucial physical phenomena that drive this unique mode of dispersal. The immersed boundary method has been used to solve this complex multi-scale problem.

Dr. Zhao is an Assistant Professor in the Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University. Dr. Zhao earned her PhD degree in Mathematics from the University of North Carolina at Chapel Hill in 2010. Afterwards, she did her postdoctoral studies at the University of Minnesota, and joined Case Western Reserve University in 2013. Her research in applied mathematics focuses on interactions between fluid flows and structures, with applications in biology and medicine. Some specific applications include cilia, helical flagella, micro- fluidic tweezers, and spider-dragline systems. Dr. Zhao's research is a combination of mathematical modeling, numerical simulation, and analytical methods, along with experimental verification.