Update docs: bond_quartic

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Richard Berger
2019-11-16 22:27:08 -05:00
parent 2150415888
commit d13ec0d098
4 changed files with 34 additions and 153 deletions

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\documentclass[12pt]{article}
\begin{document}
$$
E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 +
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$
\end{document}

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.. index:: bond\_style quartic
.. index:: bond_style quartic
bond\_style quartic command
===========================
bond_style quartic command
==========================
bond\_style quartic/omp command
===============================
bond_style quartic/omp command
==============================
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
bond_style quartic
@ -18,7 +18,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
bond_style quartic
bond_coeff 2 1200 -0.55 0.25 1.3 34.6878
@ -28,11 +28,12 @@ Description
The *quartic* bond style uses the potential
.. image:: Eqs/bond_quartic.jpg
:align: center
.. math::
E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 + 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
to define a bond that can be broken as the simulation proceeds (e.g.
due to a polymer being stretched). The sigma and epsilon used in the
due to a polymer being stretched). The :math:`\sigma` and :math:`\epsilon` used in the
LJ portion of the formula are both set equal to 1.0 by LAMMPS.
The following coefficients must be defined for each bond type via the
@ -40,23 +41,31 @@ The following coefficients must be defined for each bond type via the
the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands:
* K (energy/distance\^4)
* B1 (distance)
* B2 (distance)
* Rc (distance)
* U0 (energy)
* :math:`K` (energy/distance\^4)
* :math:`B_1` (distance)
* :math:`B_2` (distance)
* :math:`R_c` (distance)
* :math:`U_0` (energy)
This potential was constructed to mimic the FENE bond potential for
coarse-grained polymer chains. When monomers with sigma = epsilon =
1.0 are used, the following choice of parameters gives a quartic
potential that looks nearly like the FENE potential: K = 1200, B1 =
-0.55, B2 = 0.25, Rc = 1.3, and U0 = 34.6878. Different parameters
can be specified using the :doc:`bond\_coeff <bond_coeff>` command, but
you will need to choose them carefully so they form a suitable bond
potential.
coarse-grained polymer chains. When monomers with :math:`\sigma = \epsilon = 1.0`
are used, the following choice of parameters gives a quartic potential that
looks nearly like the FENE potential:
Rc is the cutoff length at which the bond potential goes smoothly to a
local maximum. If a bond length ever becomes > Rc, LAMMPS "breaks"
.. math::
K &= 1200 \\
B_1 &= -0.55 \\
B_2 &= 0.25 \\
R_c &= 1.3 \\
U_0 &= 34.6878
Different parameters can be specified using the :doc:`bond_coeff <bond_coeff>`
command, but you will need to choose them carefully so they form a suitable
bond potential.
:math:`R_c` is the cutoff length at which the bond potential goes smoothly to a
local maximum. If a bond length ever becomes :math:`> R_c`, LAMMPS "breaks"
the bond, which means two things. First, the bond potential is turned
off by setting its type to 0, and is no longer computed. Second, a
pairwise interaction between the two atoms is turned on, since they
@ -75,7 +84,7 @@ Note that when bonds are dumped to a file via the :doc:`dump local <dump>` comma
status of broken bonds or permanently delete them, e.g.:
.. parsed-literal::
.. code-block:: LAMMPS
delete_bonds all stats
delete_bonds all bond 0 remove
@ -124,8 +133,3 @@ Related commands
:doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>`
**Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html