A Metropolis adjusted Nosé-Hoover thermostat
Leimkuhler, Benedict ; Reich, Sebastian
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009), p. 743-755 / Harvested from Numdam

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.

Publié le : 2009-01-01
DOI : https://doi.org/10.1051/m2an/2009023
Classification:  65C05,  65C20,  65C60,  82B80,  60H30
@article{M2AN_2009__43_4_743_0,
     author = {Leimkuhler, Benedict and Reich, Sebastian},
     title = {A Metropolis adjusted Nos\'e-Hoover thermostat},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {43},
     year = {2009},
     pages = {743-755},
     doi = {10.1051/m2an/2009023},
     mrnumber = {2542875},
     zbl = {1171.82317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2009__43_4_743_0}
}
Leimkuhler, Benedict; Reich, Sebastian. A Metropolis adjusted Nosé-Hoover thermostat. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 743-755. doi : 10.1051/m2an/2009023. http://gdmltest.u-ga.fr/item/M2AN_2009__43_4_743_0/

[1] E. Akhmatskaya and S. Reich, GSHMC: An efficient method for molecular simulations. J. Comput. Phys. 227 (2008) 4934-4954. | MR 2414842 | Zbl 1148.82316

[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. | MR 2414842 | Zbl 1148.82316

[3] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids. Clarendon Press, Oxford (1987) | Zbl 0703.68099

[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. | MR 1701573 | Zbl 0933.81058

[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. B 195 (1987) 216-222.

[7] D. Frenkel and B. Smit, Understanding Molecular Simulation. Academic Press, New York (1996). | Zbl 0889.65132

[8] W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695-1697.

[9] A.M. Horowitz, A generalized guided Monte-Carlo algorithm. Phys. Lett. B 268 (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. | Zbl 1115.65383

[11] A.D. Kennedy and B. Pendleton, Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456-510. | MR 1850796 | Zbl 0969.81639

[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. | MR 2299758 | Zbl 1122.82002

[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. | MR 2136523 | Zbl 1075.92057

[15] B. Leimkuhler, E. Noorizadeh and F. Theil, A gentle ergodic thermostat for molecular dynamics. J. Stat. Phys. (2009), doi: 10.1007/s10955-009-9734-0. | MR 2505736 | Zbl pre05586412

[16] J.S. Liu, Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001). | MR 1842342 | Zbl 0991.65001

[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). | Zbl 0567.60055

[20] J.-P. Ryckaert and A. Bellemans, Molecular dynamics of liquid alkanes. Faraday Discussions 66 (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. | MR 2352012 | Zbl 1128.82006