# Granular ensembles

Dear LAMMPS community,
I am trying to understand what statistical ensembles are used for simulation of granular matter in LAMMPS. I already did a simulation using the nve/sphere. Are other ensembles applicable? Does the temperature in the nvt/sphere ensemble for granular matter correspond to the compactivity, as in the full canonical ensemble proposed by Edwards?
Thank you for any insights on the subject.
Ana

It is almost always a mistake to think of time integration fixes in LAMMPS as “ensembles”.
The documentation says what they do and how. Whether this leads to a specific statistical-mechanical ensemble depends on many other factors and features that you are using in your input.

For example “fix nve” will perform a plain time integration without any other manipulations. If you have an equilibrated system of point particles in a fully periodic box and no other fixes manipulating the system, then the resulting trajectory will be in the NVE ensemble. If your system is non-periodic or you use fix deform and so on, you are no longer simulating NVE.
if you are using “fix nvt” instead, you essentially have what fix nve provides plus nose-hoover thermostat chains and thus you will get an NVT ensemble only under the same kind of conditions as previously for fix nve and the NVE ensemble.

similarly fix nve/sphere does the same for particles with a finite size (i.e. have rotational degrees of freedom). fix nvt/sphere correspondingly adds a nose-hoover thermostat to that. that is it. whether this conforms to some specific conditions you are looking for is for you to decide.
just always keep in mind that software doesn’t know physics, it always follows simple rules and those rules are described in the manual. the interpretation of that is up to the person doing the simulation.

axel.

Thank you, Axel.
So, if granular systems are not affected by a change in temperature, a thermostat would not make any difference in the results. Is that correct?

No

I’ll add that granular models are not typically run with a thermostats
(e.g. NVT) because the pairwise interactions are non-conservative,
i.e. dissipative due to friction. Hence kinetic energy is typically
added by gravity (particles poured into a hopper, and watching
them pack and settle). Hence KE and temp go to zero during
the simulation.

Steve