.. index:: compute stress/mop
.. index:: compute stress/mop/profile

compute stress/mop command
==========================

compute stress/mop/profile command
==================================

Syntax
""""""

.. code-block:: LAMMPS

   compute ID group-ID style dir args keywords ...

* ID, group-ID are documented in :doc:`compute <compute>` command
* style = *stress/mop* or *stress/mop/profile*
* dir = *x* or *y* or *z* is the direction normal to the plane
* args = argument specific to the compute style
* keywords = *kin* or *conf* or *total* or *pair* or *bond* or *angle* or *dihedral* (one or more can be specified)

.. parsed-literal::

     *stress/mop* args = pos
       pos = *lower* or *center* or *upper* or coordinate value (distance units) is the position of the plane
     *stress/mop/profile* args = origin delta
       origin = *lower* or *center* or *upper* or coordinate value (distance units) is the position of the first plane
       delta = value (distance units) is the distance between planes

Examples
""""""""

.. code-block:: LAMMPS

   compute 1 all stress/mop x lower total
   compute 1 liquid stress/mop z 0.0 kin conf
   fix 1 all ave/time 10 1000 10000 c_1[*] file mop.time
   fix 1 all ave/time 10 1000 10000 c_1[2] file mop.time

   compute 1 all stress/mop/profile x lower 0.1 total
   compute 1 liquid stress/mop/profile z 0.0 0.25 kin conf
   fix 1 all ave/time 500 20 10000 c_1[*] ave running overwrite file mopp.time mode vector

Description
"""""""""""

Compute *stress/mop* and compute *stress/mop/profile*
calculate components of the local stress tensor using
the method of planes :ref:`(Todd) <mop-todd>`.  Specifically, compute
*stress/mop* calculates 3 components in directions :math:`ix`,
:math:`iy`, and :math:`iz` where :math:`i` is the direction
normal to the plane, while compute *stress/mop/profile* calculates the profile
of the local stress along the :math:`i` direction.

Contrary to methods based on histograms of atomic stress (i.e., using
:doc:`compute stress/atom <compute_stress_atom>`), the method of planes
is compatible with mechanical balance in heterogeneous systems and at
interfaces :ref:`(Todd) <mop-todd>`.

The stress tensor is the sum of a kinetic term and a configurational
term, which are given respectively by Eq. (21) and Eq. (16) in
:ref:`(Todd) <mop-todd>`. For the kinetic part, the algorithm considers
that atoms have crossed the plane if their positions at times
:math:`t-\Delta t` and :math:`t` are one on either side of the plane,
and uses the velocity at time :math:`t-\Delta t/2` given by the velocity
Verlet algorithm.

.. versionadded:: 15Jun2023

   contributions from bond, angle and dihedral potentials

Between one and seven keywords can be used to indicate which contributions
to the stress must be computed: total stress (total), kinetic stress
(kin), configurational stress (conf), stress due to bond stretching
(bond), stress due to angle bending (angle), stress due to dihedral terms (dihedral)
and/or due to pairwise non-bonded interactions (pair).

NOTE 1: The configurational stress is computed considering all pairs of
atoms where at least one atom belongs to group group-ID.

NOTE 2: The local stress does not include any Lennard-Jones tail
corrections to the stress added by the :doc:`pair_modify tail yes
<pair_modify>` command, since those are contributions to the global
system pressure.

NOTE 3: The local stress profile generated by compute
*stress/mop/profile* is similar to that obtained by compute
:doc:`stress/cartesian <compute_stress_cartesian>`.
A key difference is that compute *stress/mop/profile*
considers particles crossing a set of planes, while
*stress/cartesian* computes averages for a set
of small volumes.
Moreover, *stress/cartesian* compute computes the diagonal components of the stress
tensor :math:`P_{xx}`, :math:`P_{yy}`, and :math:`P_{zz}`, while
*stress/mop/profile* computes the components
:math:`P_{ix}`, :math:`P_{iy}`, and :math:`P_{iz}`, where :math:`i` is the
direction normal to the plane.

Output info
"""""""""""

Compute *stress/mop* calculates a global vector (indices starting at 1),
with 3 values for each declared keyword (in the order the keywords have
been declared). For each keyword, the stress tensor components are
ordered as follows: :math:`P_{ix}`, :math:`P_{iy}`, and :math:`P_{iz}`,
where :math:`i` is the direction normal to the plane.

Compute *stress/mop/profile* instead calculates a global array, with 1
column giving the position of the planes where the stress tensor was
computed, and with 3 columns of values for each declared keyword (in the
order the keywords have been declared). For each keyword, the profiles
of stress tensor components are ordered as follows: :math:`P_{ix}`,
:math:`P_{iy}`, and :math:`P_{iz}`.

The values are in pressure :doc:`units <units>`.

The values produced by this compute can be accessed by various
:doc:`output commands <Howto_output>`.  For instance, the results can be
written to a file using the :doc:`fix ave/time <fix_ave_time>`
command. Please see the example in the examples/PACKAGES/mop folder.

Restrictions
""""""""""""

These styles are part of the EXTRA-COMPUTE package. They are only
enabled if LAMMPS is built with that package. See the :doc:`Build
package <Build_package>` doc page on for more info.

The method is implemented for orthogonal simulation boxes whose
size does not change in time, and axis-aligned planes.

Compute *stress/mop* and *stress/mop/profile* do not work with manybody
non-bonded interactions, long range (kspace) interactions and
improper intramolecular interactions. The reason is that the current
implementation requires the class method ``Pair::single()`` to be implemented,
which is not possible for manybody potentials.

The impact of fixes that affect the stress (e.g. fix langevin) is
also not included in the stress computed here.

Related commands
""""""""""""""""

:doc:`compute stress/atom <compute_stress_atom>`,
:doc:`compute pressure <compute_pressure>`,
:doc:`compute stress/cartesian <compute_stress_cartesian>`,
:doc:`compute stress/cylinder <compute_stress_curvilinear>`,
:doc:`compute stress/spherical <compute_stress_curvilinear>`

Default
"""""""

none

----------

.. _mop-todd:

**(Todd)** B. D. Todd, Denis J. Evans, and Peter J. Daivis: "Pressure tensor for inhomogeneous fluids",
Phys. Rev. E 52, 1627 (1995).

.. _Ikeshoji3:

**(Ikeshoji)** Ikeshoji, Hafskjold, Furuholt, Mol Sim, 29, 101-109, (2003).
