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Volumn 31, Issue 2, 2008, Pages 1363-1378

What makes molecular dynamics work?

Author keywords

Divergence free; Ergodic; Molecular dynamics; Perturbation; Statistical mechanics; Symplectic integrator

Indexed keywords

COMPUTATION THEORY; EQUATIONS OF MOTION; ERRORS; STATISTICAL MECHANICS;

EID: 67649565653     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070683660     Document Type: Article
Times cited : (22)

References (35)
  • 1
    • 21344491735 scopus 로고
    • On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms
    • G. BENETTIN AND A. GLORGILLI, On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms. J. Statist. Phys., 74 (1994). pp. 1117-1143.
    • (1994) J. Statist. Phys , vol.74 , pp. 1117-1143
    • BENETTIN, G.1    GLORGILLI, A.2
  • 2
    • 67649483892 scopus 로고    scopus 로고
    • S. BOND, Numerical Methods for Extended Hamiltonian Systems with Applications in Statistical Mechanics. Ph.D. thesis. Dept. of Mathematics. University of Kansas. Lawrence. KS. 2000.
    • S. BOND, Numerical Methods for Extended Hamiltonian Systems with Applications in Statistical Mechanics. Ph.D. thesis. Dept. of Mathematics. University of Kansas. Lawrence. KS. 2000.
  • 4
    • 35348893389 scopus 로고    scopus 로고
    • Molecular dynamics and the accuracy of numerically computed averages
    • S. D. BOND AND B. J. lEIMKUHLER, Molecular dynamics and the accuracy of numerically computed averages. Acta Numer., 16 (2007). pp. 1-65.
    • (2007) Acta Numer , vol.16 , pp. 1-65
    • BOND, S.D.1    lEIMKUHLER, B.J.2
  • 5
    • 0033483891 scopus 로고    scopus 로고
    • J. M. BORWEIN AND R. M. CORLESS, Emerging tools for experimental mathematics.Amer. Math. Monthly. 106 (1999). pp. 889-909.
    • J. M. BORWEIN AND R. M. CORLESS, Emerging tools for experimental mathematics.Amer. Math. Monthly. 106 (1999). pp. 889-909.
  • 6
    • 33748374124 scopus 로고    scopus 로고
    • D. CHANDLER, Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys., 68 (1978). pp. 2 959-2970.
    • D. CHANDLER, Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys., 68 (1978). pp. 2 959-2970.
  • 7
    • 0000094135 scopus 로고    scopus 로고
    • Collective motion artifacts arising in long-duration molecular dynamics simulations
    • S. W. CHIU, M. CLARK, S. SUBRAMANIAM, AND E. JAK OBSSON, Collective motion artifacts arising in long-duration molecular dynamics simulations. J. Comput. Chem., 21 (2000). pp. 121-131.
    • (2000) J. Comput. Chem , vol.21 , pp. 121-131
    • CHIU, S.W.1    CLARK, M.2    SUBRAMANIAM, S.3    JAK OBSSON, E.4
  • 8
    • 34247338100 scopus 로고    scopus 로고
    • Automatic discovery of metastable states for the construction of Markov models of macromolecular conforma- tional dynamics
    • 17 pp
    • J. D. CHODERA, N. SINGHAL, V. S. PANDE, K. A. DILL, AND W. C. SWOPE, Automatic discovery of metastable states for the construction of Markov models of macromolecular conforma- tional dynamics. J. Chem. Phys., 126 (2007). p. 155101 (17 pp.).
    • (2007) J. Chem. Phys , vol.126 , pp. 155101
    • CHODERA, J.D.1    SINGHAL, N.2    PANDE, V.S.3    DILL, K.A.4    SWOPE, W.C.5
  • 9
    • 4244210758 scopus 로고
    • On the effects of an uncertainty on the evolution law in dynamical systems
    • A. CRISANTI, M. FALCIONI, AND A. VULPIANI, On the effects of an uncertainty on the evolution law in dynamical systems. Phys. A. 160 (1989). pp. 482-502.
    • (1989) Phys. A , vol.160 , pp. 482-502
    • CRISANTI, A.1    FALCIONI, M.2    VULPIANI, A.3
  • 10
    • 84869299858 scopus 로고    scopus 로고
    • P. DEUFLHARD, M. DELLNITZ, O. JUNGE, AND Ch. SCHÜT TE. Computation of essential molecular dynamics by subdivision techniques I: Basic concepts. in Computational Molecular Dynamics: Challenges. Methods. Ideas. Lect. Notes Comput. Sci. Eng. 4. P. Deuflhard. J. Hermans. B. Leimkuhler. A. Mark. S. Reich. and R. D. Skeel. eds., Springer-Verlag. Berlin. 1998. pp. 91-108.
    • P. DEUFLHARD, M. DELLNITZ, O. JUNGE, AND Ch. SCHÜT TE. Computation of essential molecular dynamics by subdivision techniques I: Basic concepts. in Computational Molecular Dynamics: Challenges. Methods. Ideas. Lect. Notes Comput. Sci. Eng. 4. P. Deuflhard. J. Hermans. B. Leimkuhler. A. Mark. S. Reich. and R. D. Skeel. eds., Springer-Verlag. Berlin. 1998. pp. 91-108.
  • 11
    • 18144377695 scopus 로고    scopus 로고
    • Monitoring energy drift with shadow Hamiltonians
    • R. D. ENGLE, R. D. SKEEL, AND M. DREES, Monitoring energy drift with shadow Hamiltonians. J. Comput. Phys., 206 (2005). pp. 432-452.
    • (2005) J. Comput. Phys , vol.206 , pp. 432-452
    • ENGLE, R.D.1    SKEEL, R.D.2    DREES, M.3
  • 12
    • 18244388472 scopus 로고    scopus 로고
    • Energy conservation with non-symplectic methods: Examples and counter-examples
    • E. FAOU, E. HAIRER, and T.-L. PHAM, Energy conservation with non-symplectic methods: Examples and counter-examples. BIT. 44 (2004). pp. 699-709.
    • (2004) BIT , vol.44 , pp. 699-709
    • FAOU, E.1    HAIRER, E.2    PHAM, T.-L.3
  • 14
    • 0031505057 scopus 로고    scopus 로고
    • The life-span of backward error analysis for numerical integrators
    • E. HAIRER AND C. LUBICH, The life-span of backward error analysis for numerical integrators. Numer. Math., 76 (1997). pp. 441-462.
    • (1997) Numer. Math , vol.76 , pp. 441-462
    • HAIRER, E.1    LUBICH, C.2
  • 17
    • 0001430231 scopus 로고    scopus 로고
    • The flying ice cube-velocity rescaling in molecular dynamics leads to violation of energy e quipartition
    • S. C. HARVEY, R. K. Z. TAN, AND T. E. cHEATHAM, The flying ice cube-velocity rescaling in molecular dynamics leads to violation of energy e quipartition. J. Comput. Chem., 19 (1998). pp. 726-740.
    • (1998) J. Comput. Chem , vol.19 , pp. 726-740
    • HARVEY, S.C.1    TAN, R.K.Z.2    cHEATHAM, T.E.3
  • 18
    • 0037422921 scopus 로고    scopus 로고
    • Shadowing high-dimensional Hamiltonian systems: The gravitational n-body problem
    • 4 pp
    • W. HAYES, Shadowing high-dimensional Hamiltonian systems: The gravitational n-body problem. Phys. Rev. Lett., 90 (2003). p. 54104 (4 pp.).
    • (2003) Phys. Rev. Lett , vol.90 , pp. 54104
    • HAYES, W.1
  • 19
    • 67649460138 scopus 로고    scopus 로고
    • A. R. LEACH, Molecular Modelling: Principles and Applications. 2nd ed., Prentice Hall. En- glewood Cliffs. NJ. 2001.
    • A. R. LEACH, Molecular Modelling: Principles and Applications. 2nd ed., Prentice Hall. En- glewood Cliffs. NJ. 2001.
  • 21
    • 0001444647 scopus 로고    scopus 로고
    • Backward error analysis for numerical integrators
    • S. REICH, Backward error analysis for numerical integrators. SIAM J. Numer. Anal., 36 (1999). pp. 1549-1570.
    • (1999) SIAM J. Numer. Anal , vol.36 , pp. 1549-1570
    • REICH, S.1
  • 22
    • 67649457546 scopus 로고    scopus 로고
    • J. M. SANZ-SERNA, Numerical ordinary differential equations vs. dynamical systems.in The Dynamics of Numerics and the Numerics of Dynamics. D. S. Broomhead and A. Iserles. eds., Clarendon Press. Oxford. 1992. pp. 81-106.
    • J. M. SANZ-SERNA, Numerical ordinary differential equations vs. dynamical systems.in The Dynamics of Numerics and the Numerics of Dynamics. D. S. Broomhead and A. Iserles. eds., Clarendon Press. Oxford. 1992. pp. 81-106.
  • 23
    • 67649501862 scopus 로고    scopus 로고
    • T. SCHLICK, Some failures and successes of long-timestep approaches to biomolecular simulations. in Algorithms for Macromolecular Modelling. Lect. Notes Comput. Sci. Eng. 4. P. Deuflhard. J. Hermans. B. Leimkuhler. A. Mark. S. Reich. and R. D. Skeel. eds., Springer-Verlag. Berlin. 1998. pp. 221-250.
    • T. SCHLICK, Some failures and successes of long-timestep approaches to biomolecular simulations. in Algorithms for Macromolecular Modelling. Lect. Notes Comput. Sci. Eng. 4. P. Deuflhard. J. Hermans. B. Leimkuhler. A. Mark. S. Reich. and R. D. Skeel. eds., Springer-Verlag. Berlin. 1998. pp. 221-250.
  • 25
    • 0036345029 scopus 로고    scopus 로고
    • Practical construction of modified Hamiltonians.SIAM
    • R. D. SKEEL AND D. J. HARDY, Practical construction of modified Hamiltonians.SIAM J. Sci. Comput., 23 (2001). pp. 1172-1188.
    • (2001) J. Sci. Comput , vol.23 , pp. 1172-1188
    • SKEEL, R.D.1    HARDY, D.J.2
  • 26
    • 36749110571 scopus 로고
    • A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters
    • W. C. SWOPE, H. C. ANDERSEN, P. H. BERENS, AND K. R. WILSON, A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys., 76 (1982). pp. 637-649.
    • (1982) J. Chem. Phys , vol.76 , pp. 637-649
    • SWOPE, W.C.1    ANDERSEN, H.C.2    BERENS, P.H.3    WILSON, K.R.4
  • 27
    • 0003105059 scopus 로고
    • Formal energy of a symplectic scheme for Hamiltonian systems and its applications (I)
    • Y.-F. TANG, Formal energy of a symplectic scheme for Hamiltonian systems and its applications (I). Comput. Math. Appl., 27 (1994). pp. 31-39.
    • (1994) Comput. Math. Appl , vol.27 , pp. 31-39
    • TANG, Y.-F.1
  • 28
    • 0035933983 scopus 로고    scopus 로고
    • Non-Hamiltonian molecular dynamics: Generalizing Hamiltonian phase space principles to non-Hamiltonian systems
    • M. E. TUCKERMAN, Y. LIU, G. CLCCOTTI, AND G. J. MA RTYNA, Non-Hamiltonian molecular dynamics: Generalizing Hamiltonian phase space principles to non-Hamiltonian systems. J. Chem. Phys., 115 (2001). pp. 1678-1702.
    • (2001) J. Chem. Phys , vol.115 , pp. 1678-1702
    • TUCKERMAN, M.E.1    LIU, Y.2    CLCCOTTI, G.3    MA RTYNA, G.J.4
  • 29
    • 19844381193 scopus 로고    scopus 로고
    • P. F. TUPPER, Ergodicity and the numerical simulation of Hamiltonian systems.SIAM J.Appl. Dyn. Sys., 4 (2005). pp. 563-587.
    • P. F. TUPPER, Ergodicity and the numerical simulation of Hamiltonian systems.SIAM J.Appl. Dyn. Sys., 4 (2005). pp. 563-587.
  • 30
    • 25844453508 scopus 로고    scopus 로고
    • A test problem for molecular dynamics integrators
    • P. F. TUPPER, A test problem for molecular dynamics integrators. IMA J. Numer. Anal., 25 (2005). pp. 286-309.
    • (2005) IMA J. Numer. Anal , vol.25 , pp. 286-309
    • TUPPER, P.F.1
  • 31
    • 34248151420 scopus 로고    scopus 로고
    • Computing statistics for Hamiltonian systems: A case study
    • P. F. TUPPER, Computing statistics for Hamiltonian systems: A case study. J. Comput. Appl. Math., 205 (2007). pp. 826-834.
    • (2007) J. Comput. Appl. Math , vol.205 , pp. 826-834
    • TUPPER, P.F.1
  • 32
    • 67649469907 scopus 로고    scopus 로고
    • The relation between approximation in distribution and shadowing in molecular dynamics
    • submitted
    • P. F. TUPPER, The relation between approximation in distribution and shadowing in molecular dynamics. SIAM J. Appl. Dyn. Syst., submitted.
    • SIAM J. Appl. Dyn. Syst
    • TUPPER, P.F.1
  • 33
    • 0002722683 scopus 로고
    • Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime
    • A. F. VOTER AND J. D. DOLL, Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime. J. Chem. Phys., 82 (1985). pp. 80-92.
    • (1985) J. Chem. Phys , vol.82 , pp. 80-92
    • VOTER, A.F.1    DOLL, J.D.2
  • 34
    • 39749147672 scopus 로고    scopus 로고
    • Determining the density ofstates for classical statistical models: A random walk algorithm to produce a flat histogram
    • 16 pages
    • F. WANG AND D. P. LANDAU, Determining the density ofstates for classical statistical models: A random walk algorithm to produce a flat histogram. Phys. Rev. E. 64 (2001). p. 056101 (16 pages).
    • (2001) Phys. Rev. E , vol.64 , pp. 056101
    • WANG, F.1    LANDAU, D.P.2
  • 35
    • 67649481844 scopus 로고    scopus 로고
    • J. WISDOM, M. HOLMAN, AND J. TOUMA, Symplectic correctors. in Integration Algorithms and ClassicalMechanics. J.E.Marsden. G.W.Patrick.and W. F. Shadwick. eds.,Fields Inst. Commun. 10. American Mathematical Society. Providence. RI. 1996. pp. 217-244.
    • J. WISDOM, M. HOLMAN, AND J. TOUMA, Symplectic correctors. in Integration Algorithms and ClassicalMechanics. J.E.Marsden. G.W.Patrick.and W. F. Shadwick. eds.,Fields Inst. Commun. 10. American Mathematical Society. Providence. RI. 1996. pp. 217-244.


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