Merge pull request #1739 from evoyiatzis/shape_chunk

* :doc:`group/group <compute_group_group>` - energy/force between two groups of atoms

* :doc:`gyration <compute_gyration>` - radius of gyration of group of atoms

* :doc:`gyration/chunk <compute_gyration_chunk>` - radius of gyration for each chunk

* :doc:`gyration/shape <compute_gyration_shape>` - compute shape parameters from radius of gyration tensor

* :doc:`gyration/shape <compute_gyration_shape>` - shape parameters from gyration tensor

* :doc:`gyration/shape/chunk <compute_gyration_shape_chunk>` - shape parameters from gyration tensor for each chunk

* :doc:`heat/flux <compute_heat_flux>` - heat flux through a group of atoms

* :doc:`heat/flux/tally <compute_tally>` -

* :doc:`hexorder/atom <compute_hexorder_atom>` - bond orientational order parameter q6

.. parsed-literal::

   compute ID group-ID gyration compute-ID

   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

.. image:: Eqs/compute_shape_parameters.jpg

   :align: center

where lx <= ly <= lz are the three eigenvalues of the gyration tensor.

where lx <= ly <= lz 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

----------

.. _Theodorou:

.. _Mattice1:

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

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

.. _Mattice:

.. _Theodorou1:

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

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

.. _lws: http://lammps.sandia.gov

.. index:: compute gyration/shape/chunk

compute gyration/shape/chunk command

====================================

Syntax

""""""

.. parsed-literal::

   compute ID group-ID gyration/shape/chunk compute-ID

* ID, group-ID are documented in :doc:`compute <compute>` command

* gyration/shape/chunk = style name of this compute command

* compute-ID = ID of :doc:`compute gyration/chunk <compute_gyration_chunk>` command

Examples

""""""""

.. parsed-literal::

   compute 1 molecule gyration/shape/chunk pe

Description

"""""""""""

Define a computation that calculates the eigenvalues of the gyration tensor and 

three shape parameters of multiple chunks of atoms. The computation includes 

all effects due to atoms passing through periodic boundaries.

The three computed shape parameters are the asphericity, b, the acylindricity, c,

and the relative shape anisotropy, k:

.. image:: Eqs/compute_shape_parameters.jpg

   :align: center

where lx <= ly <= lz are the three eigenvalues of the gyration tensor. A general description 

of these parameters is provided in :ref:`(Mattice) <Mattice2>` while an application to polymer systems 

can be found in :ref:`(Theodorou) <Theodorou2>`. 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).

The tensor keyword must be specified in the compute gyration/chunk command.

.. 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 array with six columns, 

which can be accessed by indices 1-6. The first three columns 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 array values from a compute as input.  See the :doc:`Howto output <Howto_output>` doc page for an overview of LAMMPS output

options.

The array calculated by this compute is

"intensive".  The first five columns will be in

distance\^2 :doc:`units <units>` while the sixth one is dimensionless.

Restrictions

""""""""""""

This compute is part of the USER-MISC package.  It is only enabled if

LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` doc page for more info.

Related commands

""""""""""""""""

:doc:`compute gyration/chunk <compute_gyration_chunk>`

:doc:`compute gyration/shape <compute_gyration_shape>`

**Default:** none

----------

.. _Mattice2:

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

.. _Theodorou2:

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

.. _lws: http://lammps.sandia.gov

.. _ld: Manual.html

.. _lc: Commands_all.html

"gyration"_compute_gyration.html,

"gyration/chunk"_compute_gyration_chunk.html,

"gyration/shape"_compute_gyration_shape.html,

"gyration/shape/chunk"_compute_gyration_shape_chunk.html,

"heat/flux"_compute_heat_flux.html,

"heat/flux/tally"_compute_tally.html,

"hexorder/atom"_compute_hexorder_atom.html,