[MMTK] Relaxation times, relation to W_S and W_V (Kneller et al.)?

[Konrad Hinsen]

On Feb 19, 2008, at 9:54, Andreas Kring wrote:

> How are the relaxation times for the NoseThermostat and the
> AndersenBarostat related to the parameters W_S and W_V (Kneller et  
> al.,
> Phys. Rev. E, 54, 6825 (1996)), respectively?
>
> Are the related in the following way?
>
> Thermostat:
> W_S = 3*N*k_B*Temp*(rexalation time)**2,
> where N is the number of atoms in the system.
>
> Barostat:
> W_V = [P_ext*(relaxation time)**2]/(some reference length)**3

In the MMTK source code (MMTK_dynamics.c), the parameter W_S is  
called t_mass, and W_V is called b_mass. For the thermostat, lines  
502 and 503 define:

     t_energy = df*t_temp*kB;
     t_mass = t_energy*t_tau*t_tau;

where df is the number of degrees of freedom (3N minus the number of  
constraints), t_temp is the temperature of the thermostat, and t_tau  
is the thermostat relaxation time. kB is just the Boltzmann constant.  
The formula that you give is thus correct in the absence of constraints.

For the barostat, line 639 defines

     b_mass = df*t_temp*kB*b_tau*b_tau/(volume*volume);

where b_tau is the barostat relaxation time and volume is the  
(instantaneous) volume. If there is no thermostat, the kinetic energy  
of the thermostat (df*t_temp*kB) is replaced by the instantaneous  
kinetic energy of the system (line 692):

       b_mass = 0.5*k_energy*b_tau*b_tau/(volume*volume);

Konrad.
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Konrad Hinsen
Centre de Biophysique Moléculaire, CNRS Orléans
Synchrotron Soleil - Division Expériences
Saint Aubin - BP 48
91192 Gif sur Yvette Cedex, France
Tel. +33-1 69 35 97 15
E-Mail: hinsen at cnrs-orleans.fr
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