Extensible Simulation of Planets and Comets Natalie Wiser-Orozco Dr. Keith Evan Schubert Dr. Ernesto...
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Transcript of Extensible Simulation of Planets and Comets Natalie Wiser-Orozco Dr. Keith Evan Schubert Dr. Ernesto...
Extensible Simulation of Planets and Comets
Natalie Wiser-OrozcoDr. Keith Evan Schubert
Dr. Ernesto GomezDr. Richard J. Botting
July 22, 2009
Exoplanet Discovery
● Dr. Paul Kalas (UC Berkeley) confirms that Fomalhaut b orbits it's parent star
1.
● Increased frequency of discoveries of this nature.
● Questions that arise as a result.
Movement of Objects In Space
● Carl Sundman 3-body
● Qiu-Dong Wang n-body
● Solar system stability
Simulation of Objects In Space
● Computational power
● Existing simulators focus on ● Pre-determined sets of bodies● Specific algorithm or method
● Extensible Simulator ● Arbitrary number of bodies● Choose different numerical methods and
gravitational functions.
Overview Of The Extensible Simulator
● Numerical Methods and Gravitational Functions
● Project Structure and Management
● Visualizations
● Cameras
● Bodies
● Heuristics
● Results and Future Work
Numerical Methods
● Taylor Series – derivatives of original function
● Runge-Kutta – finite difference approximations
● Extrapolation – very accurate, inefficient
● Multistep – needs help of a single-step method
● Multivalue – easy to change step size
Gravitational Solutions
● Law of Universal Gravitation (Newton)● General Relativity (Einstein)● Quantum Gravity (String Theory, M Theory)● Solar Wind● Different classes of numerical techniques
Particle-Particle Particle-Mesh Particle-Particle/Particle-Mesh (P3M) Particle-Multi-Mesh(PM2)
Simulation Flexibility
• No one technique handles all
• Try different techniques on the same data
• Extensible Simulator allows for any
technique
• Limited only by what is implemented,
therefore limitless.
Project Management
● Fashioned after well known Integrated Development Environments (IDEs)• Projects• Body Configuration
Files
Project Functions
● Project Functions Create/Edit New Project
Add/Edit Body Configuration Files
Choose Gravitational Function/Numerical
Method
Calculate / Simulate
Simulation Screen-shots
Visualization and Heuristics
● Application Programming Interface
● Cameras
● Bodies
● Scene Navigation
● Heuristics
● Body Scaling
Application Programming Interface
● Base Body and Camera objects
● Body and Camera wrapper objects
● Manager objects
● Work together to help the simulation run smoothly
Scene Navigation
● Built in navigation
● Extensible navigation via
camera implementation
Body Scaling
Results
• Error analysis yielded accuracy to an average of 2 significant digits
• Aim of research:• Extensibility of numerical methods, gravitational
functions, cameras and bodies• Appeal to all levels of knowledge• Convey ideas and discoveries with confident
results
Facilitate Future Research
● Programmatic Video Capture
● Additional Numeric Methods
● Additional Dynamics Equations
● GPGPU Integration
● Other general improvements
References1. Paul Kalas et al. Optical Images of an Exosolar Planet 25 Light-Years from Earth Science (322):1345-1348, November 20082. Michael T. Heath. Scientific Computing, An Introductory Survey. McGraw-Hill, Second Edition, 2002.3. E. Saar I. Suisalu A. Klypin A. Melott, J. Einasto and S. Shandarin. Cluster analysis of the nonlinear evolution of large scale
structure in an axion/gravitino/photino dominated universe. Physical Review Letters, (51):935, 1983.4. Srinivas Aluru. Greengard’s n-body algorithm is not order n. SIAM Journal on Scientific Computing, 17(3), May 1996. 5. A.W. Appel. An efficient program for many- body simulation. SIAM J. Sci. Stat. Comput., (6):85–103, 1985. 6. J. S. Bagla. Cosmological N-Body simulation: Techniques, Scope and Status. Current Science, 88:1088–1100, April 2005.7. J. Barnes. A modified tree code: Don’t laugh; it runs. J. Comput. Phys., (87):161–170, 1990.8. J. Barnes and P. Hut. A hierarchical o(n log n) force-calculation algorithm. Nature, (324):446–449, 1986.9. M. Davis, G. Efstathiou, C. Frenk, and S.D.M. White. The evolution of large-scale structure in a universe dominated by cold dark
matter. ApJ, (292):371–394, 1985.10. D. J. D. Earn and J. A. Sellwood. The Optimal N-Body Method for Stability Studies of Galaxies. The Astrophysical Journal,
451:533–+, October 1995.11. Sergio Gelato, David F. Chernoff, and Ira Wasserman. An adaptive hierarchical particle-mesh code with isolated boundary
conditions. ApJ, May 1997.12. L. Greengard and V. Rokhlin. A fast algorithm for particle simulations. J. Comp. Phys., (73):325–348, 1987. 13. Randall Splinter. A nested grid particle-mesh code for high resolution simulations of gravitational instability in cosmology.
MNRAS, (281), 1996.14. K.F. Sundman. M´emoire sur le probl`eme des trois corps. Acta Math., (36):105–179, 1913.15. Qiu-Dong Wang. The global solution of the n-body problem. Celestial Mechanics and Dynamical Astronomy, 50(1):73–88, 1991.16. M.S. Warren and J.K. Salmon. Astrophysical n-body simulations using hierarchical tree data structures. In Proc. Supercomputing
’92, pages 570– 576, 1992.17. M.S. Warren and J.K. Salmon. A parallel hashed oct-tree n-body algorithm. In Proc. Supercomputing ’93, pages 1–12, 1993.18. Dr. Bernd Wirsing. Supercomputer simulations explain the formation of galaxies and quasars in the universe, June 2005.19. F. Zhao and L. Johnsson. The parallel multipole method on the connection machine. SIAM. J. Sci. Stat. Comput., (12):1420–
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Q & A
• Code is open source and can be found here:
http://code.google.com/p/extensiblesimulationofplanetsandcomets/