Update docs: angle_cosine_shift

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\begin{document}

$$

E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]

$$

\end{document}

.. index:: angle\_style cosine/shift

.. index:: angle_style cosine/shift

angle\_style cosine/shift command

angle_style cosine/shift command

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

angle\_style cosine/shift/omp command

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

angle_style cosine/shift/omp command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/shift

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/shift

   angle_coeff \* 10.0 45.0

   angle_coeff * 10.0 45.0

Description

"""""""""""

The *cosine/shift* angle style uses the potential

.. image:: Eqs/angle_cosine_shift.jpg

   :align: center

.. math::

where theta0 is the equilibrium angle. The potential is bounded

between -Umin and zero. In the neighborhood of the minimum E=- Umin +

Umin/4(theta-theta0)\^2 hence the spring constant is umin/2.

   E = -\frac{U_{\text{min}}}{2} \left[ 1 + \cos(\theta-\theta_0) \right]

where :math:`\theta_0` is the equilibrium angle. The potential is bounded

between :math:`-U_{\text{min}}` and zero. In the neighborhood of the minimum

:math:`E = - U_{\text{min}} + U_{\text{min}}/4(\theta - \theta_0)^2` hence

the spring constant is :math:`\frac{U_{\text{min}}}{2}`.

The following coefficients must be defined for each angle type via the

:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in

the data file or restart files read by the :doc:`read\_data <read_data>`

or :doc:`read\_restart <read_restart>` commands:

* umin (energy)

* theta (angle)

* :math:`U_{\text{min}}` (energy)

* :math:`\theta` (angle)

----------

:doc:`angle\_cosine\_shift\_exp <angle_cosine_shift_exp>`

**Default:** none

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

.. _ld: Manual.html

.. _lc: Commands_all.html

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Commands_all.html)

:line

angle_style cosine/shift command :h3

angle_style cosine/shift/omp command :h3

[Syntax:]

angle_style cosine/shift :pre

[Examples:]

angle_style cosine/shift

angle_coeff * 10.0 45.0 :pre

[Description:]

The {cosine/shift} angle style uses the potential

:c,image(Eqs/angle_cosine_shift.jpg)

where theta0 is the equilibrium angle. The potential is bounded

between -Umin and zero. In the neighborhood of the minimum E=- Umin +

Umin/4(theta-theta0)^2 hence the spring constant is umin/2.

The following coefficients must be defined for each angle type via the

"angle_coeff"_angle_coeff.html command as in the example above, or in

the data file or restart files read by the "read_data"_read_data.html

or "read_restart"_read_restart.html commands:

umin (energy)

theta (angle) :ul

:line

Styles with a {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are

functionally the same as the corresponding style without the suffix.

They have been optimized to run faster, depending on your available

hardware, as discussed on the "Speed packages"_Speed_packages.html doc

page.  The accelerated styles take the same arguments and should

produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,

USER-OMP and OPT packages, respectively.  They are only enabled if

LAMMPS was built with those packages.  See the "Build

package"_Build_package.html doc page for more info.

You can specify the accelerated styles explicitly in your input script

by including their suffix, or you can use the "-suffix command-line

switch"_Run_options.html when you invoke LAMMPS, or you can use the

"suffix"_suffix.html command in your input script.

See the "Speed packages"_Speed_packages.html doc page for more

instructions on how to use the accelerated styles effectively.

:line

[Restrictions:]

This angle style can only be used if LAMMPS was built with the

USER-MISC package.

[Related commands:]

"angle_coeff"_angle_coeff.html,

"angle_cosine_shift_exp"_angle_cosine_shift_exp.html

[Default:] none