Research Centers and Groups
CENTER FOR FLUID MECHANICS
Established in 1986, the Center for Fluid Mechanics, Turbulence and Computation was founded to promote research at Brown University in fluid mechanics, the study of turbulent flows and transition phenomena, the use of scientific computation in fluid mechanics research, and topics of related scientific interest. Permanent members of the Center include faculty from the Division of Applied Mathematics, the Division of Engineering as well as faculty from other departments. Each year the Center attracts distinguished visiting scientists and provides a strong program for post-doctoral students, through sponsored research. The Center sponsors research seminars in fluid mechanics. The Center has also established a scientific computation facility for fluid mechanics research which is maintained by the staff within the Center. A major goal of the facility is to enable animated, three-dimensional, color graphics for the visualization of complex fluid flows. Given the complexity of present-day research problems, this is a vital tool for the analysis of results in areas such as drag reduction and turbulence control, or the study of ocean currents. This facility is also linked to national supercomputer centers and is available to participating researchers on campus.
CRUNCH GROUP
The CRUNCH group is a research group in the Division of Applied Mathematics. The thrust of its research is the development of stochastic multiscale methods for physical and biological applications, specifically numerical algorithms, visualization methods and parallel software for continuum and atomistic simulations in biophysics, fluid and solid mechanics, biomedical modeling 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
LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
The Lefschetz Center for Dynamical Systems at Brown University promotes research in dynamical systems interpreted in its broadest sense as the study of evolving systems, including partial differential and functional equations, stochastic processes and finite-dimensional systems. Interactions and collaborations among its members and other scientists, engineers and mathematicians have made the Lefschetz Center for Dynamical Systems one of the leading groups in dynamical systems and control theory.
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.
Please visit our seminars page.
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.
STATISTICAL MOLECULAR BIOLOGY GROUP
Statistical Inference of high dimensional discrete unknowns from molecular biological, genetic, genomic and geological stratigraphic data sequences is the main focus the Statistical Molecular Biology group's research. Our work includes the development of theory, methods, and applications of these high-D inferences in the biological science areas of regulatory motif finding, RNA secondary structure prediction, and genome wide studies of epigenetics; and in the geoscience areas of change point estimators of paleoclimate records and probabilistic alignment of geological stratigraphic sequences. Theoretical interests are focused on high-D ensemble based estimators and Bayesian confidence limits, and application models of stochastic grammars.
CENTER FOR VISION RESEARCH
The Center for Vision Research, part of Brown’s interdisciplinary Brain Science Program, promotes and facilitates research on biological vision, computational aspects of machine vision, visual disorders, and the brain mechanisms underlying vision. The CVR provides in-depth training in vision research to postdoctoral fellows, medical residents, graduate students, and undergraduates and serves as a unifying organization spanning traditional departments, as well helping to bridge the gap between basic research and clinical practice. Vision Research at Brown includes over 30 faculty from 10 departments. What sets the Brown vision community apart is the unusually strong interactions between departments, and especially between faculty members in more quantitative disciplines (e.g. applied math, computer science, engineering, physics) and faculty in more biological or behavior-oriented disciplines (e.g. cognitive science, neuroscience, psychology). Our goal is to nurture multidisciplinary and translational research. Examples include theoretical studies of vision and visual plasticity in concert with experimental tests; biologically-inspired vision models implemented in artificial systems; and models of visual-cortical processing to address "high-level" visual deficits in developmental disorders such as Autism Spectrum Disorder.
