keyes - Office of Science & Technology Policy Briefing 4...

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Computational and Applied Mathematics in Scientific Discovery David Keyes Columbia University 4 May 2004
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OSTP Briefing, 4 May 2004 Presentation plan Emergence of simulation a third modality for scientific and technological research Applications drivers and trends in simulation infrastructure outstanding opportunities Hurdles to simulation role of applied and computational mathematics Success factors and recommendations current pathfinding U.S. programs
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OSTP Briefing, 4 May 2004 Three pillars of scientific understanding Theory Experiment Simulation “theoretical experiments” Computational simulation : “a means of scientific discovery that employs a computer system to simulate a physical system according to laws derived from theory and experiment”
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OSTP Briefing, 4 May 2004 Example: turbulent combustion Simulation models and methods: Acoustically filtered hydrodynamics: 10 2 × speedup Cartesian adaptive mesh refinement: 10 4 speedup Message-passing SIMD parallelism on 2048 procs Reaction zone location a delicate balance of fluxes of: species, momentum, internal energy Directly relevant to: engines, turbines, furnaces, incinerators (energy efficiency, pollution mitigation) Component model of other computational apps: firespread, stellar dynamics, chemical processing This simulation sits at the pinnacle of numerous prior achievements in experiment, theory , applied mathematics, and computer science
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OSTP Briefing, 4 May 2004 Theory, experiment and simulation check, spur and enrich each other! Images c/o R. Cheng (left), J. Bell (right) Instantaneous flame front imaged by density of inert marker Instantaneous flame front imaged by fuel concentration
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OSTP Briefing, 4 May 2004 What would we do with 100-1000x more? Example: probe the structure of particles Constraints on the Standard Model parameters ρ and η . For the Standard Model to be correct, they must be restricted to the region of overlap of the solidly colored bands. The figure on the left shows the constraints as they exist today. The figure on the right shows the constraints as they would exist with no improvement in the experimental errors, but with lattice gauge theory uncertainties reduced to 3%.
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OSTP Briefing, 4 May 2004 What would we do with 100-1000x more? Example:
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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keyes - Office of Science & Technology Policy Briefing 4...

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