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Introduction to Computational Science

Explore the tripartite approach of Computational Science through Chemistry, Physics, Biology, and more. Learn about algorithms, architecture, and tools used to solve intricate scientific problems. Discover the importance of Computational Science in addressing Grand Challenges of the 21st Century. Engage in hands-on activities like Surface Water Runoff Model and Fire! simulation.

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Introduction to Computational Science

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  1. Robert R. Gotwals, Jr. Kirstin Riesbeck UNC-Chapel Hill/ NSF REU Fellow The Shodor Education Foundation, Inc. O3 creation ~ O Molecules Ozone Guess ~ O3 per cl radical ~ normal decay Post 1994 message impact of cl depletion Introduction to Computational Science PRESENTERS: Ozone

  2. SCIENCE: the study of how nature behaves Observational Science Experimental Science Theoretical Science Computational Science

  3. Computational Science: A Tripartite Approach

  4. Applications • Chemistry: electronic structure determinations • Physics: astrophysics (galaxy simulations) • Biology: population dynamics • Mathematics: fractals • Environmental Science: acid rain deposition models • Linguistics: analysis of language transference • Economics: Adam Smith models • Political Science/History: causative factors in Bosnian War conflict • Medicine: epidemiology, pharmacokinetics models

  5. Algorithms • creating a mathematical representation of the problem -- the "mathematical model" • choosing the appropriate numerical "recipe" to solve the problem • Examples • Linear Least Squares: for fitting data to a line • Newton's Method: for finding roots of an equation • Euler's Method: for solving integrals • Runge-Kutta Methods: for solving integrals • Cramer's Rule: for solving systems of equations

  6. Architecture • choosing the appropriate "platform" to solve the problem • single-user personal computer (IBM PC, Macintosh) • scientific workstation (SGI Indy 2) • workstation clusters • supercomputer (Cray T3D MPP system) • scalar/serial processors • vector processors • parallel processors • vector/parallel machines

  7. Computational Science Tools • Types of Tools for solving computational problems • Programming: Fortran, BASIC, C, Pascal • Spreadsheets • Equation-Solvers: Mathematica, TKSolver, Maple, MathCAD • Dynamic Modelers: STELLA II, VenSim • Scientific Visualization Programs: NCSA Scientific Visualization Tools, Spyglass, AVS, Wavefront • Discipline-Specific Software: GAUSSIAN94, MOPAC, UAM, PAVE, etc.

  8. BUT!! Why do we need this? • solve hard problems that are: • too tedious to solve problems using calculators • too dangerous to try to solve problems in the laboratory • too expensive to try to solve problems in the laboratory • only solvable using mathematical techniques or models • establish a true marriage between mathematics, computing and science • Who cares?

  9. Who Cares? • 21st Century Science: The Grand Challenges • Molecular and structural biology • Cosmology • Environmental Hydrology • Warfare and Survivability • Chemical Engineering and electronic structure • Weather prediction • Nanomaterials • Solve any PART of one of these problems, and ….

  10. Hand-on Activities

  11. Surface Water Runoff Model • http://www.shodor.org/master/environmental/water/runoff • Exploration: • What is the difference in runoff between: • Woods • Woods with Grass • Open Urban Area • Residential • Parking Lots • Run conditions • Hydrologic Soil Group B • Good hydrologic conditions • 25-year, 24-hour storm

  12. Surface Water Runoff Results

  13. Fire! • http://www.shodor.org/interactivate/activities/firealt • Exploration • Run fire on different size forests • Run fire with different burn speeds • Run fire after changing configuration probabilities

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