Update docs: bond_fene_expand

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Richard Berger
2019-11-16 19:07:16 -05:00
parent 5f89fde6bc
commit a3b3b761ef
4 changed files with 18 additions and 126 deletions

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\documentclass[12pt]{article}
\begin{document}
$$
E = -0.5 K R_0^2
\ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] +
4 \epsilon \left[ \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^6 \right] + \epsilon
$$
\end{document}

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.. index:: bond\_style fene/expand
.. index:: bond_style fene/expand
bond\_style fene/expand command
===============================
bond_style fene/expand command
==============================
bond\_style fene/expand/omp command
===================================
bond_style fene/expand/omp command
==================================
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
bond_style fene/expand
@ -18,7 +18,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
bond_style fene/expand
bond_coeff 1 30.0 1.5 1.0 1.0 0.5
@ -28,29 +28,30 @@ Description
The *fene/expand* bond style uses the potential
.. image:: Eqs/bond_fene_expand.jpg
:align: center
.. math::
E = -0.5 K R_0^2 \ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] + 4 \epsilon \left[ \left(\frac{\sigma}{\left(r - \Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r - \Delta\right)}\right)^6 \right] + \epsilon
to define a finite extensible nonlinear elastic (FENE) potential
:ref:`(Kremer) <feneexpand-Kremer>`, used for bead-spring polymer models. The first
term is attractive, the 2nd Lennard-Jones term is repulsive.
The *fene/expand* bond style is similar to *fene* except that an extra
shift factor of delta (positive or negative) is added to *r* to
shift factor of :math:`\Delta` (positive or negative) is added to :math:`r` to
effectively change the bead size of the bonded atoms. The first term
now extends to R0 + delta and the 2nd term is cutoff at 2\^(1/6) sigma
+ delta.
now extends to :math:`R_0 + \Delta` and the 2nd term is cutoff at :math:`2^\frac{1}{6} \sigma + \Delta`.
The following coefficients must be defined for each bond type via the
:doc:`bond\_coeff <bond_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:
* K (energy/distance\^2)
* R0 (distance)
* epsilon (energy)
* sigma (distance)
* delta (distance)
* :math:`K` (energy/distance\^2)
* :math:`R_0` (distance)
* :math:`\epsilon` (energy)
* :math:`\sigma` (distance)
* :math:`\Delta` (distance)
----------
@ -106,8 +107,3 @@ Related commands
**(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html