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<div class="section" id="fix-ehex-command">
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<span id="index-0"></span><h1>fix ehex command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">ehex</span> <span class="n">nevery</span> <span class="n">F</span> <span class="n">keyword</span> <span class="n">value</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
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<li>ehex = style name of this fix command</li>
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<li>nevery = add/subtract heat every this many timesteps</li>
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<li>F = energy flux into the reservoir (energy/time units)</li>
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<li>zero or more keyword/value pairs may be appended to args</li>
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<li>keyword = <em>region</em> or <em>constrain</em> or <em>com</em> or <em>hex</em></li>
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</ul>
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<pre class="literal-block">
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<em>region</em> value = region-ID
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region-ID = ID of region (reservoir) atoms must be in for added thermostatting force
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<em>constrain</em> value = none
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apply the constraint algorithm (SHAKE or RATTLE) again at the end of the timestep
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<em>com</em> value = none
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rescale all sites of a constrained cluster of atom if its COM is in the reservoir
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<em>hex</em> value = none
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omit the coordinate correction to recover the HEX algorithm
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Lennard-Jones, from examples/in.ehex.lj</span>
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</pre></div>
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</div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">fnve</span> <span class="nb">all</span> <span class="n">nve</span>
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<span class="c1"># specify regions rhot and rcold</span>
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<span class="o">...</span>
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<span class="n">fix</span> <span class="n">fhot</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="mf">0.15</span> <span class="n">region</span> <span class="n">rhot</span>
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<span class="n">fix</span> <span class="n">fcold</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">0.15</span> <span class="n">region</span> <span class="n">rcold</span>
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</pre></div>
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</div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># SPC/E water, from examples/in.ehex.spce</span>
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<span class="n">fix</span> <span class="n">fnve</span> <span class="nb">all</span> <span class="n">nve</span>
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<span class="c1"># specify regions rhot and rcold</span>
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<span class="o">...</span>
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<span class="n">fix</span> <span class="n">fhot</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="mf">0.075</span> <span class="n">region</span> <span class="n">rhot</span> <span class="n">constrain</span> <span class="n">com</span>
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<span class="n">fix</span> <span class="n">fcold</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">0.075</span> <span class="n">region</span> <span class="n">rcold</span> <span class="n">constrain</span> <span class="n">com</span>
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<span class="n">fix</span> <span class="n">frattle</span> <span class="nb">all</span> <span class="n">rattle</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">10</span> <span class="mi">400</span> <span class="mi">0</span> <span class="n">b</span> <span class="mi">1</span> <span class="n">a</span> <span class="mi">1</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>This fix implements the asymmetric version of the enhanced heat
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exchange algorithm <a class="reference internal" href="#wirnsberger"><span class="std std-ref">(Wirnsberger)</span></a>. The eHEX algorithm is
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an extension of the heat exchange algorithm <a class="reference internal" href="#ikeshoji"><span class="std std-ref">(Ikeshoji)</span></a> and
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adds an additional coordinate integration to account for higher-order
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truncation terms in the operator splitting. The original HEX
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algorithm (implemented as <a class="reference internal" href="fix_heat.html"><span class="doc">fix heat</span></a>) is known to
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exhibit a slight energy drift limiting the accessible simulation times
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to a few nanoseconds. This issue is greatly improved by the new
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algorithm decreasing the energy drift by at least a factor of a
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hundred (LJ and SPC/E water) with little computational overhead.</p>
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<p>In both algorithms (non-translational) kinetic energy is constantly
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swapped between regions (reservoirs) to impose a heat flux onto the
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system. The equations of motion are therefore modified if a particle
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<em>i</em> is located inside a reservoir</p>
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<img alt="Eqs/fix_ehex01.jpg" class="align-center" src="Eqs/fix_ehex01.jpg" />
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<p>where</p>
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<img alt="Eqs/fix_ehex02.jpg" class="align-center" src="Eqs/fix_ehex02.jpg" />
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<p>We use</p>
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<img alt="Eqs/fix_ehex03.jpg" class="align-center" src="Eqs/fix_ehex03.jpg" />
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<p>to label those parts of the simulation box which are not
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thermostatted.) The input parameter <em>region-ID</em> of this fix
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corresponds to <em>k</em>. The energy swap is modelled by introducing an
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additional thermostatting force to the equations of motion, such that
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the time evolution of coordinates and momenta of particle <em>i</em> becomes
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<a class="reference internal" href="#wirnsberger"><span class="std std-ref">(Wirnsberger)</span></a></p>
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<img alt="Eqs/fix_ehex04.jpg" class="align-center" src="Eqs/fix_ehex04.jpg" />
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<p>The thermostatting force is given by</p>
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<img alt="Eqs/fix_ehex05.jpg" class="align-center" src="Eqs/fix_ehex05.jpg" />
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<p>where</p>
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<img alt="Eqs/fix_ehex06.jpg" class="align-center" src="Eqs/fix_ehex06.jpg" />
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<p>is the mass and</p>
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<img alt="Eqs/fix_ehex07.jpg" class="align-center" src="Eqs/fix_ehex07.jpg" />
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<p>maps the particle position to the respective reservoir. The quantity</p>
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<img alt="Eqs/fix_ehex08.jpg" class="align-center" src="Eqs/fix_ehex08.jpg" />
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<p>corresponds to the input parameter <em>F</em>, which is the energy flux into
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the reservoir. Furthermore,</p>
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<img alt="Eqs/fix_ehex09.jpg" class="align-center" src="Eqs/fix_ehex09.jpg" />
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<p>and</p>
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<img alt="Eqs/fix_ehex10.jpg" class="align-center" src="Eqs/fix_ehex10.jpg" />
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<p>denote the non-translational kinetic
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energy and the centre of mass velocity of that reservoir. The
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thermostatting force does not affect the centre of mass velocities of
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the individual reservoirs and the entire simulation box. A derivation
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of the equations and details on the numerical implementation with
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velocity Verlet in LAMMPS can be found in reference
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“(Wirnsberger)”#_Wirnsberger.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">This fix only integrates the thermostatting force and must be
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combined with another integrator, such as <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a>, to
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solve the full equations of motion.</p>
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</div>
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<p>This fix is different from a thermostat such as <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a>
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or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a> in that energy is
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added/subtracted continually. Thus if there isn’t another mechanism
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in place to counterbalance this effect, the entire system will heat or
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cool continuously.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">If heat is subtracted from the system too aggressively so that
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the group’s kinetic energy would go to zero, then LAMMPS will halt
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with an error message. Increasing the value of <em>nevery</em> means that
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heat is added/subtracted less frequently but in larger portions. The
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resulting temperature profile will therefore be the same.</p>
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</div>
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<p>This fix will default to <a class="reference internal" href="fix_heat.html"><span class="doc">fix_heat</span></a> (HEX algorithm) if
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the keyword <em>hex</em> is specified.</p>
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<hr class="docutils" />
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<p><strong>Compatibility with SHAKE and RATTLE (rigid molecules)</strong>:</p>
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<p>This fix is compatible with <a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> and <span class="xref doc">fix rattle</span>. If either of these constraining algorithms is
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specified in the input script and the keyword <em>constrain</em> is set, the
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bond distances will be corrected a second time at the end of the
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integration step. It is recommended to specify the keyword <em>com</em> in
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addition to the keyword <em>constrain</em>. With this option all sites of a
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constrained cluster are rescaled, if its centre of mass is located
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inside the region. Rescaling all sites of a cluster by the same factor
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does not introduce any velocity components along fixed bonds. No
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rescaling takes place if the centre of mass lies outside the region.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">You can only use the keyword <em>com</em> along with <em>constrain</em>.</p>
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</div>
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<p>To achieve the highest accuracy it is recommended to use <span class="xref doc">fix rattle</span> with the keywords <em>constrain</em> and <em>com</em> as
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shown in the second example. Only if RATTLE is employed, the velocity
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constraints will be satisfied.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">Even if RATTLE is used and the keywords <em>com</em> and <em>constrain</em>
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are both set, the coordinate constraints will not necessarily be
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satisfied up to the target precision. The velocity constraints are
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satisfied as long as all sites of a cluster are rescaled (keyyword
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<em>com</em>) and the cluster does not span adjacent reservoirs. The current
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implementation of the eHEX algorithm introduces a small error in the
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bond distances, which goes to zero with order three in the
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timestep. For example, in a simulation of SPC/E water with a timestep
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of 2 fs the maximum relative error in the bond distances was found to
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be on the order of :c,image(Eqs/fix_ehex07.jpg) for relatively large
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temperature gradients. A higher precision can be achieved by
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decreasing the timestep.</p>
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</div>
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</div>
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<hr class="docutils" />
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<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
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<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
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<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options
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are relevant to this fix.</p>
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<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
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the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions</h2>
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<p>This fix is part of the RIGID package. It is only enabled if LAMMPS
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was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands</h2>
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<p><a class="reference internal" href="fix_heat.html"><span class="doc">fix heat</span></a>, <a class="reference internal" href="fix_thermal_conductivity.html"><span class="doc">fix thermal/conductivity</span></a>,
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<a class="reference internal" href="compute_temp.html"><span class="doc">compute temp</span></a>, <a class="reference internal" href="compute_temp_region.html"><span class="doc">compute temp/region</span></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<p id="ikeshoji"><strong>(Ikeshoji)</strong> Ikeshoji and Hafskjold, Molecular Physics, 81, 251-261 (1994).</p>
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<p id="wirnsberger"><strong>(Wirnsberger)</strong> Wirnsberger, Frenkel, and Dellago, J Chem Phys, 143,
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124104 (2015).</p>
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