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## Re: [ESPResSo-devel] Somewhat strange trajectory

 From: Stefan Kesselheim Subject: Re: [ESPResSo-devel] Somewhat strange trajectory Date: Tue, 8 Apr 2014 13:25:00 +0200

```Dear Peter,
there is one question I have:
Do you observe a diffusive (a) or a directed (b) motion along 1,1,1? From the
trajectory it looks like a directed motion but that would lead to a quadratic
MSD. To quantify (a), it should be possible to derive a drift velocity, and for
(b) you could calculated the off-diagonal elements of the diffusion tensor for
<(x(t)-x(t+tau))(y(t)-y(t+tau))>. This would mean implementing the correlation
operation "dyadic_product" which I want to do now for some time :-).
Regarding the reason: Variant a would be related to a correlation of subsequent
numbers, and Variant b would be a nonzero mean. In principle, both should be
easy to distinguish and in both cases, the same should apply for a single
isolated particle. Maybe this would be an even easier test case. Use cellsystem
nsquare.
Maybe that helps….
Cheers
Stefan

On Apr 8, 2014, at 12:32 PM, Peter Košovan <address@hidden> wrote:

> Hi Espressies,
>
> Simulating a single polymer chain of the Kremer-Grest model, we observed that
> the centre of mass "diffuses" in narrow a slab, with a normal vector approx.
> (1,1,1). In order to see that, one needs to run about 10^8 LJ time units
> (~10^10 time steps, ~1cpu-day), plot the centre of mass trajectory and tilt
> it in an appropriate angle. With shorter trajectories it's not obvious if the
> bias is in the trajectory or in the observer's eye.
>
> I could partly fix the problem replacing the call to l_random() (ran1 RNG) in
> d_random() of random.hpp with the built-in rand() function. The trajectory
> might still be biased, but at least it's not a slab.
>
> Attached files: sample tcl script, gnuplot script to plot what I have
> described and its source data: centre-of-mass and monomer msds (average over
> 20 runs), com trajectory with the l_random() and with rand() RNG.
>
> I think that we should replace the l_random() by some other RNG. Surely,
> rand() is not a good choice either, it was just the first hack I tried. Any
> suggestions / opinions are welcome. I intend to investigate it further: test
> other RNGs and check if/how they affect dynamical and thermodynamic
> properties.
>
> Some more detail of what I learned:
> I asked a student to simulate the Kremer-Grest polymer in Langevin thermostat
> and compute msd(t), from 20 independent starting configurations, to get 20
> independent msds's and estimate the error. Plotting msd(t)/t, it first
> converges to approx. 2/N, as it should for Rouse-like dynamics, but at
> t~3*10^4, it drops to ~3/4 of this value, while the error is much smaller. We
> suspected a mistaken input or a subtle correlator bug, so I repeated the
> simulations with my own script, various chain lengths, box sizes, gammas,
> timesteps, correlator parameters, initial conditions, and the result was
> robust. Finally, I printed the centre of mass coordinates and asked a
> colleague to compute the msd(t) using his own independent tool. Plotting the
> output trajectory revealed the problem. The tilt of the plane appears robust
> with respect to initial conditions, random seed and chain length. I have not
> yet checked other parameters, since other runs did not write the trajectory.
> I also checked the original Grest+Kremer paper (Phys.Rev.A,33,3628,1986), and
> their msds also change slope on long times (g3 in Fig.3), but they have not
> specified their RNG.
>
>
> Cheers,
>
> peter
>
> --
> Dr. Peter Košovan
>
> Departmtent of Physical and Macromolecular Chemistry
> Faculty of Science, Charles University in Prague, Czech Republic
>
> Katedra fyzikální a makromolekulární chemie
> Přírodovědecká fakulta Univerzity Karlovy v Praze
>
> www.natur.cuni.cz/chemistry/fyzchem/
> Tel. +420221951290
> Fax +420224919752
>
> Pokud je tento e-mail součástí obchodního jednání, Přírodovědecká fakulta
> Univerzity Karlovy v Praze:
> a) si vyhrazuje právo jednání kdykoliv ukončit a to i bez uvedení důvodu,
> b) stanovuje, že smlouva musí mít písemnou formu,
> c) vylučuje přijetí nabídky s dodatkem či odchylkou,
> d) stanovuje, že smlouva je uzavřena teprve výslovným dosažením shody na
> všech náležitostech smlouvy.
> <msds.tar.gz>

```