112 lines
3.9 KiB
ReStructuredText
112 lines
3.9 KiB
ReStructuredText
.. index:: compute gyration/shape/chunk
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compute gyration/shape/chunk command
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====================================
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Syntax
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""""""
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.. code-block:: LAMMPS
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compute ID group-ID gyration/shape/chunk compute-ID
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* ID, group-ID are documented in :doc:`compute <compute>` command
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* gyration/shape/chunk = style name of this compute command
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* compute-ID = ID of :doc:`compute gyration/chunk <compute_gyration_chunk>` command
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Examples
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""""""""
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.. code-block:: LAMMPS
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compute 1 molecule gyration/shape/chunk pe
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Description
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"""""""""""
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Define a computation that calculates the eigenvalues of the gyration tensor and
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three shape parameters of multiple chunks of atoms. The computation includes
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all effects due to atoms passing through periodic boundaries.
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The three computed shape parameters are the asphericity, :math:`b`,
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the acylindricity, :math:`c`, and the relative shape anisotropy, :math:`k`,
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viz.,
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.. math::
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b &= l_z - \frac12(l_y+l_x) \\
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c &= l_y - l_x \\
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k &= \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
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where :math:`l_x \le l_y \le l_z` are the three eigenvalues of the gyration
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tensor. A general description of these parameters is provided in
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:ref:`(Mattice) <Mattice2>` while an application to polymer systems
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can be found in :ref:`(Theodorou) <Theodorou2>`. The asphericity is always
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non-negative and zero only when the three principal moments are equal.
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This zero condition is met when the distribution of particles is spherically
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symmetric (hence the name asphericity) but also whenever the particle
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distribution is symmetric with respect to the three coordinate axes (e.g.,
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when the particles are distributed uniformly on a cube, tetrahedron, or other
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Platonic solid). The acylindricity is always non-negative and zero only when
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the two principal moments are equal. This zero condition is met when the
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distribution of particles is cylindrically symmetric (hence the name,
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acylindricity), but also whenever the particle distribution is symmetric with
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respect to the two coordinate axes (e.g., when the particles are distributed
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uniformly on a regular prism). The relative shape anisotropy
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is bounded between 0 (if all points are spherically symmetric) and 1
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(if all points lie on a line).
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The tensor keyword must be specified in the compute gyration/chunk command.
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.. note::
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The coordinates of an atom contribute to the gyration tensor in
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"unwrapped" form, by using the image flags associated with each atom.
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See the :doc:`dump custom <dump>` command for a discussion of "unwrapped"
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coordinates. See the Atoms section of the :doc:`read_data <read_data>`
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command for a discussion of image flags and how they are set for each
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atom. You can reset the image flags (e.g., to 0) before invoking this
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compute by using the :doc:`set image <set>` command.
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Output info
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"""""""""""
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This compute calculates a global array with six columns,
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which can be accessed by indices 1--6. The first three columns are the
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eigenvalues of the gyration tensor followed by the asphericity, the
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acylindricity and the relative shape anisotropy. The computed values can be
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used by any command that uses global array values from a compute as input.
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See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
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output options.
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The array calculated by this compute is
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"intensive". The first five columns will be in
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distance\ :math:`^2` :doc:`units <units>` while the sixth one is dimensionless.
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Restrictions
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""""""""""""
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This compute is part of the EXTRA-COMPUTE package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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:doc:`compute gyration/chunk <compute_gyration_chunk>`
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:doc:`compute gyration/shape <compute_gyration_shape>`
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Default
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"""""""
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none
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----------
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.. _Mattice2:
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**(Mattice)** Mattice, Suter, Conformational Theory of Large Molecules, Wiley, New York, 1994.
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.. _Theodorou2:
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**(Theodorou)** Theodorou, Suter, Macromolecules, 18, 1206 (1985).
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