A Projective Thermostatting Dynamics Technique

A dynamical framework is developed with several variations for modeling multiple timescale molecular dynamics at constant temperature. The described approach can be adapted to various applications, including mixtures of heavy and light particles and models with stiff potentials. Canonical sampling properties are proved under the ergodicity assumption. Implications for numerical method development are discussed, and the technique is validated in numerical experiments with model problems, including a simple model of a diatomic gas with anharmonic weak interaction.

[1]  V. Arnold,et al.  Mathematical aspects of classical and celestial mechanics , 1997 .

[2]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[3]  Benedict J. Leimkuhler,et al.  A Hamiltonian Formulation for Recursive Multiple Thermostats in a Common Timescale , 2005, SIAM J. Appl. Dyn. Syst..

[4]  Mark E. Tuckerman,et al.  Erratum: Molecular dynamics algorithm for multiple time scales: Systems with disparate masses [J. Chem. Phys. 94, 1465 (1991)] , 1991 .

[5]  J. Jeans,et al.  XI. On the partition of energy between matter and Æther , 1905 .

[6]  Benedict J. Leimkuhler,et al.  Generating generalized distributions from dynamical simulation , 2003 .

[7]  Irwin Oppenheim,et al.  Molecular theory of Brownian motion , 1970 .

[8]  Berry,et al.  Generalization of Nosé's isothermal molecular dynamics. , 1988, Physical review. A, General physics.

[9]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[10]  Christopher R Sweet,et al.  The canonical ensemble via symplectic integrators using Nosé and Nosé-Poincaré chains. , 2004, The Journal of chemical physics.

[11]  B. Leimkuhler,et al.  A reversible averaging integrator for multiple time-scale dynamics , 2001 .

[12]  Folkmar Bornemann,et al.  Homogenization in Time of Singularly Perturbed Conservative Mechanical Systems , 1998 .

[13]  D. Kusnezov.  Diffusive aspects of global demons , 1992 .

[14]  Benedict Leimkuhler,et al.  Integration Methods for Molecular Dynamics , 1996 .

[15]  M. Ortiz,et al.  Quasicontinuum analysis of defects in solids , 1996 .

[16]  D. Kusnezov,et al.  Canonical ensemble averages from pseudomicrocanonical dynamics. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[17]  R. Zwanzig.  Ensemble Method in the Theory of Irreversibility , 1960 .

[18]  Benedict Leimkuhler,et al.  Asymptotic Error Analysis of the Adaptive Verlet Method , 1999 .

[19]  Jesús A. Izaguirre,et al.  Targeted Mollified Impulse: A Multiscale Stochastic Integrator for Long Molecular Dynamics Simulations , 2003, Multiscale Model. Simul..

[20]  Mark E. Tuckerman,et al.  Molecular dynamics algorithm for multiple time scales: Systems with disparate masses , 1991 .

[21]  A. Stuart,et al.  Extracting macroscopic dynamics: model problems and algorithms , 2004 .

[22]  Cho,et al.  Constant-temperature molecular dynamics with momentum conservation. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Wolfram Just,et al.  Elimination of Fast Chaotic Degrees of Freedom: On the Accuracy of the Born Approximation , 2003 .

[24]  Stephen D. Bond,et al.  The Nosé-Poincaré Method for Constant Temperature Molecular Dynamics , 1999 .

[25]  Antonio Giorgilli,et al.  Exponential law for the equipartition times among translational and vibrational degrees of freedom , 1987 .

[26]  Sebastian Reich,et al.  Smoothed dynamics of highly oscillatory Hamiltonian systems , 1995 .

[27]  J. Jeans,et al.  XXXV. On the vibrations set up in molecules by collisions , 1903 .

[28]  N. G. van Kampen,et al.  Brownian motion as a problem of eliminating fast variables , 1986 .

[29]  Brian B. Laird,et al.  Symplectic algorithm for constant-pressure molecular dynamics using a Nosé–Poincaré thermostat , 2000 .

[30]  Ernst Hairer,et al.  Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations , 2000, SIAM J. Numer. Anal..

[31]  J. Izaguirre.  Longer Time Steps for Molecular Dynamics , 1999 .

[32]  Benedict J. Leimkuhler,et al.  A parallel multiple time-scale reversible integrator for dynamics simulation , 2003, Future Gener. Comput. Syst..

[33]  T. Schlick,et al.  Special stability advantages of position-Verlet over velocity-Verlet in multiple-time step integration , 2001 .

[34]  Shuichi Nosé,et al.  Constant Temperature Molecular Dynamics Methods , 1991 .

[35]  H. Kantz,et al.  Stochastic modelling: replacing fast degrees of freedom by noise. , 2001 .

[36]  Christof Schütte,et al.  Homogenization approach to smoothed molecular dynamics , 1997 .

[37]  L. Boltzmann.  On Certain Questions of the Theory of Gases , 1895, Nature.