SCREMS: Multiscale Computing in Astrophysics, Geophysics, Hydrodynamics, Kinetic and Quantum Applications

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

This award supports the purchase of a mid-size computational system that will support computational mathematics research by four faculty members and their student research associates in the department of Mathematics at the University of Wisconsin-Madison. The four projects are in distinct areas of science. One project aims to develop and test computational methods to study how mass is accreted onto (sucked into) black holes. Black holes are massive compact objects that induce such strong gravity that not even light can escape them and occur in our universe in several forms including as super-massive black holes at the center of galaxies and at the scale of stars in the form of x-ray binaries. The detailed physics of the accretion process and the resulting dynamics are not yet fully understood. The goal of this project is the development of accurate and efficient computational methods for further understanding of these processes. A second project is to study the impact of `small scale' physical effects that have not been explicitly included in current computational models of the atmosphere, oceans and the climate. Those effects are either ignored for lack of computer power, even on today's -- and tomorrow's-- state of the art supercomputers, or are indirectly included through crude, semi-empirical formulas. Computer calculations and theory on `simplified' mathematical models (i.e. the 3D Boussinesq equations for rotating and stratified flow) of relevance to weather and climate modeling, have shown that these small scales effects can be very significant and contrary to the semi-empirical formulas. A third project aims to develop and test numerical methods that can efficiently deal with multiscale problems in quantum and classical mechanics. The study of these problems is central to many areas of mathematical physics and modern technology (e.g. Nanoscience, plasmas, micro-electro-mechanical-systems [MEMS],...). In recent years we have made significant progress in devising robust and efficient numerical methods to compute multivalued solutions that arise in quantum mechanics and geometric optics. In this proposal that work will be extended to compute solutions with interfaces that couple classical and quantum regimes. The goal is to provide a semiclassical approach that is slightly more expensive than a classical approach but much less expensive than a quantum simulation based on solving directly the Schrodinger equation. One particularly important application is the nano-scale quantum dots that are a standard product of modern semiconductor manufacturing procedures. The fourth project continues the study of recurrent unstable coherent states that have been discovered in the flow of simple fluids such as air or water flowing in pipes, channels or over airplane wings, around boats, cars or other vessels. Such flows are typically in a complex `turbulent' state characterized by apparently random eddy motions, but the newly discovered coherent states (i.e. structured and well-organized) capture many key features and characteristics of turbulent flows. These discoveries suggest that some deep theoretical ideas that have been successful for small systems in `chaos' theory may be applied and extended to much more complex fluid systems. One aim of the project is to provide a catalog of key unstable coherent states that might be considered a `turbulence genome project'.