In recent years there has been an explosion of interest in the study of nonlinear waves and dynamical systems with analytical results often motivated by the use of computers. The faculty in the Program is actively and intensively involved in this growing field; research areas include integrable and near-integrable systems, conservative and dissipative chaos, as well as numerical computation.
Topics of interest include solitons, dispersive shock waves, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena. Program courses in this field include dynamical systems, nonlinear wave motion and many advanced seminars.
Suitable background courses are: analysis, computation, partial differential equations, and methods in applied mathematics. Valuable supplemental courses include mechanics and fluid dynamics.
Physical Applied Mathematics
Physical Applied Mathematics is a term which generally refers to the study of mathematical problems with direct physical application. This area of research is intrinsically interdisciplinary. In addition to mathematical analysis, it requires a deep understanding of the underlying applications area, and usually requires knowledge and experience in numerical computation.
The Program's affiliated faculty have a wide variety of expertise in various areas of application, e.g. atmospheric and fluid dynamics, theoretical physics, plasma physics, genetic structure, etc. The course requirements of the Program are designed to provide students with a foundation for their study (analysis and computation).
The Program also requires supplemental courses in one of the science or engineering fields which are needed to begin doing thesis research in physical applied mathematics.
Probability and Statistics
Almost all natural phenomena in the technological, biological, physical and social sciences have random components. Applied probability is the application of probabilistic methods to understand the random elements in real-life problems. Statistics is the science of using data, which typically arises from the randomness inherent in nature, to gain new knowledge.
Research areas of the applied math and affiliated faculty exhibit this interplay between mathematics and real-life problems. Areas of current interest include optimization of stochastic networks; the study of stochastic processes and stochastic differential equations in hydrology and telecommunications; probabilistic models, and statistical tests based on these models, in genetics and RNA sequencing; extreme value theory in estimation of maximal wind speeds.