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git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@15140 f3b2605a-c512-4ea7-a41b-209d697bcdaa

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doc/html/_sources/fix_ehex.txt
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@ -71,69 +71,33 @@ hundred (LJ and SPC/E water) with little computational overhead.
In both algorithms (non-translational) kinetic energy is constantly
swapped between regions (reservoirs) to impose a heat flux onto the
system. The equations of motion are therefore modified if a particle
*i* is located inside a reservoir
.. image:: Eqs/fix_ehex01.jpg
:align: center
where
.. image:: Eqs/fix_ehex02.jpg
:align: center
We use
.. image:: Eqs/fix_ehex03.jpg
:align: center
to label those parts of the simulation box which are not
thermostatted.) The input parameter *region-ID* of this fix
corresponds to *k*\ . The energy swap is modelled by introducing an
:math:`i` is located inside a reservoir :math:`\Gamma_\ *k*\` where :math:`k>0`. We
use :math:`\Gamma_\ *0*\` to label those parts of the simulation box which
are not thermostatted.) The input parameter *region-ID* of this fix
corresponds to :math:`k`. The energy swap is modelled by introducing an
additional thermostatting force to the equations of motion, such that
the time evolution of coordinates and momenta of particle *i* becomes
:ref:`(Wirnsberger) <Wirnsberger>`
the time evolution of coordinates and momenta of particle :math:`i`
becomes :ref:`(Wirnsberger) <Wirnsberger>`
.. image:: Eqs/fix_ehex04.jpg
.. image:: src/Eqs/fix_ehex_eom.jpg
:align: center
The thermostatting force is given by
.. image:: Eqs/fix_ehex05.jpg
.. image:: src/Eqs/fix_ehex_f.jpg
:align: center
where
.. image:: Eqs/fix_ehex06.jpg
:align: center
is the mass and
.. image:: Eqs/fix_ehex07.jpg
:align: center
maps the particle position to the respective reservoir. The quantity
.. image:: Eqs/fix_ehex08.jpg
:align: center
corresponds to the input parameter *F*\ , which is the energy flux into
the reservoir. Furthermore,
.. image:: Eqs/fix_ehex09.jpg
:align: center
and
.. image:: Eqs/fix_ehex10.jpg
:align: center
denote the non-translational kinetic
energy and the centre of mass velocity of that reservoir. The
thermostatting force does not affect the centre of mass velocities of
the individual reservoirs and the entire simulation box. A derivation
of the equations and details on the numerical implementation with
velocity Verlet in LAMMPS can be found in reference
"(Wirnsberger)"#_Wirnsberger.
where :math:`m_i` is the mass and :math:`k(\mathbf r_i)` maps the particle
position to the respective reservoir. The quantity
:math:`F_*\Gamma_*k(\mathbf r_i)**` corresponds to the input parameter
*F*\ , which is the energy flux into the reservoir. Furthermore,
:math:`K_*\Gamma_*k(\mathbf r_i)**` and :math:`v_*\Gamma_*k(\mathbf r_i)**`
denote the non-translational kinetic energy and the centre of mass
velocity of that reservoir. The thermostatting force does not affect
the centre of mass velocities of the individual reservoirs and the
entire simulation box. A derivation of the equations and details on
the numerical implementation with velocity Verlet in LAMMPS can be
found in reference "(Wirnsberger)"#_Wirnsberger.
.. note::
@ -193,7 +157,7 @@ constraints will be satisfied.
bond distances, which goes to zero with order three in the
timestep. For example, in a simulation of SPC/E water with a timestep
of 2 fs the maximum relative error in the bond distances was found to
be on the order of :c,image(Eqs/fix_ehex07.jpg) for relatively large
be on the order of :math:`10^\ *-7*\` for relatively large
temperature gradients. A higher precision can be achieved by
decreasing the timestep.
@ -220,8 +184,7 @@ was built with that package. See the :ref:`Making LAMMPS <start_3>` section for
Related commands
""""""""""""""""
:doc:`fix heat <fix_heat>`, :doc:`fix thermal/conductivity <fix_thermal_conductivity>`,
:doc:`compute temp <compute_temp>`, :doc:`compute temp/region <compute_temp_region>`
:doc:`fix heat <fix_heat>`, :doc:`fix thermal/conductivity <fix_thermal_conductivity>`, :doc:`compute temp <compute_temp>`, :doc:`compute temp/region <compute_temp_region>`
**Default:** none