Speaker: Calvin Zhang, Mathematics
Title: Some research topics in mathematical neuroscience and bio-fluid dynamics
Abstract:
I will present three research topics in mathematical neuroscience and bio-fluid dynamics. The first topic is on synaptic transmission, the process by which neurons communicate with each other, and also with the outside world via sensory and motor systems. I will discuss mathematical models of presynaptic processes, synaptic cleft processes, and postsynaptic processes. The second topic is concerned with the rhythmic movements of animals, such as walking, swimming, breathing, and chewing. These movements are programmed in part by specialized neural circuits in the central nervous system that produce endogenous rhythmic activities. I will use the forward swimming of long-tailed crustaceans as an example to illustrate how nonlinear dynamics and perturbation theory can be used to study the neural mechanism underlying the crustacean limb coordination. The third topic is about the mathematical modeling and computer simulation of flows with immersed elastic boundaries and/or complicated geometry. In particular, I will describe the immersed boundary method, a general framework for simulating fluid-structure interactions that has been applied to a wide variety of problems in bio-fluid dynamics, such as the fluid dynamics of heart valves, wave propagation in the inner ear, blood clotting, fish swimming, and insect flight.