Graduate Program
RESEARCH CENTERS
The Division is not formally structured into isolated research groups; instead, it emphasizes applied mathematics as a unifying theme in its own right. However, in order to facilitate cooperation among faculty and students, some of the research programs are partly organized around several interdepartmental research centers. On the whole, the centers are loosely organized with many joint affiliations and interaction among them. The centers facilitate funding and cooperative research and help to maintain at the highest level the research and educational atmosphere of the Division.
The funding of these research centers supports several positions for long and short-term postdoctoral visitors in the Division. There is also a special endowment from IBM to support visitors from industrial and governmental laboratories.
LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
The Lefschetz Center provides a unique environment in which high-level mathematical research is carried out alongside intensive collaborations with researchers in the applied sciences and engineering. The Center is named after the famous mathematician, Solomon Lefschetz, who was one of its founders and early leaders. Faculty and students from the Division of Applied Mathematics, Department of Mathematics, and Division of Engineering with common interests in the theory and applications of nonlinear analysis are brought together through the activities of the center. The research of the group is focused on modern approaches to dynamical systems, partial differential equations (particularly nonlinear wave propagation and conservation laws) and stochastic control. Mathematical techniques are developed and applied in a broad range of fields, including continuum mechanics, mathematical biology, nonlinear optics, economics and finance, oceanography, celestial mechanics, fluids and astrophysics.
CENTER FOR FLUID MECHANICS, TURBULENCE AND COMPUTATION
The Center for Fluid Mechanics, Turbulence and Computation was established in 1986 when the university received an award from DARPA for a Center of Excellence in the Study of Turbulence. The Center attracts distinguished visiting scientists and provides a strong program for graduate students and postdoctoral fellows. Its research is concerned with experimental, theoretical and computational problems in fluid mechanics, with emphasis on turbulence and transitional flows in a variety of physical applications. The Center has established a well-equipped computing facility maintained by its own staff. The computing facility includes resources acquired by faculty throughout the Division and is used by the whole Division. Sophisticated methods of scientific computation and computer graphics are used in large-scale simulations, management of very large databases, and visualization of complex fluid flows. It recently acquired an IBM SP2 supercomputer, a state-of-the-art 24-node parallel processor, which is one of the most powerful computers available anywhere. The facility is linked to the national supercomputer centers and accessible by participating members over the campus network. There is also a well-instrumented wind tunnel, maintained by the Division of Engineering, for the study of turbulence and transition.
CRUNCH GROUP
The CRUNCH group is a research group in the Division of Applied Mathematics. The thrust of its research is the development of numerical algorithms, visualization methods and parallel software for continuum and atomistic simulations in fluid mechanics and related applications. The main approach to numerical discretization is based on spectral/hp element methods, on multi-element polynomial chaos, and on stochastic molecular dynamics (DPD). The group is directed by Prof. George Em Karniadakis.
PATTERN THEORY GROUP
The Brown University pattern theory group is working with the belief that the world is complex, and to understand it, or a part of it, requires realistic representations of knowledge about it. We create such representations using a mathematical formalism, pattern theory, that is compositional in that the representations are built from simple primitives, combined into (often) complicated structures according to rules that can be deterministic or random. This is similar to the formation of molecules from atoms connected by various forms of bonds. Pattern theory is transformational in that groups or semigroups of transformations operate on the primitives. These transformations express the invariances of the worlds we are looking at. Pattern theory is variational in that it describes the variability of the phenomena observed in different applications in terms of probability measures that are used with a Bayesian interpretation. This leads to inferences that will be realized by computer algorithms. Our aim is to realize them through codes that can be executed on currently available hardware.
SCIENTIFIC COMPUTING GROUP
The Scientific Computing and Numerical Analysis group has its particular strength in the analysis and application of high order numerical methods including spectral and spectral element methods, discontinuous Galerkin finite element methods, ENO and WENO finite difference and finite volume methods, compact and other high-order finite difference methods. The applications of these methods span wide including modeling and analysis of problems in computational biology, electromagnetics, high speed flows, material science, semiconductor device simulations as well as problems in optical communication systems and fiberoptics to name a few.
In addition to these Centers, the Division of Applied Mathematics also cooperates actively with Computation and Mathematics of Mind (CMM), The Center for Computational Molecular Biology (CCMB), Institute for Brain and Neural Systems, the Center for Biophysical and Biomedical Engineering, the Center for Gerontology and Health Care Research and the Center for Statistical Science, the latter two being operated by the Brown University School of Medicine. These affiliations reflect growing interest in the Division with the applications of mathematics to the nonphysical sciences.
Updated November 28, 2006
