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.
Mots clés : molecular dynamics, thermostats, hybrid Monte Carlo, canonical ensemble
@article{M2AN_2009__43_4_743_0, author = {Leimkuhler, Benedict and Reich, Sebastian}, title = {A {Metropolis} adjusted {Nos\'e-Hoover} thermostat}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {743--755}, publisher = {EDP-Sciences}, volume = {43}, number = {4}, year = {2009}, doi = {10.1051/m2an/2009023}, mrnumber = {2542875}, zbl = {1171.82317}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2009023/} }
TY - JOUR AU - Leimkuhler, Benedict AU - Reich, Sebastian TI - A Metropolis adjusted Nosé-Hoover thermostat JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 743 EP - 755 VL - 43 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009023/ DO - 10.1051/m2an/2009023 LA - en ID - M2AN_2009__43_4_743_0 ER -
%0 Journal Article %A Leimkuhler, Benedict %A Reich, Sebastian %T A Metropolis adjusted Nosé-Hoover thermostat %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 743-755 %V 43 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009023/ %R 10.1051/m2an/2009023 %G en %F M2AN_2009__43_4_743_0
Leimkuhler, Benedict; Reich, Sebastian. A Metropolis adjusted Nosé-Hoover thermostat. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 4, pp. 743-755. doi : 10.1051/m2an/2009023. http://www.numdam.org/articles/10.1051/m2an/2009023/
[1] GSHMC: An efficient method for molecular simulations. J. Comput. Phys. 227 (2008) 4934-4954. | MR | Zbl
and ,[2] Generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 227 (2008) 4934-4954. | MR | Zbl
, and ,[3] Computer Simulation of Liquids. Clarendon Press, Oxford (1987) | Zbl
and ,[4] The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114-134. | MR | Zbl
, and ,[5] Canonical sampling through velocity rescaling. J. Chem. Phys. 126 (2007) 014101.
, and ,[6] Hybrid Monte-Carlo. Phys. Lett. B 195 (1987) 216-222.
, , and ,[7] Understanding Molecular Simulation. Academic Press, New York (1996). | Zbl
and ,[8] Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695-1697.
,[9] A generalized guided Monte-Carlo algorithm. Phys. Lett. B 268 (1991) 247-252.
,[10] Shadow Hybrid Monte Carlo: An efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581-604. | Zbl
and ,[11] Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456-510. | MR | Zbl
and ,[12] Pressure and temperature control in molecular dynamics simulations: a unitary approach in discrete time. Modelling Simul. Mater. Sci. Eng. 6 (1998) 405-421.
,[13] Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal. 184 (2007) 449-463. | MR | Zbl
, and ,[14] A Hamiltonian formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst. 4 (2005) 187-216. | MR | Zbl
and ,[15] A gentle ergodic thermostat for molecular dynamics. J. Stat. Phys. (2009), doi: 10.1007/s10955-009-9734-0. | MR
, and ,[16] Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001). | MR | Zbl
,[17] Nose-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97 (1992) 2635-2643.
, and ,[18] A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 81 (1984) 511-519.
,[19] Stochastic Differential Equations. 5th Edition, Springer-Verlag, Berlin-Heidelberg (2000). | Zbl
,[20] Molecular dynamics of liquid alkanes. Faraday Discussions 66 (1978) 95-107.
and ,[21] Thermostats for “slow'' configurational modes. J. Stat. Phys. 128 (2007) 1321-1336. | MR | Zbl
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