# Peculiar phenomenon of collective translational escape of rigid bodies out of the range of simulation box

Dear LAMMPS users,

I am a newbie in the field, thus please excuse me if my problem might appear trivial.

I am trying to simulate (NPT) a set of rigid bodies (11 spheres arranged in a crescent-like manner) via WCA potential. Below I attach the input script. The thing that bothers me is that around the 4x10^6 timestep the whole system collectively starts to perform the translation move across the simulation box (see the video). Frankly, I have no clue what might be the cause. Any hints/advices are highly appreciated.
initial_script.in (2.3 KB)

This is not as unusual as you might think.
The phenomenon is generally referred to as â€śflying ice cube syndromeâ€ť. This is because the thermostat cannot remove the center of mass drift, so to maintain the total temperature more and more kinetic energy will be transferred from vibrations to translation until the system freezes and at the same time accelerate a lot as a whole.

Its origin lies in the use of floating-point math and the fact that it summing floating-point numbers is inexact and that their resolution depends on their magnitude. Thus something that (theoretically) should sum up to (exactly) zero does not. Most of the time, this is not a problem. There will be some fluctuations around the origin of the cell, but it would mostly cancel out. But sometimes a center of mass drift will appear and then problems start, since there usually is nothing in a typical simulation that can dissipate it.

There are multiple contributing factors.

• the way how the initial temperature is set (but you used the `mom yes` option, that will remove it)
• the initial system geometry (you have an â€śasymmetricâ€ť geometry in your constituent molecules), an atomic system is less prone
• the equilibration protocol: it is often a good idea to let a system equilibrate until the worst potential energy â€śhot spotsâ€ť are well dissipated and then use â€śvelocity all scale mom yesâ€ť or similar
• using a variable cell time integration (because it converts all positions to fractional coordinates and conventional coordinates multiple times during a timestep and that adds numerical noise). this is a mechanism that becomes more dominant the larger your center of mass drift is
• using a rigid body fix: there are additional issues with how time integration for rigid bodies work, specifically there are different errors and timestep requirements for translation and rotation. using a shorter timestep can help a lot
• using a non-dissipative thermostat (worst are temp/rescale or temp/berendsen).
• using GPU acceleration with mixed or single precision
• using (too) aggressive compiler optimization
• bugs in the code: try with the latest LAMMPS patch version (27 May 2021 as of this writing)

There are some cures, but since you are using a rigid fix, your options are limited, since you cannot use most of them (the rigid fix stores per rigid object velocities and positions). You can break down your simulation into multiple chunks and issue a velocity command in between to remove any residual center of mass drift. After that it is crucial that you repeat the fix rigid command (you do not have to unfix it, if you use the same fix) with the same settings. That will trigger initialization of the rigid body velocities (you will get a message in the screen and logfile output).

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Dear Dr. Kohlmeyer,

thank you very much for your comprehensive and insightful response. According to the hints you have provided I went through the following steps:

I have tried with the latest LAMMPS patch version, namely: LAMMPS-64bit-27May2021-MPI. For the record, I execute the script throught the command:

mpiexec -localonly 4 lmp_mpi -pk omp 4 -sf omp -in .\initial_script.in

Unfortunately, the problem persists (even for twofold shorter timestep than initially).

Onward, I have included in the script:

fix mm1 all momentum 1000000 linear 1 1 1 rescale

and run the simulation for 500 rigid bodies (x11, ergo 5500 â€śatomsâ€ť). Below I attach the results for the components of systemâ€™s COM speed (v_x, v_y, v_z), which were monitored throughout the simulation via:

variable vcmx equal vcm(all,x)
variable vcmy equal vcm(all,y)
variable vcmz equal vcm(all,z)

As one can see up to 1.2*10^7 Timestep there is no drift, afterwards â€śthe ice cube syndrom starts to kick-inâ€ť. â€śHorizontal linesâ€ť are results of the fix mm1, however it is visible that after each â€śresetâ€ť the system builds up to the state from before the â€śresetâ€ť and â€śstep-by-stepâ€ť the whole system gradually drift away. Frankly, I am in a blind spot.

Fix momentum cannot have a lasting effect as the per-rigid-body velocities are cached in the rigid body fix. Only if you break your run into sections, reissue the fix rigid command, and remove the center of mass momentum with the velocity command, should you be able to properly remove it.

So â€śtechnicallyâ€ť speaking, I should follow the scheme:

(INITIALL STUFF)
fix rigid all rigid/npt/small molecule temp 1.0 1.0 1.0 iso 1.0 1.0 1.0
run 10000000
unfix rigid
velocity all zero linear
fix rigid all rigid/npt/small molecule temp 1.0 1.0 1.0 iso 1.0 1.0 1.0
run 10000000
etc.

Am I correct?

Yes. But I would do it like shown below:

• using a loop makes things simpler
• since you are overwriting the same fix, there is no need to unfix it, just reinitialize it
• I would remove the momentum more often so there is no significant drop in kinetic energy
• with index variables their value can be overwritten from the command line with the -var flag
• depending on how you run, you may need to replace SELF with the file name
``````variable ntotal index  70000000
variable nchunk index 1000000
variable nloop  index \$(round(v_ntotal/v_nchunk))

variable i loop \${nloop}
label loop

run \${nchunk} post no
velocity all zero linear
fix rigid all rigid/npt/small molecule temp 1.0 1.0 1.0 iso 1.0 1.0 1.0

next i
jump SELF loop
``````

Dear Dr. Kohlmeyer,

thank you very much for your help, insights, and valuable hints. I have implemented your suggestions and now everything seems to work fine.

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Thanks for reporting back to the forum.
This will hopefully help others in the future that have similar issues and search for help.