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high-performance computing hardware 389✞✝for j = 1, N; { // Initializationfor i = 1, N; {c(i , j ) = 0.0 }for k = 1, N; {for i = 1, N; {c(i,j) = c(i,j) + a(i,k)∗b(k, j) }}}☎Listing 14.11 GOOD f90, BAD Java/C Program; minimum, maximum stride.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 389
16Simulating Matter withMolecular DynamicsProblem: Determine whether a collection of argon molecules placed in a box willform an ordered structure at low temperature.You may have seen in your introductory classes that the ideal gas law can be derived fromfirst principles if gas molecules are treated as billiard balls bouncing off the walls but notinteracting with each other. We want to extend this model so that we can solve for themotion of every molecule in a box interacting with every other molecule via a potential. Wepicked argon because it is an inert element with a closed shell of electrons and so can bemodeled as almost-hard spheres.16.1 Molecular Dynamics (Theory)Molecular dynamics (MD) is a powerful simulation technique for studying the physicaland chemical properties of solids, liquids, amorphous materials, and biologicalmolecules. Even though we know that quantum mechanics is the proper theoryfor molecular interactions, MD uses Newton’s laws as the basis of the techniqueand focuses on bulk properties, which do not depend much on small-r behaviors.In 1985 Car and Parrinello showed how MD can be extended to includequantum mechanics by applying density functional theory to calculate the force[C&P 85]. This technique, known as quantum MD, is an active area of researchbut is beyond the realm of the present chapter. 1 For those with more interestin the subject, there are full texts [A&T 87, Rap 95, Hock 88] on MD and gooddiscussions [G,T&C 06, Thij 99, Fos 96], as well as primers [Erco] and codes,[NAMD, Mold, ALCMD] available on-line.MD’s solution of Newton’s laws is conceptually simple, yet when applied to avery large number of particles becomes the “high school physics problem fromhell.” Some approximations must be made in order not to have to solve the10 23 –10 25 equations of motion describing a realistic sample but instead to limit theproblem to ∼10 6 particles for protein simulations and ∼10 8 particles for materialssimulations. If we have some success, then it is a good bet that the model willimprove if we incorporate more particles or more quantum mechanics, somethingthat becomes easier as computing power continues to increase.1 We thank Satoru S. Kano for pointing this out to us.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 424
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viiicontents2.3 Experimental Error
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solitons & computational fluid dyna
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Appendix A: Glossaryabsolute value
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glossary 557control character — A
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glossary 559log in (on) — To sign
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glossary 561supercomputer — The c
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installing ptplot & java developer
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industrial-strength data visualizat
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Appendix D: An MPI TutorialIn this
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an mpi tutorial 595• Open a shell
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an mpi tutorial 597of all the compu
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an mpi tutorial 599TABLE D.1Some Co
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an mpi tutorial 601jobs to MPI. 2 A
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an mpi tutorial 603✞> cd $HOME Do
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an mpi tutorial 605✞/ / MPIhello
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an mpi tutorial 611D.4 Parallel Tun
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an mpi tutorial 621D.9 List of MPI
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Appendix E: Calling LAPACK from CCa
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calling LAPACK from C 625E.2 Compil
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software on the CD 627JavaCodes Con
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software on the CD 629JavaCodes Con
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software on the CD 631Applets Direc
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software on the CD 633Fortran77code
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Appendix G: Compression via DWTwith
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compression via DWT with thresholdi
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compression via DWT with thresholdi
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BIBLIOGRAPHY[Abar 93] Abarbanel, H.
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ibliography 643[Erco] Ercolessi, F.
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ibliography 645[L&F 93] Landau, R.
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ibliography 647[P&W 91] Pinson, L.
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ibliography 649[VdeV 94] van de Vel
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IndexAbstract data structures,70Abs
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index 653drand, 114Driving force, 2
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index 655Libraries, see Subroutines
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index 657structured, 10for virtual
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