Research Abstracts Online
January 2009 - March 2010
University of Minnesota Twin Cities
Institute of Technology
School of Mathematics
Institute for Mathematics and Its Applications
PI: Markus Keel
Complex Fluids/Complex Flows
The Institute for Mathematics and Its Applications (IMA) provides post-doctoral fellowships to researchers in advanced mathematics. There have been two such programs during this period. During academic year 2008–2009, the focus was the mathematics of chemistry. Computational chemistry has reached a stage of development where many chemical properties of both simple and complex systems may be computed more accurately, more economically, or more speedily than they can be measured. Further progress in computational chemistry will require that the ties between chemistry and mathematics be strengthened. This program focused on issues in electronic structure, dynamics, and statistical mechanics, including both the mathematical underpinnings of modern molecular modeling and simulation and practical issues in state-of-the-art applications. Applications areas included organic and inorganic chemistry, biochemistry, solid-state chemistry, nanochemistry, advanced materials, photochemistry, catalysis, and environmental chemistry.
For academic year 2009–2010, the program is broadly concerned with fundamental challenges of modeling, analysis, and computation for (mostly) incompressible fluid dynamics. Much attention will be focused on non-Newtonian fluids in which complex material constitutions produce nonlinear and/or nonlocal relationships between stresses and rates-of-strain (and sometimes strains) leading to unique and often unforeseen flow phenomena. Complex fluids are ubiquitous in engineering applications and the applied sciences from biology to geology. They serve as the focus of active areas of research within the larger fluid dynamics community. Complex flows include those of both simple and complex fluids in simple and complex domains, in the presence of moving boundaries, and turbulent flows. Key questions for such flows include transport and mixing properties, and flow-structure interactions generating motions including swimming, flying, sliding, and crawling. Recent research has revealed new connections between fluid characteristics, flow complexity, and transport properties that are in part serving as a unifying theme throughout the program.
Daniel Dix, Visiting Researcher
Christopher Fraser, Computer Science Professional Program, University of Chicago, Chicago, Illinois
Kara Maki, Research Associate
Vasileios Maroulas, Research Associate
Cecilia Ortiz-Duenas, Research Associate
Erkan Tuzel, Research Associate