\(\renewcommand{\AA}{\text{Å}}\)

# fix propel/self command

## Syntax

    fix ID group-ID propel/self mode magnitude keyword values

- ID, group-ID are documented in fix command

- propel/self = style name of this fix command

- mode = dipole or velocity or quat

- magnitude = magnitude of self-propulsion force

- zero or one keyword/value pairs may be appended

- keyword = qvector

      qvector value = direction of force in ellipsoid frame
       sx, sy, sz = components of qvector

## Examples

    fix active all propel/self dipole 40.0
    fix active all propel/self velocity 10.0
    fix active all propel/self quat 15.7 qvector 1.0 0.0 0.0

## Description

Add a force to each atom in the group due to a self-propulsion force. The force is given by

\[F_i = f_P e_i\]

where i is the particle the force is being applied to, \(f_P\) is the magnitude of the force, and \(e_i\) is the vector direction of the force. The specification of \(e_i\) is based on which of the three keywords (dipole or velocity or quat) one selects.

For mode dipole, \(e_i\) is just equal to the dipole vectors of the atoms in the group. Therefore, if the dipoles are not unit vectors, the \(e_i\) will not be unit vectors.

Note

If another command changes the magnitude of the dipole, this force will change accordingly (since \(|e_i|\) will change, which is physically equivalent to re-scaling \(f_P\) while keeping \(|e_i|\) constant), and no warning will be provided by LAMMPS. This is almost never what you want, so ensure you are not changing dipole magnitudes with another LAMMPS fix or pair style. Furthermore, self-propulsion forces (almost) always set \(e_i\) to be a unit vector for all times, so it’s best to set all the dipole magnitudes to 1.0 unless you have a good reason not to (see the set command on how to do this).

For mode velocity, \(e_i\) points in the direction of the current velocity (a unit-vector). This can be interpreted as a velocity-dependent friction, as proposed by e.g. (Erdmann).

For mode quat, \(e_i\) points in the direction of a unit vector, oriented in the coordinate frame of the ellipsoidal particles, which defaults to point along the x-direction. This default behavior can be changed by via the quatvec keyword.

The optional quatvec keyword specifies the direction of self-propulsion via a unit vector (sx,sy,sz). The arguments sx, sy, and sz, are defined within the coordinate frame of the atom’s ellipsoid. For instance, for an ellipsoid with long axis along its x-direction, if one wanted the self-propulsion force to also be along this axis, set sx equal to 1 and sy, sz both equal to zero. This keyword may only be specified for mode quat.

Note

In using keyword quatvec, the three arguments sx, sy, and sz will be automatically normalized to components of a unit vector internally to avoid users having to explicitly do so themselves. Therefore, in mode quat, the vectors \(e_i\) will always be of unit length.

Along with adding a force contribution, this fix can also contribute to the virial (pressure) of the system, defined as \(f_P \sum_i <e_i . r_i>/(d V)\), where \(r_i\) is the unwrapped coordinate of particle i in the case of periodic boundary conditions. See (Winkler) for a discussion of this active pressure contribution.

For modes dipole and quat, this fix is by default included in pressure computations.

For mode velocity, this fix is by default not included in pressure computations.

Note

In contrast to equilibrium systems, pressure of active systems in general depends on the geometry of the container. The active pressure contribution as calculated in this fix is only valid for certain boundary conditions (spherical walls, rectangular walls, or periodic boundary conditions). For other geometries, the pressure must be measured via explicit calculation of the force per unit area on a wall, and so one must not calculate it using this fix. (Use fix_modify as described below to turn off the virial contribution of this fix). Again, see (Winkler) for discussion of why this is the case.

Furthermore, when dealing with active systems, the temperature is no longer well defined. Therefore, one should ensure that the virial flag is used in the compute pressure command (turning off temperature contributions).

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

No information about this fix is written to binary restart files.

The fix_modify virial option is supported by this fix to add the contribution due to the added forces on atoms to the system’s virial as part of thermodynamic output. The default is virial yes for keywords dipole and quat. The default is virial no for keyword velocity.

No parameter of this fix can be used with the start/stop keywords of the run command.

## Restrictions

This fix is part of the BROWNIAN package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.

With keyword dipole, this fix only works when the DIPOLE package is also enabled. See the Build package page for more info.

## Related commands

fix align/self, fix efield, fix setforce, fix addforce

## Default

none

(Erdmann) U. Erdmann , W. Ebeling, L. Schimansky-Geier, and F. Schweitzer, Eur. Phys. J. B 15, 105-113, 2000.

(Winkler) Winkler, Wysocki, and Gompper, Soft Matter, 11, 6680 (2015).