In this paper we reformulate the configurational temperature Nosé-Hoover thermostat of Braga and Travis (2005) by means of a quasi-Hamiltonian theory in phase space Sergi and Ferrario (2001). The quasi-Hamiltonian structure is exploited to introduce a hybrid configurational-kinetic temperature Nosé-Hoover chain thermostat that can achieve a uniform sampling of phase space (also for stiff harmonic systems), as illustrated by simulating the dynamics of one-dimensional harmonic and quartic oscillators. An integration algorithm, based on the symmetric Trotter decomposition of the propagator, is presented and tested against implicit geometric algorithms with a structure similar to the velocity and position Verlet. In order to obtain an explicit form for the symmetric Trotter propagator algorithm, in the case of non-harmonic and non-linear interaction potentials, a position-dependent harmonically approximated propagator is introduced. Such a propagator approximates the dynamics of the configurational degrees of freedom as if they were locally moving in a harmonic potential. The resulting approximated locally harmonic dynamics is tested with good results in the case of a one-dimensional quartic oscillator: The integration is stable and locally time-reversible. Instead, the implicit geometric integrator is stable and time-reversible globally (when convergence is achieved). We also verify the stability of the approximated explicit integrator for a three-dimensional N-particle system interacting through a soft Weeks-Chandler-Andersen potential.

On the configurational temperature Nosè-Hoover thermostat / Beckedahl, Derrick; Obaga, Emmanuel O.; Uken, Daniel A.; Sergi, Alessandro; Ferrario, Mauro. - In: PHYSICA. A. - ISSN 0378-4371. - 461:(2016), pp. 19-35. [10.1016/j.physa.2016.05.008]

On the configurational temperature Nosè-Hoover thermostat

FERRARIO, Mauro
2016

Abstract

In this paper we reformulate the configurational temperature Nosé-Hoover thermostat of Braga and Travis (2005) by means of a quasi-Hamiltonian theory in phase space Sergi and Ferrario (2001). The quasi-Hamiltonian structure is exploited to introduce a hybrid configurational-kinetic temperature Nosé-Hoover chain thermostat that can achieve a uniform sampling of phase space (also for stiff harmonic systems), as illustrated by simulating the dynamics of one-dimensional harmonic and quartic oscillators. An integration algorithm, based on the symmetric Trotter decomposition of the propagator, is presented and tested against implicit geometric algorithms with a structure similar to the velocity and position Verlet. In order to obtain an explicit form for the symmetric Trotter propagator algorithm, in the case of non-harmonic and non-linear interaction potentials, a position-dependent harmonically approximated propagator is introduced. Such a propagator approximates the dynamics of the configurational degrees of freedom as if they were locally moving in a harmonic potential. The resulting approximated locally harmonic dynamics is tested with good results in the case of a one-dimensional quartic oscillator: The integration is stable and locally time-reversible. Instead, the implicit geometric integrator is stable and time-reversible globally (when convergence is achieved). We also verify the stability of the approximated explicit integrator for a three-dimensional N-particle system interacting through a soft Weeks-Chandler-Andersen potential.
2016
461
19
35
On the configurational temperature Nosè-Hoover thermostat / Beckedahl, Derrick; Obaga, Emmanuel O.; Uken, Daniel A.; Sergi, Alessandro; Ferrario, Mauro. - In: PHYSICA. A. - ISSN 0378-4371. - 461:(2016), pp. 19-35. [10.1016/j.physa.2016.05.008]
Beckedahl, Derrick; Obaga, Emmanuel O.; Uken, Daniel A.; Sergi, Alessandro; Ferrario, Mauro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1137550
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