# [lammps-users] Langevin rotational equation

Dear lammps user,

Could you please tell me where someone can find the reference explaining the integrating algorithm of the Langevin rotational equation associated with fix langevin or fix nve/asphere ?

Best regards
Mohammed

Best regards
Mohammed

You will probably have to ask a more specific question.

Time integration is done in LAMMPS with the Velocity Verlet algorithm, which is explained in about every text book on MD that I have seen.
This applies to rotation as well as translation.

If you have a question that is specific to the rotation, you have to provide more details, probably best with reference to the lines of code that you are referring to.

Following the below message, my questions is:

In the case of finite size particles like ellipsoids, How does LAMMPS set the moment of inertia tensor for every particle?

It seems to me that LAMMPS assumes continuous mass distribution and then computes the moment of inertia from the integral that includes the mass density.

Best regards
Mohammed

Following the below message, my questions is:

In the case of finite size particles like ellipsoids, How does LAMMPS set the moment of inertia tensor for every particle?

You should look this up in the source code. E.g. here: https://github.com/lammps/lammps/blob/798975b8090c5cc41b434ebcbe4baa59aa395701/src/fix_langevin.cpp#L895

Much thanks Axel.

However, I feel I still need to ask more. What is the paper explaining it ?.

The integration of the translational equation of motion, implemented in “fix langevin”, is explained in an appendix in the paper by Schneider and Stoll, mentioned in the LAMMPS documentation.

What is the integrator that the “fix langevin” implements for the rotational equation of motion ?

More precisely, I would like to understand the emergence of the keywords angmom and omega in the theory itself.

Best regards
Mohamemd

Much thanks Axel.

However, I feel I still need to ask more. What is the paper explaining it ?.

i don’t know. I didn’t implement it. at this point this is becoming a matter of research for yourself. if you want to know at that level of detail. you have to search and find it in the literature by yourself. I would start by searching through the citations given in the papers listed in the LAMMPS documentation. perhaps there also may be some hints in the mailing list archives in previous discussions about thermostatting ellipsoids.

mind you fix langevin does not implement the time integration. that is done by fix nve with a plain velocity verlet.

Hi, I remember a similar exchange on this list regarding how different versions of fix langevin project atomic forces on the atoms within rigid bodies in the same manner as they would be on independent atoms. Then fix nve or fix rigid would integrate the EOMs accordingly. But the langevin option of fix rigid would account for the inertia tensor.

For “atom_style body”, I don’t know what the workflow is, but it is probably very similar.

As Axel said, at this point some independent research is warranted, so please do search the mailing list.

Giacomo

Thank you so much Axel and Giacomo for your suggestions. Your suggestions were helpful.

I read the LAMMPS mailing list. I found that LAMMPS updates the quaternions according to the Richardson iteration method for the finite-size spherical/aspherical particles in the microcanonical ensemble. As mentioned in LAMMPS documentation, the time integration is not done in the “fix langevin” but it is done in “fix nve/asphere” for aspherical particles. I am talking about my system which is composed of ellipoids ineracting through Gay-Beren potential. I am doing Langevin simulation.

I also found that LAMMPS has a fix that does the time integration and themrostatting at the same time which is “fix nve/dotc/langevin command”. According to the documentation, this fix also does the Langevin simulation but with additional advantage; it allows for a larger timestep. The nice thing is that the reference for the implementation of this fix is clearly mentioned in the documentation.

However, I have not found in the LAMMPS mailing list any references containing the physical equations used by LAMMPS to do the thermstatting of the rotational degrees of freedom for “finite-size spherical/aspherical particles” from the physical point of view, i.e., the treatment that starts from a Hamiltonian and then ends up with the equations for the integrators. I am talking about the “fix langevin” command in LAMMPS.

In case someone can recommend certain references for how LAMMPS implements the Langevin thermostatting of the rotational degrees of freedom for the “finite size spherical/aspherical particles”, I would be thankful and grateful for them if they can tell me about that.

Sorry In case I miss something that I should already understand by myself.

Best regards
Mohammed