.. index:: fix accelerate/cos

fix accelerate/cos command
==========================

Syntax
""""""


.. parsed-literal::

   fix ID group-ID accelerate value

* ID, group-ID are documented in :doc:`fix <fix>` command
* accelerate/cos = style name of this fix command
* value = amplitude of acceleration (in unit of force/mass)


Examples
""""""""


.. code-block:: LAMMPS

   fix 1 all accelerate/cos 0.02e-5

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

Give each atom a acceleration in x-direction based on its z coordinate.
The acceleration is a periodic function along the z-direction:

.. math::

   a_{x}(z) = A \cos \left(\frac{2 \pi z}{l_{z}}\right)

where :math:`A` is the acceleration amplitude, :math:`l_z` is the z-length
of the simulation box.
At steady state, the acceleration generates a velocity profile:

.. math::

   v_{x}(z) = V \cos \left(\frac{2 \pi z}{l_{z}}\right)

The generated velocity amplitude :math:`V` is related to the
shear viscosity :math:`\eta` by:

.. math::

   V = \frac{A \rho}{\eta}\left(\frac{l_{z}}{2 \pi}\right)^{2}


and it can be obtained from ensemble average of the velocity profile:

.. math::

   V = \frac{\sum_i 2 m_{i} v_{i, x} \cos \left(\frac{2 \pi z_i}{l_{z}}\right)}{\sum_i m_{i}}

where :math:`m_i`, :math:`v_{i,x}` and :math:`z_i` are the mass,
x-component velocity and z coordinate of a particle.

The velocity amplitude :math:`V` can be calculated with :doc:`compute viscosity/cos <compute_viscosity_cos>`,
which enables viscosity calculation with periodic perturbation method,
as described by :ref:`Hess<Hess2>`.
Because the applied acceleration drives the system away from equilibration,
the calculated shear viscosity is lower than the intrinsic viscosity
due to the shear-thinning effect.
Extrapolation to zero acceleration should generally be performed to
predict the zero-shear viscosity.
As the shear stress decreases, the signal-noise ratio decreases rapidly,
the simulation time must be extended accordingly to get converged result.

In order to get meaningful result, the group ID of this fix should be all.

----------

**Restart, fix_modify, output, run start/stop, minimize info:**

No information about this fix is written to binary restart files.
None of the fix_modify options are relevant to this fix.
No global or per-atom quantities are stored by this fix for access by various output commands.
No parameter of this fix can be used with the start/stop keywords of the run command.
This fix is not invoked during energy minimization.

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

This command is only available when LAMMPS was built with the USER-MISC package.
Since this fix depends on the z-coordinate of atoms, it cannot be used in 2d simulations.

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

:doc:`compute viscosity/cos <compute_viscosity_cos>`

Default
"""""""
 none

----------

.. _Hess2:

**(Hess)** Hess, B. The Journal of Chemical Physics 2002, 116 (1), 209-217.
