Update docs: bond_fene_expand

\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}

.. 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

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   bond_style fene/expand

   bond_coeff 1 30.0 1.5 1.0 1.0 0.5

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)

----------

**(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990).

.. _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

bond_style fene/expand command :h3

bond_style fene/expand/omp command :h3

[Syntax:]

bond_style fene/expand :pre

[Examples:]

bond_style fene/expand

bond_coeff 1 30.0 1.5 1.0 1.0 0.5 :pre

[Description:]

The {fene/expand} bond style uses the potential

:c,image(Eqs/bond_fene_expand.jpg)

to define a finite extensible nonlinear elastic (FENE) potential

"(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

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.

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

"bond_coeff"_bond_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:

K (energy/distance^2)

R0 (distance)

epsilon (energy)

sigma (distance)

delta (distance) :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 bond style can only be used if LAMMPS was built with the MOLECULE

package.  See the "Build package"_Build_package.html doc page for more

info.

You typically should specify "special_bonds fene"_special_bonds.html

or "special_bonds lj/coul 0 1 1"_special_bonds.html to use this bond

style.  LAMMPS will issue a warning it that's not the case.

[Related commands:]

"bond_coeff"_bond_coeff.html, "delete_bonds"_delete_bonds.html

[Default:] none

:line

:link(feneexpand-Kremer)

[(Kremer)] Kremer, Grest, J Chem Phys, 92, 5057 (1990).