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<li><a class="reference internal" href="#">fix ti/rs command</a><ul>
<li><a class="reference internal" href="#syntax">Syntax</a></li>
<li><a class="reference internal" href="#description">Description</a></li>
<li><a class="reference internal" href="#restart-fix-modify-output-run-start-stop-minimize-info">Restart, fix_modify, output, run start/stop, minimize info</a></li>
<li><a class="reference internal" href="#related-commands">Related commands</a></li>
<li><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li><a class="reference internal" href="#default">Default</a></li>
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<div class="section" id="fix-ti-rs-command">
<span id="index-0"></span><h1>fix ti/rs command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<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">ti</span><span class="o">/</span><span class="n">rs</span> <span class="n">lambda_initial</span> <span class="n">lambda_final</span> <span class="n">t_switch</span> <span class="n">t_equil</span> <span class="n">keyword</span> <span class="n">value</span> <span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
<li>ti/rs = style name of this fix command</li>
<li>lambda_initial/lambda_final = initial/final values of the coupling parameter</li>
<li>t_switch/t_equil = number of steps of the switching/equilibration procedure</li>
<li>keyword = <em>function</em></li>
</ul>
<pre class="literal-block">
<em>function</em> value = function-ID
function-ID = ID of the switching function (1, 2 or 3)
</pre>
<p><strong>Example:</strong></p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ref</span> <span class="nb">all</span> <span class="n">ti</span><span class="o">/</span><span class="n">rs</span> <span class="mf">50.0</span> <span class="mi">2000</span> <span class="mi">1000</span>
<span class="n">fix</span> <span class="n">vf</span> <span class="n">vacancy</span> <span class="n">ti</span><span class="o">/</span><span class="n">rs</span> <span class="mf">10.0</span> <span class="mi">70000</span> <span class="mi">50000</span> <span class="n">function</span> <span class="mi">2</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>This fix allows you to compute the free energy temperature dependence
by performing a thermodynamic integration procedure known as
Reversible Scaling <a class="reference internal" href="#dekoning99"><span class="std std-ref">(de Koning99,</span></a> <a class="reference internal" href="#dekoning00a"><span class="std std-ref">de Koning00a)</span></a>. The thermodynamic integration is performed
using the nonequilibrium method of Adiabatic Switching
<a class="reference internal" href="fix_ti_spring.html#watanabe"><span class="std std-ref">(Watanabe,</span></a> <a class="reference internal" href="fix_ti_spring.html#dekoning96"><span class="std std-ref">de Koning96)</span></a>.</p>
<p>The forces on the atoms are dynamically scaled during the simulation,
the rescaling is done in the following manner:</p>
<img alt="_images/fix_ti_rs_force.jpg" class="align-center" src="_images/fix_ti_rs_force.jpg" />
<p>where F_int is the total force on the atoms due to the interatomic
potential and lambda is the coupling parameter of the thermodynamic
integration.</p>
<p>The fix acts as follows: during the first <em>t_equil</em> steps after the
fix is defined the value of lambda is <em>lambda_initial</em> , this is the
period to equilibrate the system in the lambda = <em>lambda_initial</em>
state. After this the value of lambda changes continuously from
<em>lambda_initial</em> to <em>lambda_final</em> according to the function defined
using the keyword <em>function</em> (described below), this is done in
<em>t_switch</em> steps. Then comes the second equilibration period of
<em>t_equil</em> to equilibrate the system in the lambda = <em>lambda_final</em>
state. After that the switching back to the lambda = <em>lambda_initial</em>
state is done using <em>t_switch</em> timesteps and following the same
switching function. After this period the value of lambda is kept
equal to <em>lambda_initial</em> indefinitely or until a <a class="reference internal" href="unfix.html"><span class="doc">unfix</span></a>
erase the fix.</p>
<p>The description of thermodynamic integration in both directions is
done in <a class="reference internal" href="#dekoning00b"><span class="std std-ref">de Koning00b</span></a>, the main reason is to try to
eliminate the dissipated heat due to the nonequilibrium process.</p>
<p>The <em>function</em> keyword allows the use of three different switching
rates. The option <em>1</em> results in a constant rescaling where the lambda
parameter changes at a constant rate during the switching time
according to the switching function</p>
<img alt="_images/fix_ti_rs_function_1.jpg" class="align-center" src="_images/fix_ti_rs_function_1.jpg" />
<p>where tau is the scaled time variable t/t_switch. This switching
function has the characteristic that the temperature scaling is faster
at temperatures closer to the final temperature of the procedure. The
option number <em>2</em> performs the switching at a rate defined by the
following switching function</p>
<img alt="_images/fix_ti_rs_function_2.jpg" class="align-center" src="_images/fix_ti_rs_function_2.jpg" />
<p>This switching function has the characteristic that the temperature
scaling occurs at a constant rate during all the procedure. The option
number <em>3</em> performs the switching at a rate defined by the following
switching function</p>
<img alt="_images/fix_ti_rs_function_3.jpg" class="align-center" src="_images/fix_ti_rs_function_3.jpg" />
<p>This switching function has the characteristic that the temperature
scaling is faster at temperatures closer to the initial temperature of
the procedure.</p>
<p>An example script using this command is provided in the
examples/USER/misc/ti directory.</p>
</div>
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>.</p>
<p>This fix computes a global vector quantitie which can be accessed by
various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. The vector has
2 positions, the first one is the coupling parameter lambda and the
second one is the time derivative of lambda. The scalar and vector
values calculated by this fix are &#8220;extensive&#8221;.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command.</p>
<p>The forces due to this fix are imposed during an energy minimization,
invoked by the <a class="reference internal" href="minimize.html"><span class="doc">minimize</span></a> command.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="fix_ti_spring.html"><span class="doc">fix ti/spring</span></a></p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This command is part of the USER-MISC package. It is only enabled if
LAMMPS was built with those packages. See the <span class="xref std std-ref">Making LAMMPS</span> section for more info.</p>
</div>
<div class="section" id="default">
<h2>Default</h2>
<p>The keyword default is function = 1.</p>
<hr class="docutils" />
<p id="dekoning99"><strong>(de Koning 99)</strong> M. de Koning, A. Antonelli and S. Yip, Phys Rev Lett, 83, 3973 (1999).</p>
<p id="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
<p id="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
<p id="dekoning00a"><strong>(de Koning 00a)</strong> M. de Koning, A. Antonelli and S. Yip, J Chem Phys, 115, 11025 (2000).</p>
<p id="dekoning00b"><strong>(de Koning 00b)</strong> M. de Koning et al., Computing in Science &amp; Engineering, 2, 88 (2000).</p>
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