Update docs: bond_quartic

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\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

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   bond_style quartic

   bond_coeff 2 1200 -0.55 0.25 1.3 34.6878

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

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.

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"

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: 

.. 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

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

:doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>`

**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

bond_style quartic command :h3

bond_style quartic/omp command :h3

[Syntax:]

bond_style quartic :pre

[Examples:]

bond_style quartic

bond_coeff 2 1200 -0.55 0.25 1.3 34.6878 :pre

[Description:]

The {quartic} bond style uses the potential

:c,image(Eqs/bond_quartic.jpg)

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

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

"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^4)

B1 (distance)

B2 (distance)

Rc (distance)

U0 (energy) :ul

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 "bond_coeff"_bond_coeff.html command, but

you will need to choose them carefully so they form a suitable bond

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"

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

are no longer bonded.

LAMMPS does the second task via a computational sleight-of-hand.  It

subtracts the pairwise interaction as part of the bond computation.

When the bond breaks, the subtraction stops.  For this to work, the

pairwise interaction must always be computed by the

"pair_style"_pair_style.html command, whether the bond is broken or

not.  This means that "special_bonds"_special_bonds.html must be set

to 1,1,1, as indicated as a restriction below.

Note that when bonds are dumped to a file via the "dump

local"_dump.html command, bonds with type 0 are not included.  The

"delete_bonds"_delete_bonds.html command can also be used to query the

status of broken bonds or permanently delete them, e.g.:

delete_bonds all stats

delete_bonds all bond 0 remove :pre

: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.

The {quartic} style requires that "special_bonds"_special_bonds.html

parameters be set to 1,1,1.  Three- and four-body interactions (angle,

dihedral, etc) cannot be used with {quartic} bonds.

[Related commands:]

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

[Default:] none