Dynamics Summary

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Dynamics Summary
http//www.math.iastate.edu/wu/math597x.html
http//www.math.iastate.edu/wu/Math597xHW0000

• Math/BCB/ComS597x
• Zhijun Wu
• Department of Mathematics

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Newtons Equations
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Verlet 1967
potential energy
force field
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Argon Molecule
s 3.405 ?, e / kB 119.8 K, mi 36
dalton
? 10-10 m kB 1.38110-23 J / K dalton
1.710-27 kg
s 3.40510-10 m e 165.410-23 J mi
61.210-27 kg
kg m / sec2 newton
Let s be the unit of length, e the unit of
energy. Scale mi to 48es-2 lt the unit of time
2.99010-13 sec.
The unit for mass becomes 8.93710-26 kg.
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Argon Molecule
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Argon Molecule
s 3.40510-10 m e 165.410-23 J t
2.99010-13 sec
Verlet
?t 0.032
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For proteins, the time scale usually is in order
of femto seconds (10-15). Simulation has been
used for study of short-time motions (pico- to
nano- seconds). Simulation of protein folding
is still out of reach with current computing
technology.
Questions Can we reduce the computational cost?
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Potential Energy Functions
O (n2)
O (n)
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The Fast Multipole Method
Greengard 1987 Ph.D. Thesis, Yale
Multipole Expansion O (n log n) Calculations
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Parallel Force Field Calculation
Long Time-Step Simulation
Elber 1996