University of Vermont

Department of Mathematics & Statistics

Applied Mathematics

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    Daniel Bentil, Associate Professor, does research at the interface of Applied Mathematics and Mathematical Biology. His work, which focuses on mathematical modeling in biology and medicine, is highly interdisciplinary. In physiology, for example, he is currently working on model mechanisms for muscle contraction, aerosol deposition in the lungs, and the dynamics of hemodialysis administered to end-stage renal disease patients. Some ecological studies have involved modeling invasive species spread and host-parasite interactions. Together with his collaborators and graduate students, Daniel Bentil has been developing and analyzing mathematical models, and interpreting and comparing modeling results to real experimental data. He is very well funded and his graduate students have always had no difficulty obtaining jobs right after graduation.

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    Christopher Danforth, Associate Professor, works on accurately representing uncertainty in probabilistic weather and climate forecasts. He has developed novel techniques to improve predictions of physical systems using mathematical models. The National Oceanic and Atmospheric Administration (NOAA) have invited to him to apply his techniques to a version of the computer model used by the National Weather Service (NWS) to issue predictions to the government and media. He is also developing a high-performance computing project to explore the sensitivity of the Earth's climate to small changes in the composition of the atmosphere. Together with Peter Dodds, also in the math department, Chris is analyzing the spread of contagions (ideas, videos, emotions, etc.) over the internet, as well as the transportation network associated with university commuters. He is also doing theoretical research on applications of chaos theory to synchronization of fundamental nonlinear systems like the double-pendulum.

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    Peter Dodds, Professor, works on problems in geomorphology, biology, ecology, and sociology, with an overriding interest in complex systems and networks.

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    Taras Lakoba, Assistant Professor, applies his expertise in perturbation methods to a variety of topics in applied mathematics. Most recently, he has been interested in proving convergence of certain numerical iterative schemes for finding stationary solutions of nonlinear wave equations. In the past, he developed perturbation theories for a number of nonlinear wave equations integrable by the inverse scattering transform. Taras also worked, and still maintains interest, in fiber optics, where his expertise lies in nonlinear signal transmission, polarization effects, and noise accumulation. He was part of the team at Lucent Technologies that developed an ultra-long haul, dense wavelength-division multiplexed transmission (WDM) system in 2002.

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    Jianke Yang, Professor, works in the area of nonlinear waves and their physical applications. Nonlinear waves are prevalent in science and engineering, and they are described mathematically by nonlinear partial differential equations. His recent research interest is on nonlinear wave phenomena in optics, soliton perturbation theory, as well as numerical methods for nonlinear wave equations. He is one of the top researchers in these areas in the world.

  • picture Jun Yu, Professor, works in the area of applied mathematics with applications in biomedicine, geophysics, fluid mechanics and combustion. A major focus of his research has been on the dynamics of the intracranial system in the human brain. This problem involves a blending of fluid mechanics, elasticity, and theoretical and computational methods with both clinical and experimental aspects of human physiology. Recently, he has become involved in the study of the dynamics and thermodynamics of oceans and ice mass of the Earth, using satellite data from NASA as well as mathematical modeling techniques. At the same time he continues to do research in the area of classical fluid mechanics. There, his research focus is on nonlinearity and stability of water waves. He has examined the evolution of the weakly nonlinear solution for the case in which a parameter (Froude number) goes through its critical value and the linear solution fails. More recently, a solid combustion model was studied, and the onset of linear instability as well as the weakly nonlinear solution behavior in the presence of the linear instability was also analyzed.