Re: [ESPResSo-users] Educated guess about gamma in Langevin thermostat

[Ulf Schiller]

Hi Salvador,

On 12/19/2012 06:34 PM, Salvador H-V wrote:
> I am doing some simulations for a two-dimensional  hard-sphere
> rigig-dumbbells.
> The interaction potential is the purely repulsive Lennard-Jones (WCA)
> using the rigid_bond feature to constraint the bond in the dimers.
>
> I would like to choose a value  of the the friction coefficient (gamma =
> 6.0*Pi*dynamic_viscosity*sphere_radius / mass  )  in the Langevin thermostat
> such as is representative of the solvent experimental viscosity.
>
> Using the experimental data, I obtain the following
> M ~ 4.4x10^(-15) kg
> T ~ 293.15 K
> tao = sigma * ( mass / kbT)^1/2 ~ 2.08x10^-3 s
> viscosity ~ 0.001002 Pa * s
> sigma = 2x10^-6 m
>
> Then, gamma_langevin = 6 * Pi * viscosity * radius / mass
> and in reduced units  gamma / tao = gamma_reduced ~ 8930
>
> If my above simple calculations are right and if I understood well,
> accordingly to previous post in the mail list,  we have to use a value
> of time_step
> such as:  gamma_reduced * dt  / 2.0 is < 1 and preferably around  0.1.
>
> Then, I should use a time_step <= 0.00002 that is very small and will
> require very long simulations to obtain the experimental time window.
>
> I was wondering if somebody could provide suggestions of how to reduce
> the value of gamma (so, i can increase the time_step) but still
> representing the solvent viscosity.

I think that depends on what physics you want to look at. If inertial 
effects can be neglected in your system, you could try to use an 
artificial mass instead of matching the experimental mass. Keep in mind 
that a too high value of gamma will also affect the accuracy of the 
integrator (the Verlet algorithm with velocity dependent forces is first 
order only).

Another possibility is to think whether you really need the exact value 
of the viscosity. It might be enough to match dimensionless quantities 
such as the Reynolds number, Peclet number, etc. One can then typically 
scale the simulation parameters to obtain reasonable values. The details 
depend again on what you want to simulate/measure.

Hope this helps,
Ulf

--
Dr. Ulf D. Schiller                        Building 04.16, Room 3006
Institute of Complex Systems (ICS-2)       Phone:   +49 2461 61-6144
Forschungszentrum Jülich, Germany          Fax:     +49 2461 61-3180

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