# Finite-size spherical and aspherical particles

Typical MD models treat atoms or particles as point masses. Sometimes it
is desirable to have a model with finite-size particles such as
spheroids or ellipsoids or generalized aspherical bodies. The difference
is that such particles have a moment of inertia, rotational energy, and
angular momentum. Rotation is induced by torque coming from interactions
with other particles.

LAMMPS has several options for running simulations with these kinds of
particles. The following aspects are discussed in turn:

-   atom styles
-   pair potentials
-   time integration
-   computes, thermodynamics, and dump output
-   rigid bodies composed of finite-size particles

Example input scripts for these kinds of models are in the body,
colloid, dipole, ellipse, line, peri, pour, and tri directories of the
[examples directory](Examples) in the LAMMPS distribution.

## Atom styles

There are several [atom styles](atom_style) that allow for definition of
finite-size particles: sphere, dipole, ellipsoid, line, tri, peri, and
body.

The sphere style defines particles that are spheroids and each particle
can have a unique diameter and mass (or density). These particles store
an angular velocity (omega) and can be acted upon by torque. The \"set\"
command can be used to modify the diameter and mass of individual
particles, after then are created.

The dipole style does not actually define finite-size particles, but is
often used in conjunction with spherical particles, via a command like

``` LAMMPS
atom_style hybrid sphere dipole
```

This is because when dipoles interact with each other, they induce
torques, and a particle must be finite-size (i.e. have a moment of
inertia) in order to respond and rotate. See the [atom_style
dipole](atom_style) command for details. The \"set\" command can be used
to modify the orientation and length of the dipole moment of individual
particles, after then are created.

The ellipsoid style defines particles that are ellipsoids and thus can
be aspherical. Each particle has a shape, specified by 3 diameters, and
mass (or density). These particles store an angular momentum and their
orientation (quaternion), and can be acted upon by torque. They do not
store an angular velocity (omega), which can be in a different direction
than angular momentum, rather they compute it as needed. The \"set\"
command can be used to modify the diameter, orientation, and mass of
individual particles, after then are created. It also has a brief
explanation of what quaternions are.

The line style defines line segment particles with two end points and a
mass (or density). They can be used in 2d simulations, and they can be
joined together to form rigid bodies which represent arbitrary polygons.

The tri style defines triangular particles with three corner points and
a mass (or density). They can be used in 3d simulations, and they can be
joined together to form rigid bodies which represent arbitrary particles
with a triangulated surface.

The peri style is used with [Peridynamic models](pair_peri) and defines
particles as having a volume, that is used internally in the [pair_style
peri](pair_peri) potentials.

The body style allows for definition of particles which can represent
complex entities, such as surface meshes of discrete points, collections
of sub-particles, deformable objects, etc. The body style is discussed
in more detail on the [Howto body](Howto_body) doc page.

Note that if one of these atom styles is used (or multiple styles via
the [atom_style hybrid](atom_style) command), not all particles in the
system are required to be finite-size or aspherical.

For example, in the ellipsoid style, if the 3 shape parameters are set
to the same value, the particle will be a sphere rather than an
ellipsoid. If the 3 shape parameters are all set to 0.0 or if the
diameter is set to 0.0, it will be a point particle. In the line or tri
style, if the lineflag or triflag is specified as 0, then it will be a
point particle.

Some of the pair styles used to compute pairwise interactions between
finite-size particles also compute the correct interaction with point
particles as well, e.g. the interaction between a point particle and a
finite-size particle or between two point particles. If necessary,
[pair_style hybrid](pair_hybrid) can be used to ensure the correct
interactions are computed for the appropriate style of interactions.
Likewise, using groups to partition particles (ellipsoids versus spheres
versus point particles) will allow you to use the appropriate time
integrators and temperature computations for each class of particles.
See the doc pages for various commands for details.

Also note that for [2d simulations](dimension), atom styles sphere and
ellipsoid still use 3d particles, rather than as circular disks or
ellipses. This means they have the same moment of inertia as the 3d
object. When temperature is computed, the correct degrees of freedom are
used for rotation in a 2d versus 3d system.

## Pair potentials

When a system with finite-size particles is defined, the particles will
only rotate and experience torque if the force field computes such
interactions. These are the various [pair styles](pair_style) that
generate torque:

-   [pair_style gran/history](pair_gran)
-   [pair_style gran/hertz](pair_gran)
-   [pair_style gran/no_history](pair_gran)
-   [pair_style dipole/cut](pair_dipole)
-   [pair_style gayberne](pair_gayberne)
-   [pair_style resquared](pair_resquared)
-   [pair_style brownian](pair_brownian)
-   [pair_style lubricate](pair_lubricate)
-   [pair_style line/lj](pair_line_lj)
-   [pair_style tri/lj](pair_tri_lj)
-   [pair_style body/nparticle](pair_body_nparticle)

The granular pair styles are used with spherical particles. The dipole
pair style is used with the dipole atom style, which could be applied to
spherical or ellipsoidal particles. The GayBerne and REsquared
potentials require ellipsoidal particles, though they will also work if
the 3 shape parameters are the same (a sphere). The Brownian and
lubrication potentials are used with spherical particles. The line, tri,
and body potentials are used with line segment, triangular, and body
particles respectively.

## Time integration

There are several fixes that perform time integration on finite-size
spherical particles, meaning the integrators update the rotational
orientation and angular velocity or angular momentum of the particles:

-   [fix nve/sphere](fix_nve_sphere)
-   [fix nvt/sphere](fix_nvt_sphere)
-   [fix npt/sphere](fix_npt_sphere)

Likewise, there are 3 fixes that perform time integration on ellipsoidal
particles:

-   [fix nve/asphere](fix_nve_asphere)
-   [fix nvt/asphere](fix_nvt_asphere)
-   [fix npt/asphere](fix_npt_asphere)

The advantage of these fixes is that those which thermostat the
particles include the rotational degrees of freedom in the temperature
calculation and thermostatting. The [fix langevin](fix_langevin) command
can also be used with its *omgea* or *angmom* options to thermostat the
rotational degrees of freedom for spherical or ellipsoidal particles.
Other thermostatting fixes only operate on the translational kinetic
energy of finite-size particles.

These fixes perform constant NVE time integration on line segment,
triangular, and body particles:

-   [fix nve/line](fix_nve_line)
-   [fix nve/tri](fix_nve_tri)
-   [fix nve/body](fix_nve_body)

Note that for mixtures of point and finite-size particles, these
integration fixes can only be used with [groups](group) which contain
finite-size particles.

## Computes, thermodynamics, and dump output

There are several computes that calculate the temperature or rotational
energy of spherical or ellipsoidal particles:

-   [compute temp/sphere](compute_temp_sphere)
-   [compute temp/asphere](compute_temp_asphere)
-   [compute erotate/sphere](compute_erotate_sphere)
-   [compute erotate/asphere](compute_erotate_asphere)

These include rotational degrees of freedom in their computation. If you
wish the thermodynamic output of temperature or pressure to use one of
these computes (e.g. for a system entirely composed of finite-size
particles), then the compute can be defined and the
[thermo_modify](thermo_modify) command used. Note that by default
thermodynamic quantities will be calculated with a temperature that only
includes translational degrees of freedom. See the
[thermo_style](thermo_style) command for details.

These commands can be used to output various attributes of finite-size
particles:

-   [dump custom](dump)
-   [compute property/atom](compute_property_atom)
-   [dump local](dump)
-   [compute body/local](compute_body_local)

Attributes include the dipole moment, the angular velocity, the angular
momentum, the quaternion, the torque, the end-point and corner-point
coordinates (for line and tri particles), and sub-particle attributes of
body particles.

## Rigid bodies composed of finite-size particles

The [fix rigid](fix_rigid) command treats a collection of particles as a
rigid body, computes its inertia tensor, sums the total force and torque
on the rigid body each timestep due to forces on its constituent
particles, and integrates the motion of the rigid body.

If any of the constituent particles of a rigid body are finite-size
particles (spheres or ellipsoids or line segments or triangles), then
their contribution to the inertia tensor of the body is different than
if they were point particles. This means the rotational dynamics of the
rigid body will be different. Thus a model of a dimer is different if
the dimer consists of two point masses versus two spheroids, even if the
two particles have the same mass. Finite-size particles that experience
torque due to their interaction with other particles will also impart
that torque to a rigid body they are part of.

See the \"fix rigid\" command for example of complex rigid-body models
it is possible to define in LAMMPS.

Note that the [fix shake](fix_shake) command can also be used to treat
2, 3, or 4 particles as a rigid body, but it always assumes the
particles are point masses.

Also note that body particles cannot be modeled with the [fix
rigid](fix_rigid) command. Body particles are treated by LAMMPS as
single particles, though they can store internal state, such as a list
of sub-particles. Individual body particles are typically treated as
rigid bodies, and their motion integrated with a command like [fix
nve/body](fix_nve_body). Interactions between pairs of body particles
are computed via a command like [pair_style
body/nparticle](pair_body_nparticle).