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### fix rigid

Syntax:

    fix ID group-ID rigid bodystyle args keyword values ...

- ID, group-ID are documented in fix command
- rigid = style name of this fix command
- bodystyle = single or molecule or group

        single args = none
        molecule args = none
        group args = N groupID1 groupID2 ...
          N = # of groups
          groupID1, groupID2, ... = list of N group IDs

- zero or more keyword/value pairs may be appended
- keyword = force or torque

        force values = M xflag yflag zflag
          M = which rigid body from 1-Nbody (see asterisk form below)
          xflag,yflag,zflag = off/on if component of center-of-mass force is active
        torque values = M xflag yflag zflag
          M = which rigid body from 1-Nbody (see asterisk form below)
          xflag,yflag,zflag = off/on if component of center-of-mass torque is active

Examples:

    fix 1 clump rigid single
    fix 1 clump rigid single force 1 off off on
    fix 1 polychains rigid molecule
    fix 1 polychains rigid molecule force 1*5 off off off force 6*10 off off on
    fix 2 fluid rigid group 3 clump1 clump2 clump3
    fix 2 fluid rigid group 3 clump1 clump2 clump3 torque * off off off

Description:

Treat one or more sets of atoms as independent rigid bodies. This means that each timestep the total force and torque on each rigid body is computed as the sum of the forces and torques on its constituent particles and the coordinates, velocities, and orientations of the atoms in each body are updated so that the body moves and rotates as a single entity.

Examples of large rigid bodies are a large colloidal particle, or portions of a large biomolecule such as a protein.

Example of small rigid bodies are patchy nanoparticles, such as those modeled in this paper by Sharon Glotzer's group, clumps of granular particles, lipid molecules consiting of one or more point dipoles connected to other spheroids or ellipsoids, and coarse-grain models of nano or colloidal particles consisting of a small number of constituent particles. Note that the fix shake command can also be used to rigidify small molecules of 2, 3, or 4 atoms, e.g. water molecules. That fix treats the constituent atoms as point masses.

The constituent particles within a rigid body can be point particles (the default in LAMMPS) or finite-size particles, such as spheroids and ellipsoids. See the shape command and atom_style granular for more details on these kinds of particles. Finite-size particles contribute differently to the moment of inertia of a rigid body than do point particles. Finite-size particles can also experience torque (e.g. due to frictional granular interactions) and have an orientation. These contributions are accounted for by the fix.

Forces between particles within a body do not contribute to the external force or torque on the body. Thus for computational efficiency, you may wish to turn off pairwise and bond interactions between particles within each rigid body. The neigh_modify exclude and delete_bonds commands are used to do this. For finite-size particles this also means the particles can be highly overlapped when creating the rigid body.

IMPORTANT NOTE: This fix is overkill if you simply want to hold a collection of atoms stationary or have them move with a constant velocity. A simpler way to hold atoms stationary is to not include those atoms in your time integration fix. E.g. use "fix 1 mobile nve" instead of "fix 1 all nve", where "mobile" is the group of atoms that you want to move. You can move atoms with a constant velocity by assigning them an initial velocity (via the velocity command), setting the force on them to 0.0 (via the fix setforce command), and integrating them as usual (e.g. via the fix nve command).

IMPORTANT NOTE: This fix updates the positions and velocities of the rigid atoms with a constant-energy time integration, so you should not update the same atoms via other fixes (e.g. nve, nvt, npt).

Each body must have two or more atoms. An atom can belong to at most one rigid body. Which atoms are in which bodies can be defined via several options.

For bodystyle single the entire fix group of atoms is treated as one rigid body.

For bodystyle molecule, each set of atoms in the fix group with a different molecule ID is treated as a rigid body.

For bodystyle group, each of the listed groups is treated as a separate rigid body. Only atoms that are also in the fix group are included in each rigid body.

By default, each rigid body is acted on by other atoms which induce an external force and torque on its center of mass, causing it to translate and rotate. Components of the external center-of-mass force and torque can be turned off by the force and torque keywords. This may be useful if you wish a body to rotate but not translate, or vice versa, or if you wish it to rotate or translate continuously unaffected by interactions with other particles. Note that if you expect a rigid body not to move or rotate by using these keywords, you must insure its initial center-of-mass translational or angular velocity is 0.0. Otherwise the initial translational or angular momentum the body has will persist.

An xflag, yflag, or zflag set to off means turn off the component of force of torque in that dimension. A setting of on means turn on the component, which is the default. Which rigid body(s) the settings apply to is determined by the first argument of the force and torque keywords. It can be an integer M from 1 to Nbody, where Nbody is the number of rigid bodies defined. A wild-card asterisk can be used in place of, or in conjunction with, the M argument to set the flags for multiple rigid bodies. This takes the form "*" or "*n" or "n*" or "m*n". If N = the number of rigid bodies, then an asterisk with no numeric values means all bodies from 1 to N. A leading asterisk means all bodies from 1 to n (inclusive). A trailing asterisk means all bodies from n to N (inclusive). A middle asterisk means all types from m to n (inclusive). Note that you can use the force or torque keywords as many times as you like. If a particular rigid body has its component flags set multiple times, the settings from the final keyword are used.

For computational efficiency, you may wish to turn off pairwise and bond interactions within each rigid body, as they no longer contribute to the motion. The neigh_modify exclude and delete_bonds commands are used to do this.

For computational efficiency, you should define one fix rigid which includes all the desired rigid bodies. LAMMPS will allow multiple rigid fixes to be defined, but it is more expensive.

This fix uses constant-energy NVE-style integration, so you may need to impose additional constraints to control the temperature of an ensemble of rigid bodies. You can use fix langevin for this purpose to treat the system as effectively immersed in an implicit solvent, e.g. a Brownian dynamics model. Or you can thermostat only the non-rigid atoms that surround one or more rigid bodies (i.e. explicit solvent) by appropriate choice of groups in the compute and fix commands for temperature and thermostatting.

If you calculate a temperature for particles in the rigid bodies, the degrees-of-freedom removed by each rigid body are accounted for in the temperature (and pressure) computation, but only if the temperature group includes all the particles in a particular rigid body.

A 3d rigid body has 6 degrees of freedom (3 translational, 3 rotational), except for a collection of point particles lying on a straight line, which has only 5, e.g a dimer. A 2d rigid body has 3 degrees of freedom (2 translational, 1 rotational).

IMPORTANT NOTE: You may wish to explicitly subtract additional degrees-of-freedom if you use the force and torque keywords to eliminate certain motions of one or more rigid bodies, as LAMMPS does not do this automatically.

The rigid body contribution to the pressure of the system (virial) is also accounted for by this fix.

IMPORTANT NOTE: The periodic image flags of atoms in rigid bodies are modified when the center-of-mass of the rigid body moves across a periodic boundary. They are not incremented/decremented as they would be for non-rigid atoms. This change does not affect dynamics, but means that any diagnostic computation based on the atomic image flag values must be adjusted accordingly. For example, the fix msd will not compute the expected mean-squared displacement for such atoms, and the image flag values written to a dump file will be different than they would be if the atoms were not in a rigid body. It also means that if you have bonds between a pair of rigid bodies and the bond straddles a periodic boundary, you cannot use the replicate command to increase the system size.

Restart, fix_modify, output, run start/stop, minimize info:

No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix.

This fix computes a global array of values which can be accessed by various output commands. The number of rows in the array is equal to the number of rigid bodies. The number of columns is 12. Thus for each rigid body, 12 values are stored: the xyz coords of the center of mass (COM), the xyz components of the COM velocity, the xyz components of the force acting on the COM, and the xyz components of the torque acting on the COM. The force and torque values in the array are not affected by the force and torque keywords in the fix rigid command; they reflect values before any changes are made by those keywords.

The ordering of the rigid bodies (by row in the array) is as follows. For the single keyword there is just one rigid body. For the molecule keyword, the bodies are ordered by ascending molecule ID. For the group keyword, the list of group IDs determines the ordering of bodies.

The array values calculated by this fix are "intensive".

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

Restrictions:

This fix performs an MPI_Allreduce each timestep that is proportional in length to the number of rigid bodies. Hence it will not scale well in parallel if large numbers of rigid bodies are simulated.

If the atoms in a single rigid body initially straddle a periodic boundary, the input data file must define the image flags for each atom correctly, so that LAMMPS can "unwrap" the atoms into a valid rigid body.

Related commands:

delete_bonds, neigh_modify exclude

Default:

The option defaults are force * on on on and torque * on on on meaning all rigid bodies are acted on by center-of-mass force and torque.

(Zhang) Zhang, Glotzer, Nanoletters, 4, 1407-1413 (2004).