Free Access
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
Page(s) 351 - 389
Published online 16 June 2007
  1. E. Akhmatskaya and S. Reich, The targetted shadowing hybrid Monte Carlo (TSHMC) method, in New Algorithms for Macromolecular Simulation, Lecture Notes in Computational Science and Engineering 49, B. Leimkuhler, C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schuette and R. Skeel Eds., Springer Verlag, Berlin and New York (2006) 145–158. [Google Scholar]
  2. M.P. Allen and D.J. Tildesley, Computer simulation of liquids. Oxford Science Publications (1987). [Google Scholar]
  3. H.C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature J. Chem. Phys. 72 (1980) 2384–2393. [Google Scholar]
  4. E. Barth, B.J. Leimkuhler, and C.R. Sweet, Approach to thermal equilibrium in biomolecular simulation. Proceedings of AM3-2004 conference, available at the URL [Google Scholar]
  5. S.D. Bond, B.J. Leimkuhler, and B.B. Laird, The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114–134. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Brünger, C.B. Brooks, and M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett. 105 (1983) 495–500. [Google Scholar]
  7. E. Cancès, F. Castella, P. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici, High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations. J. Chem. Phys. 121 (2004) 10346–10355. [CrossRef] [PubMed] [Google Scholar]
  8. E. Cancès, F. Castella, P. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici, Long-time averaging for integrable Hamiltonian dynamics. Numer. Math. 100 (2005) 211–232. [CrossRef] [MathSciNet] [Google Scholar]
  9. E.A. Carter, G. Ciccotti, J.T. Hynes and R. Kapral, Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 156 (1989) 472–477. [CrossRef] [Google Scholar]
  10. Y. Chen, Another look at Rejection sampling through Importance sampling. Discussion papers 04-30, Institute of Statistics and Decision Science, Duke University (2004). [Google Scholar]
  11. G. Ciccotti, R. Kapral and E. Vanden-Eijnden, Blue Moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics. Chem. Phys. Chem. 6 (2005) 1809–1814. [Google Scholar]
  12. G. Ciccotti, T. Lelièvre and E. Vanden-Eijnden, Projection of diffusions on submanifolds: Application to mean force computation. CERMICS preprint 309 (2006). [Google Scholar]
  13. S. Duane, A.D. Kennedy, B. Pendleton and D. Roweth, Hybrid Monte Carlo. Phys. Letters B. 195 (1987) 216–222. [NASA ADS] [CrossRef] [Google Scholar]
  14. M. Duflo, Random iterative models. Springer, Berlin, New York (1997). [Google Scholar]
  15. W. E, W. Ren and E. Vanden-Eijnden, Finite temperature string method for the study of rare events. J. Phys. Chem. B 109 (2005) 6688–6693. [CrossRef] [PubMed] [Google Scholar]
  16. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in advanced mathematics. CRC Press, Chapman and Hall (1991). [Google Scholar]
  17. D. Frenkel and B. Smit, Understanding Molecular Simulation, From Algorithms to Applications, 2nd edn. Academic Press (2002). [Google Scholar]
  18. G. Grimett and D. Stirzaker, Probability and Random Processes. Oxford University Press (2001). [Google Scholar]
  19. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, Structure-Preserving Algorithms For Ordinary Differential Equations, Springer Series in Computational Mathematics 31, 2nd edn. Springer-Verlag, Berlin (2006). [Google Scholar]
  20. S. Hampton, P. Brenner, A. Wenger, S. Chatterjee and J.A. Izaguirre, Biomolecular Sampling: Algorithms, Test Molecules, and Metrics, in New Algorithms for Macromolecular Simulation, Lecture Notes in Computational Science and Engineering 49, B. Leimkuhler, C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schuette and R. Skeel Eds., Springer Verlag, Berlin and New York (2006) 103–123. [Google Scholar]
  21. R.Z. Has'minskii, Stochastic Stability of Differential Equations. Sijthoff and Noordhoff (1980). [Google Scholar]
  22. W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970) 97–109. [CrossRef] [MathSciNet] [Google Scholar]
  23. F. Hérau and F. Nier, Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential. Arch. Rational Mech. Anal. 171 (2004) 151–218. [CrossRef] [Google Scholar]
  24. W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695–1697. [CrossRef] [PubMed] [Google Scholar]
  25. F.C. Hoppensteadt, M. Rahman and B.D. Welfert, Formula -Central limit theorems for Markov processes with applications to circular processes, preprint version (2003). Available at the URL [Google Scholar]
  26. A.M. Horowitz, A generalized guided Monte Carlo algorithms. Phys. Lett. B 268 (1991) 247–252. [CrossRef] [Google Scholar]
  27. J.A. Izaguirre and S.S. Hampton, Shadow Hybrid Monte Carlo: an efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581–604. [CrossRef] [Google Scholar]
  28. A.D. Kennedy and B. Pendleton, Cost of the generalised hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456–510. [CrossRef] [Google Scholar]
  29. A. Laio and M. Parrinello, Escaping free energy minima. Proc. Natl. Acad. Sci. USA 99 (2002) 12562–12566. [CrossRef] [PubMed] [Google Scholar]
  30. B. Lapeyre, E. Pardoux and R. Sentis, Méthodes de Monte Carlo pour les équations de transport et de diffusion, Mathématiques et applications 29, Springer (1998); B. Lapeyre, E. Pardoux and R. Sentis, translated by A. Craig and F. Craig, Introduction to Monte-Carlo methods for transport and diffusion equations. Oxford University Press (2003). [Google Scholar]
  31. F. Legoll, Molecular and Multiscale Methods for the Numerical Simulation of Materials. Ph.D. thesis, University of Paris VI, France (2004). [Google Scholar]
  32. F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Arch. Rat. Mech. Anal. 184 (2007) 449–463. [CrossRef] [MathSciNet] [Google Scholar]
  33. B.J. Leimkuhler and S. Reich, Simulating Hamiltonian dynamics, Cambridge monographs on applied and computational mathematics 14. Cambridge University Press (2005). [Google Scholar]
  34. B.J. Leimkuhler and C.R. Sweet, A Hamiltonian formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst. 4 (2005) 187–216. [CrossRef] [MathSciNet] [Google Scholar]
  35. J.S. Liu, Monte Carlo strategies in Scientific Computing. Springer Series in Statistics (2001). [Google Scholar]
  36. P.B. Mackenze, An improved hybrid Monte Carlo. Phys. Lett. B. 226 (1989) 369–371. [CrossRef] [Google Scholar]
  37. X. Mao, Stochastic differential equations and applications. Horwood, Chichester (1997). [Google Scholar]
  38. J.E. Marsden and M. West, Discrete mechanics and variational integrators. Acta Numer. 10 (2001) 357–514. [CrossRef] [MathSciNet] [Google Scholar]
  39. M.G. Martin and J.I. Siepmann, Transferable potentials for phase equilibria. I. United-atom description of n-alkanes. J. Phys. Chem. 102 (1998) 2569–2577. [Google Scholar]
  40. G.J. Martyna, M.L. Klein and M.E. Tuckerman, Nosé-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97 (1992) 2635–2643. [CrossRef] [Google Scholar]
  41. G.J. Martyna, M.E. Tuckerman, D.J. Tobias and M.L. Klein, Explicit reversible integrators for extended systems dynamics. Mol. Phys. 87 (1996) 1117–1157. [CrossRef] [Google Scholar]
  42. J.C. Mattingly, A.M. Stuart and D.J. Higham, Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise. Stoch. Proc. Appl. 101 (2002) 185–232. [CrossRef] [MathSciNet] [Google Scholar]
  43. K.L. Mengersen and R.L. Tweedie, Rates of convergence in the Hastings-Metropolis algorithm. Ann. Statist. 24 (1996) 101–121. [CrossRef] [MathSciNet] [Google Scholar]
  44. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equations of state calculations by fast computing machines. J. Chem. Phys. 21 (1953) 1087–1091. [NASA ADS] [CrossRef] [Google Scholar]
  45. S.P. Meyn and R.L. Tweedie, Stability of Markovian processes. II. Continuous-time processes and sampled chains. Adv. Appl. Probab. 24 (1993) 487–517. [CrossRef] [MathSciNet] [Google Scholar]
  46. S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability. Springer (1993). [Google Scholar]
  47. G.N. Milstein and M.V. Tretyakov, Quasi-symplectic methods for Langevin-type equations. IMA J. Numer. Anal. 23 (2003) 593–626. [CrossRef] [MathSciNet] [Google Scholar]
  48. B. Mishra and T. Schlick, The notion of error in Langevin dynamics: I. Linear analysis. J. Chem. Phys. 105 (1996) 299–318. [CrossRef] [Google Scholar]
  49. R.M. Neal, An improved acceptance procedure for the hybrid Monte-Carlo algorithm. J. Comput. Phys. 111 (1994) 194–203. [CrossRef] [MathSciNet] [Google Scholar]
  50. N. Niederreiter, Random Number Generation and Quasi Monte-Carlo Methods. Society for Industrial and Applied Mathematics (1992). [Google Scholar]
  51. S. Nosé, A Molecular Dynamics method for simulations in the canonical ensemble, Mol. Phys. 52 (1984) 255–268. [Google Scholar]
  52. S. Nosé, A unified formulation of the constant temperature Molecular Dynamics method, J. Chem. Phys. 81 (1985) 511–519. [Google Scholar]
  53. G. Pagès, Sur quelques algorithmes récursifs pour les probabilités numériques. ESAIM: PS 5 (2001) 141–170. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  54. D.C. Rapaport, The Art of Molecular Dynamics Simulations. Cambridge University Press (1995). [Google Scholar]
  55. S. Reich, Backward error analysis for numerical integrators. SIAM J. Numer. Anal. 36 (1999) 1549–1570. [CrossRef] [MathSciNet] [Google Scholar]
  56. G.O. Roberts and J.S. Rosenthal, Optimal scaling of discrete approximations to Langevin diffusions. J. Roy. Stat. Soc. B 60 (1998) 255–268. [CrossRef] [Google Scholar]
  57. G.O. Roberts and R.L. Tweedie, Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli 2 (1996) 341–364. [CrossRef] [MathSciNet] [Google Scholar]
  58. G.O. Roberts and R.L. Tweedie, Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 (1996) 95–110. [CrossRef] [MathSciNet] [Google Scholar]
  59. L.C.G. Rogers, Smooth transition densities for one-dimensional probabilities. Bull. London Math. Soc 17 (1985) 157–161. [CrossRef] [MathSciNet] [Google Scholar]
  60. J.P. Ryckaert and A. Bellemans, Molecular dynamics of liquid alkanes. Faraday Discuss. 66 (1978) 95–106. [CrossRef] [Google Scholar]
  61. A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès and M. Caffarel, An efficient sampling algorithm for Variational Monte Carlo. J. Chem. Phys. 125 (2006) 114105. [CrossRef] [PubMed] [Google Scholar]
  62. T. Schlick, Molecular Modeling and Simulation. Springer (2002). [Google Scholar]
  63. C. Schütte, Conformational dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules. Habilitation Thesis, Free University Berlin (1999). [Google Scholar]
  64. C. Schütte and W. Huisinga, Biomolecular conformations can be identified as metastable sets of molecular dynamics, in Handbook of Numerical Analysis (Special volume on computational chemistry), Vol. X, P.G. Ciarlet and C. Le Bris Eds., Elsevier (2003) 699–744. [Google Scholar]
  65. C. Schütte, A. Fischer, W. Huisinga and P. Deuflhard, A direct approach to conformational dynamics based on Hybrid Monte-Carlo. J. Comp. Phys. 151 (1999) 146–168. [CrossRef] [Google Scholar]
  66. T. Shardlow, Splitting for dissipative particle dynamics. SIAM J. Sci. Comput. 24 (2003) 1267–1282. [CrossRef] [MathSciNet] [Google Scholar]
  67. R.D. Skeel, in The graduate student's guide to numerical analysis, Springer Series in Computational Mathematics, M. Ainsworth, J. Levesley and M. Marletta Eds., Springer-Verlag, Berlin (1999) 119–176. [Google Scholar]
  68. R.D. Skeel and J.A. Izaguirre, An impulse integrator for Langevin dynamics. Mol. Phys. 100 (2002) 3885–3891. [CrossRef] [Google Scholar]
  69. M.R. Sorensen and A.F. Voter, Temperature accelerated dynamics for simulation of infrequent events. J. Chem. Phys. 112 (2000) 9599–9606. [CrossRef] [Google Scholar]
  70. G. Stoltz, Quelques méthodes mathématiques pour la simulation moléculaire et multiéchelle. Ph.D. Thesis (in preparation). [Google Scholar]
  71. C.R. Sweet, Hamiltonian Thermostatting Techniques for Molecular Dynamics Simulation. Ph.D. Thesis, University of Leicester (2004). [Google Scholar]
  72. D. Talay, Second-order discretization schemes of stochastic differential systems for the computation of the invariant law. Stoch. Stoch. Rep. 29 (1990) 13–36. [Google Scholar]
  73. D. Talay, Approximation of invariant measures of nonlinear Hamiltonian and dissipative stochastic differential equations, in Progress in Stochastic Structural Dynamics, R. Bouc and C. Soize Eds., Publication du L.M.A.-C.N.R.S. 152 (1999) 139–169. [Google Scholar]
  74. D. Talay, Stochastic Hamiltonian dissipative systems: exponential convergence to the invariant measure, and discretization by the implicit Euler scheme. Markov Proc. Rel. Fields 8 (2002) 163–198. [Google Scholar]
  75. M.E. Tuckerman and G.J. Martyna, Understanding modern molecular dynamics: Techniques and applications. J. Phys. Chem. B 104 (2000) 159–178. [CrossRef] [Google Scholar]
  76. L. Verlet, Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159 (1967) 98–103. [CrossRef] [Google Scholar]
  77. A.F. Voter, A method for accelerating the molecular dynamics simulation of infrequent events. J. Chem. Phys. 106 (1997) 4665–4677. [CrossRef] [Google Scholar]
  78. A.F. Voter, Parallel replica method for dynamics of infrequent events. Phys. Rev. B 57 (1998) 13985–13988. [CrossRef] [Google Scholar]
  79. W. Wang and R.D. Skeel, Analysis of a few numerical integration methods for the Langevin equation. Mol. Phys. 101 (2003) 2149–2156. [CrossRef] [Google Scholar]
  80. Z. Zhu, M.E. Tuckerman, S.O. Samuelson and G.J. Martyna, Using novel variable transformations to enhance conformational sampling in molecular dynamics. Phys. Rev. Lett. 88 (2002) 100201. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you