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<div class="section" id="fix-gld-command">
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<span id="index-0"></span><h1>fix gld 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">gld</span> <span class="n">Tstart</span> <span class="n">Tstop</span> <span class="n">N_k</span> <span class="n">seed</span> <span class="n">series</span> <span class="n">c_1</span> <span class="n">tau_1</span> <span class="o">...</span> <span class="n">c_N_k</span> <span class="n">tau_N_k</span> <span class="n">keyword</span> <span class="n">values</span> <span class="o">...</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>gld = style name of this fix command</li>
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<li>Tstart,Tstop = desired temperature at start/end of run (temperature units)</li>
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<li>N_k = number of terms in the Prony series representation of the memory kernel</li>
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<li>seed = random number seed to use for white noise (positive integer)</li>
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<li>series = <em>pprony</em> is presently the only available option</li>
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<li>c_k = the weight of the kth term in the Prony series (mass per time units)</li>
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<li>tau_k = the time constant of the kth term in the Prony series (time units)</li>
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<li>zero or more keyword/value pairs may be appended</li>
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</ul>
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<pre class="literal-block">
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keyword = <em>frozen</em> or <em>zero</em>
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<em>frozen</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = initialize extended variables using values drawn from equilibrium distribution at Tstart
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<em>yes</em> = initialize extended variables to zero (i.e., from equilibrium distribution at zero temperature)
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<em>zero</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = do not set total random force to zero
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<em>yes</em> = set total random force to zero
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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="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">gld</span> <span class="mf">1.0</span> <span class="mf">1.0</span> <span class="mi">2</span> <span class="mi">82885</span> <span class="n">pprony</span> <span class="mf">0.5</span> <span class="mf">1.0</span> <span class="mf">1.0</span> <span class="mf">2.0</span> <span class="n">frozen</span> <span class="n">yes</span> <span class="n">zero</span> <span class="n">yes</span>
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<span class="n">fix</span> <span class="mi">3</span> <span class="n">rouse</span> <span class="n">gld</span> <span class="mf">7.355</span> <span class="mf">7.355</span> <span class="mi">4</span> <span class="mi">48823</span> <span class="n">pprony</span> <span class="mf">107.1</span> <span class="mf">0.02415</span> <span class="mf">186.0</span> <span class="mf">0.04294</span> <span class="mf">428.6</span> <span class="mf">0.09661</span> <span class="mi">1714</span> <span class="mf">0.38643</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>Applies Generalized Langevin Dynamics to a group of atoms, as
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described in <a class="reference internal" href="#baczewski"><span class="std std-ref">(Baczewski)</span></a>. This is intended to model the
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effect of an implicit solvent with a temporally non-local dissipative
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force and a colored Gaussian random force, consistent with the
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Fluctuation-Dissipation Theorem. The functional form of the memory
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kernel associated with the temporally non-local force is constrained
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to be a Prony series.</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">While this fix bears many similarities to <a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>, it has one significant
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difference. Namely, <a class="reference internal" href="#"><span class="doc">fix gld</span></a> performs time integration,
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whereas <a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a> does NOT. To this end, the
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specification of another fix to perform time integration, such as <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a>, is NOT necessary.</p>
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</div>
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<p>With this fix active, the force on the <em>j</em>th atom is given as</p>
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<img alt="_images/fix_gld1.jpg" class="align-center" src="_images/fix_gld1.jpg" />
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<p>Here, the first term is representative of all conservative (pairwise,
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bonded, etc) forces external to this fix, the second is the temporally
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non-local dissipative force given as a Prony series, and the third is
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the colored Gaussian random force.</p>
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<p>The Prony series form of the memory kernel is chosen to enable an
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extended variable formalism, with a number of exemplary mathematical
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features discussed in <a class="reference internal" href="#baczewski"><span class="std std-ref">(Baczewski)</span></a>. In particular, 3N_k
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extended variables are added to each atom, which effect the action of
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the memory kernel without having to explicitly evaluate the integral
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over time in the second term of the force. This also has the benefit
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of requiring the generation of uncorrelated random forces, rather than
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correlated random forces as specified in the third term of the force.</p>
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<p>Presently, the Prony series coefficients are limited to being greater
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than or equal to zero, and the time constants are limited to being
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greater than zero. To this end, the value of series MUST be set to
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<em>pprony</em>, for now. Future updates will allow for negative coefficients
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and other representations of the memory kernel. It is with these
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updates in mind that the series option was included.</p>
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<p>The units of the Prony series coefficients are chosen to be mass per
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time to ensure that the numerical integration scheme stably approaches
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the Newtonian and Langevin limits. Details of these limits, and the
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associated numerical concerns are discussed in
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<a class="reference internal" href="#baczewski"><span class="std std-ref">(Baczewski)</span></a>.</p>
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<p>The desired temperature at each timestep is ramped from <em>Tstart</em> to
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<em>Tstop</em> over the course of the next run.</p>
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<p>The random # <em>seed</em> must be a positive integer. A Marsaglia random
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number generator is used. Each processor uses the input seed to
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generate its own unique seed and its own stream of random
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numbers. Thus the dynamics of the system will not be identical on two
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runs on different numbers of processors.</p>
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<hr class="docutils" />
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<p>The keyword/value option pairs are used in the following ways.</p>
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<p>The keyword <em>frozen</em> can be used to specify how the extended variables
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associated with the GLD memory kernel are initialized. Specifying no
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(the default), the initial values are drawn at random from an
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equilibrium distribution at <em>Tstart</em>, consistent with the
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Fluctuation-Dissipation Theorem. Specifying yes, initializes the
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extended variables to zero.</p>
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<p>The keyword <em>zero</em> can be used to eliminate drift due to the
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thermostat. Because the random forces on different atoms are
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independent, they do not sum exactly to zero. As a result, this fix
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applies a small random force to the entire system, and the
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center-of-mass of the system undergoes a slow random walk. If the
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keyword <em>zero</em> is set to <em>yes</em>, the total random force is set exactly
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to zero by subtracting off an equal part of it from each atom in the
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group. As a result, the center-of-mass of a system with zero initial
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momentum will not drift over time.</p>
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<hr class="docutils" />
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<p><strong>Restart, run start/stop, minimize info:</strong></p>
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<p>The instantaneous values of the extended variables are written to
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<a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. Because the state of the random
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number generator is not saved in restart files, this means you cannot
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do “exact” restarts with this fix, where the simulation continues on
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the same as if no restart had taken place. However, in a statistical
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sense, a restarted simulation should produce the same behavior.</p>
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<p>None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options are relevant to this
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fix. No global or per-atom quantities are stored by this fix for
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access by various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>.</p>
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<p>This fix can ramp its target temperature over multiple runs, using the
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<em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. See the
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<a class="reference internal" href="run.html"><span class="doc">run</span></a> command for details of how to do this.</p>
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<p>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 MISC 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_langevin.html"><span class="doc">fix langevin</span></a>, <a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a>,
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<a class="reference internal" href="pair_dpd.html"><span class="doc">pair_style dpd/tstat</span></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default</h2>
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<p>The option defaults are frozen = no, zero = no.</p>
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<hr class="docutils" />
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<p id="baczewski"><strong>(Baczewski)</strong> A.D. Baczewski and S.D. Bond, J. Chem. Phys. 139, 044107 (2013).</p>
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