# How to add Integration Scheme for Coupled Translational and Rotational diffusion

Dear Users,
I want to simulate Langevin dynamics in which the translational and rotational diffusion are coupled. I have a model integration scheme for this which is given below.

(theta)i+1 = (theta)I + A dt + sqrt (C dt) Wtheta,i

Xi+1 = Xi + B Cos(theta)i dt + sqrt (E dt) Wx,j

yi+1 = yi + B Sin(theta)i dt + sqrt (E dt) Wy,j

Where ‘W’ terms are random numbers and A, B, C and E are constants and dt stands for small time interval t.
As per my understanding I need to modify the fix_langevin.cpp to account for this change in the Langevin equation. I have go through the script fix_langevin.cpp, but I don’t have any idea where I need to make the changes or include this integration scheme… please give me some suggestions…

Rotation of what? Rotation how?

Fix langevin looks at point particles, which cannot rotate.

Please see the other ongoing discussion on the very same subject (with the same lack of specific information).

Also, if you look carefully, there are several langevin type thermostats available in LAMMPS, some with time integration included, some without.

Axel

ok I got your point. I have a query that If I want to simulate Lennard-Jones fluid which have atoms with finite radius in the unit of sigma. Thus it is not a point particle. In that case rotation can be considered and is it possible to simulate such a system in LAMMPS and calculate the rotational diffusion of the atoms?

ok I got your point. I have a query that If I want to simulate Lennard-Jones fluid which have atoms with finite radius in the unit of sigma. Thus it is not a point particle. In that case rotation can be considered and is it possible to simulate such a system in LAMMPS and calculate the rotational diffusion of the atoms?

but keep in mind, that such particles would have only (pairwise
additive) interactions that are dependent on the distance between two
particles only. so the only coupling between rotational motion and the
translational motion would be due the time integration fix and no part
of the force field would have an impact on that.

contain "sphere". by default all settings and automatically generated
styles assume point particles.
you need to use atom style sphere (instead of atomic), so your
particles can have have a radius, a per-atom mass (usually inferred
from radius and a density parameter), and angular velocity.
you need to use fix nve/sphere (instead of fix nve) to do time
integration, compute temp/sphere (instead of compute temp, which is
used by default for thermodynamic output, i.e. temp and ke).
you would have to then implement a fix langevin/sphere, but it may be
more straightforward to combine fix nve/sphere and fix langevin/sphere
into one fix (as is true for several other langevin variants in LAMMPS
like for example fix gle, fix gld, fix ffl)

i also noticed, that your time integration formulation only applies to
a 2d system (where there is only the orientation angle), so you would
have to either restrict your implementation to 2d or implement a
generalization to 3d (where you have to use a quaternion or 3 euler
angles to describe orientation).

most certainly, this is not something that is done by adding a few
lines to fix langevin.

axel.

Thank you for the clarification. I will try with your suggestion once…