.. index:: compute gyration/shape

compute gyration/shape command
==============================

Syntax
""""""

.. code-block:: LAMMPS

   compute ID group-ID gyration/shape compute-ID

* ID, group-ID are documented in :doc:`compute <compute>` command
* gyration/shape = style name of this compute command
* compute-ID = ID of :doc:`compute gyration <compute_gyration>` command

Examples
""""""""

.. code-block:: LAMMPS

   compute 1 molecule gyration/shape pe

Description
"""""""""""

Define a computation that calculates the eigenvalues of the gyration tensor of a
group of atoms and three shape parameters. The computation includes all effects
due to atoms passing through periodic boundaries.

The three computed shape parameters are the asphericity, :math:`b`,
the acylindricity, :math:`c`, and the relative shape anisotropy, :math:`k`,
viz.,

.. math::

 b &= l_z - \frac12(l_y+l_x) \\
 c &= l_y - l_x \\
 k &= \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}

where :math:`l_x \le l_y \le l_z` are the three eigenvalues of the gyration
tensor. A general description of these parameters is provided in
:ref:`(Mattice) <Mattice1>` while an application to polymer systems
can be found in :ref:`(Theodorou) <Theodorou1>`.
The asphericity is always non-negative and zero only when the three principal
moments are equal. This zero condition is met when the distribution of
particles is spherically symmetric (hence the name asphericity) but also
whenever the particle distribution is symmetric with respect to the three
coordinate axes (e.g., when the particles are distributed uniformly on a cube,
tetrahedron or other Platonic solid). The acylindricity is always non-negative
and zero only when the two principal moments are equal. This zero condition is
met when the distribution of particles is cylindrically symmetric (hence the
name, acylindricity), but also whenever the particle distribution is symmetric
with respect to the two coordinate axes (e.g., when the
particles are distributed uniformly on a regular prism).
The relative shape anisotropy is bounded between zero (if all points are
spherically symmetric) and one (if all points lie on a line).

.. note::

   The coordinates of an atom contribute to the gyration tensor in
   "unwrapped" form, by using the image flags associated with each atom.
   See the :doc:`dump custom <dump>` command for a discussion of "unwrapped"
   coordinates. See the Atoms section of the :doc:`read_data <read_data>`
   command for a discussion of image flags and how they are set for each
   atom.  You can reset the image flags (e.g., to 0) before invoking this
   compute by using the :doc:`set image <set>` command.

Output info
"""""""""""

This compute calculates a global vector of length 6, which can be accessed by
indices 1--6. The first three values are the eigenvalues of the gyration tensor
followed by the asphericity, the acylindricity and the relative shape
anisotropy.  The computed values can be used by any command that uses global
vector values from a compute as input.  See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.

The vector values calculated by this compute are
"intensive".  The first five vector values will be in
distance\ :math:`2` :doc:`units <units>` while the sixth one is dimensionless.

Restrictions
""""""""""""

This compute is part of the EXTRA-COMPUTE package.  It is only enabled if
LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` page for more info.

Related commands
""""""""""""""""

:doc:`compute gyration <compute_gyration>`

Default
"""""""

none

----------

.. _Mattice1:

**(Mattice)** Mattice, Suter, Conformational Theory of Large Molecules, Wiley, New York, 1994.

.. _Theodorou1:

**(Theodorou)** Theodorou, Suter, Macromolecules, 18, 1206 (1985).
