A Metropolis adjusted Nosé-Hoover thermostat

Benedict Leimkuhler; Sebastian Reich

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 4, page 743-755
  • ISSN: 0764-583X

Abstract

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We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.

How to cite

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Leimkuhler, Benedict, and Reich, Sebastian. "A Metropolis adjusted Nosé-Hoover thermostat." ESAIM: Mathematical Modelling and Numerical Analysis 43.4 (2009): 743-755. <http://eudml.org/doc/250604>.

@article{Leimkuhler2009,
abstract = { We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step. },
author = {Leimkuhler, Benedict, Reich, Sebastian},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Molecular dynamics; thermostats; hybrid Monte Carlo; canonical ensemble.; molecular dynamics; canonical ensemble},
language = {eng},
month = {7},
number = {4},
pages = {743-755},
publisher = {EDP Sciences},
title = {A Metropolis adjusted Nosé-Hoover thermostat},
url = {http://eudml.org/doc/250604},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Leimkuhler, Benedict
AU - Reich, Sebastian
TI - A Metropolis adjusted Nosé-Hoover thermostat
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/7//
PB - EDP Sciences
VL - 43
IS - 4
SP - 743
EP - 755
AB - We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nosé-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.
LA - eng
KW - Molecular dynamics; thermostats; hybrid Monte Carlo; canonical ensemble.; molecular dynamics; canonical ensemble
UR - http://eudml.org/doc/250604
ER -

References

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  1. E. Akhmatskaya and S. Reich, GSHMC: An efficient method for molecular simulations. J. Comput. Phys.227 (2008) 4934–4954.  
  2. E. Akhmatskaya, N. Bou-Rabee and S. Reich, Generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys.227 (2008) 4934–4954.  
  3. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids. Clarendon Press, Oxford (1987)  
  4. 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.  
  5. G. Bussi, D. Donadio and M. Parrinello, Canonical sampling through velocity rescaling. J. Chem. Phys.126 (2007) 014101.  
  6. S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte-Carlo. Phys. Lett. B195 (1987) 216–222.  
  7. D. Frenkel and B. Smit, Understanding Molecular Simulation. Academic Press, New York (1996).  
  8. W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A31 (1985) 1695–1697.  
  9. A.M. Horowitz, A generalized guided Monte-Carlo algorithm. Phys. Lett. B268 (1991) 247–252.  
  10. 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.  
  11. A.D. Kennedy and B. Pendleton, Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B607 (2001) 456–510.  
  12. P. Klein, Pressure and temperature control in molecular dynamics simulations: a unitary approach in discrete time. Modelling Simul. Mater. Sci. Eng.6 (1998) 405–421.  
  13. F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal.184 (2007) 449–463.  
  14. B. Leimkuhler and C. Sweet, A Hamiltonian formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst.4 (2005) 187–216.  
  15. B. Leimkuhler, E. Noorizadeh and F. Theil, A gentle ergodic thermostat for molecular dynamics. J. Stat. Phys. (2009), doi: .  DOI10.1007/s10955-009-9734-0
  16. J.S. Liu, Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001).  
  17. G.J. Martyna, M.L. Klein and M. Tuckerman, Nose-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys.97 (1992) 2635–2643.  
  18. S. Nosé, A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys.81 (1984) 511–519.  
  19. B. Oksendal, Stochastic Differential Equations. 5th Edition, Springer-Verlag, Berlin-Heidelberg (2000).  
  20. J.-P. Ryckaert and A. Bellemans, Molecular dynamics of liquid alkanes. Faraday Discussions66 (1978) 95–107.  
  21. A. Samoletov, M.A.J. Chaplain and C.P. Dettmann, Thermostats for “slow" configurational modes. J. Stat. Phys.128 (2007) 1321–1336.  

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