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### fix rigid command

### fix rigid/nve command

### fix rigid/nvt command

Syntax:

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

- ID, group-ID are documented in fix command
- style = rigid or rigid/nve or rigid/nvt
- 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 = langevin or temp or tparam or force or torque

        langevin values = Tstart Tstop Tperiod seed
          Tstart,Tstop = desired temperature at start/stop of run (temperature units)
          Tdamp = temperature damping parameter (time units)
          seed = random number seed to use for white noise (positive integer)
        temp values = Tstart Tstop Tdamp
          Tstart,Tstop = desired temperature at start/stop of run (temperature units)
          Tdamp = temperature damping parameter (time units)
        tparam values = Tchain Titer Torder
          Tchain = length of Nose/Hoover thermostat chain
          Titer = number of thermostat iterations performed
          Torder = 3 or 5 = Yoshida-Suzuki integration parameters
        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 langevin 1.0 1.0 1.0 428984
    fix 1 polychains rigid/nvt molecule temp 1.0 1.0 5.0
    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 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, irregular particles built from line segments (2d) or triangles (3d), 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.

These fixes also update the positions and velocities of the atoms in each rigid body via time integration. The rigid and rigid/nve styles do this via constant NVE integration. The only difference is that the rigid style uses an integration technique based on Richardson iterations. The rigid/nve style uses the methods described in the paper by Miller, which are thought to provide better energy conservation than an iterative approach.

The rigid/nvt style performs constant NVT integration using a Nose/Hoover thermostat with chains as described originally in (Hoover) and (Martyna), which thermostats both the translational and rotational degrees of freedom of the rigid bodies. The rigid-body algorithm used by rigid/nvt is described in the paper by Kamberaj.

IMPORTANT NOTE: You should not update the atoms in rigid bodies via other time-integration fixes (e.g. nve, nvt, npt), or you will be integrating their motion more than once each timestep.

IMPORTANT NOTE: These fixes are 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).

The constituent particles within a rigid body can be point particles (the default in LAMMPS) or finite-size particles, such as spheres or ellipsoids or line segments or triangles. See the atom_style sphere and ellipsoid and line and tri commands 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 these fixes.

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.

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.

IMPORTANT NOTE: To compute the initial center-of-mass position and other properties of each rigid body, the image flags for each atom in the body are used to "unwrap" the atom coordinates. Thus you must insure that these image flags are consistent so that the unwrapping creates a valid rigid body (one where the atoms are close together), particularly if the atoms in a single rigid body straddle a periodic boundary. This means the input data file or restart file must define the image flags for each atom consistently or that you have used the set command to specify them correctly. If a dimension is non-periodic then the image flag of each atom must be 0 in that dimension, else an error is generated.

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 typically 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.

The keyword/value option pairs are used in the following ways.

The langevin and temp and tparam keywords perform thermostatting of the rigid bodies, altering both their translational and rotational degrees of freedom. What is meant by "temperature" of a collection of rigid bodies and how it can be monitored via the fix output is discussed below.

The langevin keyword applies a Langevin thermostat to the constant NVE time integration performed by either the rigid or rigid/nve styles. It cannot be used with the rigid/nvt style. The desired temperature at each timestep is a ramped value during the run from Tstart to Tstop. The Tdamp parameter is specified in time units and determines how rapidly the temperature is relaxed. For example, a value of 100.0 means to relax the temperature in a timespan of (roughly) 100 time units (tau or fmsec or psec - see the units command). The random # seed must be a positive integer. The way the Langevin thermostatting operates is explained on the fix langevin doc page.

The temp and tparam keywords apply a Nose/Hoover thermostat to the NVT time integration performed by the rigid/nvt style. They cannot be used with the rigid or rigid/nve styles. The desired temperature at each timestep is a ramped value during the run from Tstart to Tstop. The Tdamp parameter is specified in time units and determines how rapidly the temperature is relaxed. For example, a value of 100.0 means to relax the temperature in a timespan of (roughly) 100 time units (tau or fmsec or psec - see the units command).

Nose/Hoover chains are used in conjunction with this thermostat. The tparam keyword can optionally be used to change the chain settings used. Tchain is the number of thermostats in the Nose Hoover chain. This value, along with Tdamp can be varied to dampen undesirable oscillations in temperature that can occur in a simulation. As a rule of thumb, increasing the chain length should lead to smaller oscillations.

IMPORTANT NOTE: There are alternate ways to thermostat a system of rigid bodies. You can use fix langevin to treat the individual particles in the rigid bodies as effectively immersed in an implicit solvent, e.g. a Brownian dynamics model. For hybrid systems with both rigid bodies and solvent particles, you can thermostat only the solvent particles that surround one or more rigid bodies by appropriate choice of groups in the compute and fix commands for temperature and thermostatting. The solvent interactions with the rigid bodies should then effectively thermostat the rigid body temperature as well without use of the Langevin or Nose/Hoover options associated with the fix rigid commands.

The keyword/value option pairs are used in the following ways.

If you use a temperature compute with a group that includes particles in 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. 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 altered so that the rigid body can be reconstructed correctly when it straddles periodic boundaries. The atom image flags are not incremented/decremented as they would be for non-rigid atoms as the rigid body crosses periodic boundaries. This means you cannot interpret them as you normally would. For example, 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. Likewise the compute msd will not compute the expected mean-squared displacement for such atoms if the body moves across periodic boundaries. 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. Note that this fix does define image flags for each rigid body, which are incremented when the rigid body crosses a periodic boundary in the usual way. These image flags have the same meaning as atom images (see the "dump" command) and can be accessed and output as described below.

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

No information about the rigid and rigid/nve fixes are written to binary restart files. For style rigid/nvt the state of the Nose/Hoover thermostat is written to binary restart files. See the read_restart command for info on how to re-specify a fix in an input script that reads a restart file, so that the operation of the fix continues in an uninterrupted fashion.

The fix_modify energy option is supported by the rigid/nvt fix to add the energy change induced by the thermostatting to the system's potential energy as part of thermodynamic output.

The rigid and rigid/nve fixes computes a global scalar which can be accessed by various output commands. The scalar value calculated by these fixes is "intensive". The scalar is the current temperature of the collection of rigid bodies. This is averaged over all rigid bodies and their translational and rotational degrees of freedom. The translational energy of a rigid body is 1/2 m v^2, where m = total mass of the body and v = the velocity of its center of mass. The rotational energy of a rigid body is 1/2 I w^2, where I = the moment of inertia tensor of the body and w = its angular velocity. Degrees of freedom constrained by the force and torque keywords are removed from this calculation.

The rigid/nvt fix computes a global scalar which can be accessed by various output commands. The scalar value calculated by the rigid/nvt fix is "extensive". The scalar is the cumulative energy change due to the thermostatting the fix performs.

All of these fixes compute 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 15. Thus for each rigid body, 15 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, the xyz components of the torque acting on the COM, and the xyz image flags of the COM, which have the same meaning as image flags for atom positions (see the "dump" command). 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 these fixes are "intensive", meaning they are independent of the number of atoms in the simulation.

No parameter of these fixes can be used with the start/stop keywords of the run command. These fixes are not invoked during energy minimization.

Restrictions:

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

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. Also Tchain = 10, Titer = 1, Torder = 3.

(Hoover) Hoover, Phys Rev A, 31, 1695 (1985).

(Kamberaj) Kamberaj, Low, Neal, J Chem Phys, 122, 224114 (2005).

(Martyna) Martyna, Klein, Tuckerman, J Chem Phys, 97, 2635 (1992); Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117.

(Miller) Miller, Eleftheriou, Pattnaik, Ndirango, and Newns, J Chem Phys, 116, 8649 (2002).

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