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git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@15161 f3b2605a-c512-4ea7-a41b-209d697bcdaa

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sjplimp
2016-06-09 21:55:26 +00:00
parent 84de575cc7
commit 5631254f2f
4 changed files with 21 additions and 21 deletions
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12
doc/html/_sources/fix_ehex.txt
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@ -71,8 +71,8 @@ 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
: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
: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
@ -89,9 +89,9 @@ The thermostatting force is given by
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
: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)**`
: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
@ -151,13 +151,13 @@ constraints will be satisfied.
Even if RATTLE is used and the keywords *com* and *constrain*
are both set, the coordinate constraints will not necessarily be
satisfied up to the target precision. The velocity constraints are
satisfied as long as all sites of a cluster are rescaled (keyyword
satisfied as long as all sites of a cluster are rescaled (keyword
*com*\ ) and the cluster does not span adjacent reservoirs. The current
implementation of the eHEX algorithm introduces a small error in the
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 :math:`10^\ *-7*\` 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.

16
doc/html/fix_ehex.html
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@ -187,10 +187,10 @@ hundred (LJ and SPC/E water) with little computational overhead.</p>
<p>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
<span class="math">\(i\)</span> is located inside a reservoir <span class="math">\(\Gamma_\ *k*\` where :math:`k&gt;0\)</span>. We
use <span class="math">\(\Gamma_\ *0*\` to label those parts of the simulation box which
are not thermostatted.) The input parameter *region-ID* of this fix
corresponds to :math:`k\)</span>. The energy swap is modelled by introducing an
<span class="math">\(i\)</span> is located inside a reservoir <span class="math">\(\Gamma_k\)</span> where <span class="math">\(k&gt;0\)</span>. We
use <span class="math">\(\Gamma_0\)</span> to label those parts of the simulation box which
are not thermostatted.) The input parameter <em>region-ID</em> of this fix
corresponds to <span class="math">\(k\)</span>. 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 <span class="math">\(i\)</span>
becomes <a class="reference internal" href="#wirnsberger"><span class="std std-ref">(Wirnsberger)</span></a></p>
@ -199,9 +199,9 @@ becomes <a class="reference internal" href="#wirnsberger"><span class="std std-r
<img alt="_images/fix_ehex_f.jpg" class="align-center" src="_images/fix_ehex_f.jpg" />
<p>where <span class="math">\(m_i\)</span> is the mass and <span class="math">\(k(\mathbf r_i)\)</span> maps the particle
position to the respective reservoir. The quantity
<span class="math">\(F_*\Gamma_*k(\mathbf r_i)**\)</span> corresponds to the input parameter
<span class="math">\(F_{\Gamma_{k(\mathbf r_i)}}\)</span> corresponds to the input parameter
<em>F</em>, which is the energy flux into the reservoir. Furthermore,
<span class="math">\(K_*\Gamma_*k(\mathbf r_i)**\)</span> and <span class="math">\(v_*\Gamma_*k(\mathbf r_i)**\)</span>
<span class="math">\(K_{\Gamma_{k(\mathbf r_i)}}\)</span> and <span class="math">\(v_{\Gamma_{k(\mathbf r_i)}}\)</span>
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
@ -252,13 +252,13 @@ constraints will be satisfied.</p>
<p class="last">Even if RATTLE is used and the keywords <em>com</em> and <em>constrain</em>
are both set, the coordinate constraints will not necessarily be
satisfied up to the target precision. The velocity constraints are
satisfied as long as all sites of a cluster are rescaled (keyyword
satisfied as long as all sites of a cluster are rescaled (keyword
<em>com</em>) and the cluster does not span adjacent reservoirs. The current
implementation of the eHEX algorithm introduces a small error in the
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 :math:<a href="#id1"><span class="problematic" id="id2">`</span></a>10^<em>-7</em>` for relatively large
be on the order of <span class="math">\(10^{-7}\)</span> for relatively large
temperature gradients. A higher precision can be achieved by
decreasing the timestep.</p>
</div>

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12
doc/src/fix_ehex.txt
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@ -61,8 +61,8 @@ 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 \(\Gamma_{k}\) where \(k>0\). We
use \(\Gamma_{0}\) to label those parts of the simulation box which
\(i\) is located inside a reservoir \(\Gamma_k\) where \(k>0\). We
use \(\Gamma_0\) 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
additional thermostatting force to the equations of motion, such that
@ -77,9 +77,9 @@ The thermostatting force is given by
where \(m_i\) is the mass and \(k(\mathbf r_i)\) maps the particle
position to the respective reservoir. The quantity
\(F_{\Gamma_{k(\mathbf r_i)}}\) corresponds to the input parameter
\(F_\{\Gamma_\{k(\mathbf r_i)\}\}\) corresponds to the input parameter
{F}, which is the energy flux into the reservoir. Furthermore,
\(K_{\Gamma_{k(\mathbf r_i)}}\) and \(v_{\Gamma_{k(\mathbf r_i)}}\)
\(K_\{\Gamma_\{k(\mathbf r_i)\}\}\) and \(v_\{\Gamma_\{k(\mathbf r_i)\}\}\)
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
@ -131,13 +131,13 @@ constraints will be satisfied.
NOTE: Even if RATTLE is used and the keywords {com} and {constrain}
are both set, the coordinate constraints will not necessarily be
satisfied up to the target precision. The velocity constraints are
satisfied as long as all sites of a cluster are rescaled (keyyword
satisfied as long as all sites of a cluster are rescaled (keyword
{com}) and the cluster does not span adjacent reservoirs. The current
implementation of the eHEX algorithm introduces a small error in the
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 \(10^{-7}\) for relatively large
be on the order of \(10^\{-7\}\) for relatively large
temperature gradients. A higher precision can be achieved by
decreasing the timestep.