109 lines
3.8 KiB
ReStructuredText
109 lines
3.8 KiB
ReStructuredText
.. 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).
|