.. index:: compute gyration/chunk

compute gyration/chunk command
==============================

Syntax
""""""

.. code-block:: LAMMPS

   compute ID group-ID gyration/chunk chunkID keyword value ...

* ID, group-ID are documented in :doc:`compute <compute>` command
* gyration/chunk = style name of this compute command
* chunkID = ID of :doc:`compute chunk/atom <compute_chunk_atom>` command
* zero or more keyword/value pairs may be appended
* keyword = *tensor*

  .. parsed-literal::

       *tensor* value = none

Examples
""""""""

.. code-block:: LAMMPS

   compute 1 molecule gyration/chunk molchunk
   compute 2 molecule gyration/chunk molchunk tensor

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

Define a computation that calculates the radius of gyration :math:`R_g` for
multiple chunks of atoms.

In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk).  The ID for this command is specified
as chunkID.  For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin.
See the :doc:`compute chunk/atom <compute_chunk_atom>` and
:doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.

This compute calculates the radius of gyration :math:`R_g` for each chunk,
which includes all effects due to atoms passing through periodic
boundaries.

:math:`R_g` is a measure of the size of a chunk, and is computed by the
formula

.. math::

   R_g^2 = \frac{1}{M} \sum_i m_i (r_i - r_{\text{cm}})^2

where :math:`M` is the total mass of the chunk, :math:`r_{\text{cm}}` is
the center-of-mass position of the chunk, and the sum is over all atoms in the
chunk.

Note that only atoms in the specified group contribute to the
calculation.  The :doc:`compute chunk/atom <compute_chunk_atom>` command
defines its own group; atoms will have a chunk ID = 0 if they are not
in that group, signifying they are not assigned to a chunk, and will
thus also not contribute to this calculation.  You can specify the
"all" group for this command if you simply want to include atoms with
non-zero chunk IDs.

If the *tensor* keyword is specified, then the scalar :math:`R_g` value is not
calculated, but an :math:`R_g` tensor is instead calculated for each chunk.
The formula for the components of the tensor is the same as the above
formula, except that :math:`(r_i - r_{\text{cm}})^2` is replaced by
:math:`(r_{i,x} - r_{\text{cm},x}) \cdot (r_{i,y} - r_{\text{cm},y})` for the
:math:`xy` component, and so on.  The six components of the tensor are
ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.

.. note::

   The coordinates of an atom contribute to :math:`R_g` 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.

The simplest way to output the results of the compute gyration/chunk
calculation to a file is to use the :doc:`fix ave/time <fix_ave_time>`
command, for example:

.. code-block:: LAMMPS

   compute cc1 all chunk/atom molecule
   compute myChunk all gyration/chunk cc1
   fix 1 all ave/time 100 1 100 c_myChunk file tmp.out mode vector

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

This compute calculates a global vector if the *tensor* keyword is not
specified and a global array if it is.  The length of the vector or
number of rows in the array = the number of chunks *Nchunk* as
calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>`
command.  If the *tensor* keyword is specified, the global array has six
columns.  The vector or array can
be accessed by any command that uses global values from a compute as
input.  See the :doc:`Howto output <Howto_output>` page for an
overview of LAMMPS output options.

All the vector or array values calculated by this compute are
"intensive".  The vector or array values will be in distance
:doc:`units <units>`, since they are the square root of values
represented by the formula above.

Restrictions
""""""""""""
 none

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

none


:doc:`compute gyration <compute_gyration>`

Default
"""""""

none
