105 lines
3.7 KiB
ReStructuredText
105 lines
3.7 KiB
ReStructuredText
.. index:: compute gyration/shape
|
|
|
|
compute gyration/shape command
|
|
==============================
|
|
|
|
Syntax
|
|
""""""
|
|
|
|
.. parsed-literal::
|
|
|
|
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, b, the acylindricity, c,
|
|
and the relative shape anisotropy, k:
|
|
|
|
.. math::
|
|
|
|
c = & l_z - 0.5(l_y+l_x) \\
|
|
b = & 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` <= :math:`l_y` <= :math:`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>` doc 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\^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 <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).
|