Re: [ESPResSo-devel] Somewhat strange trajectory

[Stefan Kesselheim]

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.
> 
> Looking forward to your comments.
> 
> 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>