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Re: [ESPResSo] Fwd: setmd skin


From: Axel Arnold
Subject: Re: [ESPResSo] Fwd: setmd skin
Date: Fri, 25 Jun 2010 14:05:51 +0200
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On Thursday 24 June 2010 22:14:29 Mikheil Azatov wrote:
> setmd time_step 0.0129; setmd skin 0.5
> set temp 1; set gamma 156
> thermostat langevin $temp $gamma

Just to illustrate what Burkhard was talking about:

For the discretized velocity-Verlet Langevin equation, the half-step "drag 
force" is F= -gamma*mass*v/2, the change of velocity therefore dv = F/mass*dt 
= -gamma*dt*v/2. Therefore, your simulation can only be stable if gamma*dt/2 
is smaller than 1.

In your case with gamma=156, for dt=0.0128, it is 1.0062, for dt=0.0129, 
0.9984, so it should be stable for and only for the latter time step, as you 
observe. If you play around, you will see that even being 10^-6 above the 
critical time step of  2./156 is enough to destabilize the system. As Burkhard 
said, the transition is pretty sharp...

For practical applications, I would suggest to stay at least an order of 
magnitude below this limit, since otherwise you are quite far from a proper 
discretization of the Langevin equation, in which you assume that the velocity 
change per time step is small.

Axel

-- 
JP Dr. Axel Arnold Tel: +49 711 685 67609
ICP, Universit├Ąt Stuttgart      Email: address@hidden
Pfaffenwaldring 27
70569 Stuttgart, Germany




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