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

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This award supports the purchase of a mid-size computationalsystem that will support computational mathematics researchby four faculty members and their student research associatesin 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 tostudy how mass is accreted onto (sucked into) black holes. Black holes are massive compact objects that induce such stronggravity that not even light can escape them andoccur in our universe in several forms includingas super-massive black holes at the center of galaxies andat the scale of stars in the form of x-ray binaries.The detailed physics of the accretion process andthe resulting dynamics are not yet fully understood.The goal of this project is the developmentof accurate and efficient computational methods for furtherunderstanding of these processes.A second project is to study the impact of `small scale' physical effects that have not been explicitly included in currentcomputational 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 rotatingand stratified flow) of relevance to weather and climate modeling, haveshown that these small scales effects can be very significantand contrary to the semi-empirical formulas.A third project aims to develop and test numerical methods that canefficiently deal with multiscale problems in quantum and classicalmechanics. The study of these problems is central to many areas ofmathematical physics and modern technology (e.g. Nanoscience,plasmas, micro-electro-mechanical-systems [MEMS],...). In recentyears we have made significant progress in devising robust andefficient numerical methods to compute multivalued solutions thatarise in quantum mechanics and geometric optics. In this proposalthat work will be extended to compute solutions with interfacesthat 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 coherentstates that have been discovered in the flow of simple fluids suchas 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 havebeen successful for small systems in `chaos' theory may be appliedand extended to much more complex fluid systems. One aim of the projectis to provide a catalog of key unstable coherent states that might beconsidered a `turbulence genome project'.