Applied Mathematics

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 endstage renal disease patients. Some ecological studies have involved modeling invasive species spread and hostparasite 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.

Christopher Danforth, Assistant 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 highperformance 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 doublependulum.

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

Kenneth Golden, Professor, joined the UVM faculty in 1986 and is Professor of Mathematics, Physics, and Electrical Engineering and a University Scholar. He was elected a Fellow of the American Physical Society in 1991 for "pioneering work in the theory of dynamical processes in strongly coupled plasmas." In 1996 he was elected a Fellow of the Australian Institute of Physics. He was a Visiting Fellow at the Australian National University's Institute of Advanced Studies in 1992 and returns to the A.N.U. in the same capacity in Spring 2000. He has authored and coauthored 13 invited book chapters and 77 refereed papers in many of the premier physics journals.In the early 1970s, Ken was one of a handful of scientists worldwide to propose pioneering theories about the fundamental properties of a fifth state of matter: plasma (a collection of electrically charged particles) in a strongly correlated Coulomb liquid phase. He is one of the principal architects of the powerful Nonlinear FluctuationDissipation Theorem (NLFDT), a generalization of the second law of thermodynamics. The NLFDT has been heralded as a major contribution to statistical mechanics of Coulomb systems. His research, which spans the fields of plasma physics, solid state physics, and astrophysics has been funded since the early 1980s by the National Science Foundation and is currently funded by the Department of Energy.

Bill Lakin works in the areas of applied and computational mathematics and biomedical mathematics. His current research involves the development and analysis of mathematical models for biomedical problems involving intracranial pressure dynamics and the physiological mechanisms that regulate blood pressure, cerebral blood flow, and heart function. He is the founder and coordinator of the Vermont Intracranial Pressure Modeling Group, an interdisciplinary group that includes applied mathematicians, neurosurgeons, and neurologists. Working with his research collaborators, he recently published results that resolved the "chicken or egg" question for the role played by a venous stenosis in the pathogenesis of Ideopathic Intracranial Hypertension, a condition that untreated can lead to visual impairment or blindness. He also is involved in research of interest to NASA and has determined the critical role played by the bloodbrain barrier in the development of Space Adaptation Sickness in microgravity environments.

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 ultralong haul, dense wavelengthdivision multiplexed transmission (WDM) system in 2002.

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.
 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.