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<div class="section" id="fix-phonon-command">
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<span id="index-0"></span><h1>fix phonon command<a class="headerlink" href="#fix-phonon-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>fix ID group-ID phonon N Noutput Nwait map_file prefix keyword values ...
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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"><em>fix</em></a> command</li>
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<li>phonon = style name of this fix command</li>
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<li>N = measure the Green’s function every this many timesteps</li>
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<li>Noutput = output the dynamical matrix every this many measurements</li>
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<li>Nwait = wait this many timesteps before measuring</li>
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<li>map_file = <em>file</em> or <em>GAMMA</em></li>
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</ul>
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<pre class="literal-block">
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<em>file</em> is the file that contains the mapping info between atom ID and the lattice indices.
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</pre>
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<pre class="literal-block">
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<em>GAMMA</em> flags to treate the whole simulation box as a unit cell, so that the mapping
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info can be generated internally. In this case, dynamical matrix at only the gamma-point
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will/can be evaluated.
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</pre>
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<ul class="simple">
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<li>prefix = prefix for output files</li>
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<li>one or none keyword/value pairs may be appended</li>
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<li>keyword = <em>sysdim</em> or <em>nasr</em></li>
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</ul>
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<pre class="literal-block">
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<em>sysdim</em> value = d
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d = dimension of the system, usually the same as the MD model dimension
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<em>nasr</em> value = n
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n = number of iterations to enforce the acoustic sum rule
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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<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>fix 1 all phonon 20 5000 200000 map.in LJ1D sysdim 1
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fix 1 all phonon 20 5000 200000 map.in EAM3D
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fix 1 all phonon 10 5000 500000 GAMMA EAM0D nasr 100
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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<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
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<p>Calculate the dynamical matrix from molecular dynamics simulations
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based on fluctuation-dissipation theory for a group of atoms.</p>
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<p>Consider a crystal with <em>N</em> unit cells in three dimensions labelled <em>l
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= (l<sub>1</sub>,l<sub>2</sub>,l<sub>3</sub>)</em> where <em>l<sub>i</sub></em>
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are integers. Each unit cell is defined by three linearly independent
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vectors <a href="#id1"><span class="problematic" id="id2">**</span></a>a**<sub>1</sub>, <a href="#id3"><span class="problematic" id="id4">**</span></a>a**<sub>2</sub>, <a href="#id5"><span class="problematic" id="id6">**</span></a>a**<sub>3</sub> forming a
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parallelipiped, containing <em>K</em> basis atoms labelled <em>k</em>.</p>
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<p>Based on fluctuation-dissipation theory, the force constant
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coefficients of the system in reciprocal space are given by
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(<a class="reference internal" href="#campana"><span>Campa&ntilde;&aacute;</span></a> , <a class="reference internal" href="#kong"><span>Kong</span></a>)
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<center><b>&Phi;</b><sub>k&alpha;,k’&beta;</sub>(<b>q</b>) =
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k<sub>B</sub>T
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<b>G</b><sup>-1</sup><sub>k&alpha;,k’&beta;</sub>(<b>q</b>),</center></p>
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<p>where <strong>G</strong> is the Green’s functions coefficients given by</p>
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<center><b>G</b><sub>kα,k'β</sub>(<b>q</b>) =
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<<b>u</b><sub>kα</sub>(<b>q</b>)•<b>u</b><sub>k'β</sub><sup>*</sup>(<b>q</b>)>,</center><p>where <...> denotes the ensemble average, and
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<center>**u**<sub>k&alpha;</sub>(<b>q</b>) = &sum;<sub>l</sub>
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<b>u</b><sub>lk&alpha;</sub> exp(i**qr**<sub>l</sub>)</center></p>
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<p>is the &alpha; component of the atomic displacement for the <em>k*th atom
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in the unit cell in reciprocal space at **q*</em>. In practice, the Green’s
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functions coefficients can also be measured according to the following
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formula,</p>
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<center><b>G</b><sub>kα,k'β</sub>(<b>q</b>) =
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<<b>R</b><sub>kα</sub>(<b>q</b>)•<b>R</b><sup>*</sup><sub>k'β</sub>(<b>q</b>)>
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- <<b>R</b>><sub>kα</sub>(<b>q</b>)•<<b>R</b>><sup>*</sup><sub>k'β</sub>(<b>q</b>),
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</center><p>where <strong>R</strong> is the instantaneous positions of atoms, and <<strong>R</strong>> is the
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averaged atomic positions. It gives essentially the same results as
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the displacement method and is easier to implement in an MD code.</p>
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<p>Once the force constant matrix is known, the dynamical matrix <strong>D</strong> can
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then be obtained by</p>
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<center><b>D</b><sub>kα, k'β</sub>(<b>q</b>) = (m<sub>k</sub>m<sub>k'</sub>)<sup>-1/2</sup> <b>Φ</b><sub>kα,k'β</sub>(<b>q</b>)</center><p>whose eigenvalues are exactly the phonon frequencies at <strong>q</strong>.</p>
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<p>This fix uses positions of atoms in the specified group and calculates
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two-point correlations. To achieve this. the positions of the atoms
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are examined every <em>Nevery</em> steps and are Fourier-transformed into
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reciprocal space, where the averaging process and correlation
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computation is then done. After every <em>Noutput</em> measurements, the
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matrix <strong>G**(**q</strong>) is calculated and inverted to obtain the elastic
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stiffness coefficients. The dynamical matrices are then constructed
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and written to <em>prefix</em>.bin.timestep files in binary format and to the
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file <em>prefix</em>.log for each wavevector <strong>q</strong>.</p>
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<p>A detailed description of this method can be found in
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(<a class="reference internal" href="#kong2011"><span>Kong2011</span></a>).</p>
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<p>The <em>sysdim</em> keyword is optional. If specified with a value smaller
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than the dimensionality of the LAMMPS simulation, its value is used
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for the dynamical matrix calculation. For example, using LAMMPS ot
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model a 2D or 3D system, the phonon dispersion of a 1D atomic chain
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can be computed using <em>sysdim</em> = 1.</p>
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<p>The <em>nasr</em> keyword is optional. An iterative procedure is employed to
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enforce the acoustic sum rule on &Phi; at &Gamma;, and the number
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provided by keyword <em>nasr</em> gives the total number of iterations. For a
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system whose unit cell has only one atom, <em>nasr</em> = 1 is sufficient;
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for other systems, <em>nasr</em> = 10 is typically sufficient.</p>
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<p>The <em>map_file</em> contains the mapping information between the lattice
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indices and the atom IDs, which tells the code which atom sits at
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which lattice point; the lattice indices start from 0. An auxiliary
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code, <a class="reference external" href="http://code.google.com/p/latgen">latgen</a>, can be employed to
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generate the compatible map file for various crystals.</p>
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<p>In case one simulates an aperiodic system, where the whole simulation box
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is treated as a unit cell, one can set <em>map_file</em> as <em>GAMMA</em>, so that the mapping
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info will be generated internally and a file is not needed. In this case, the
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dynamical matrix at only the gamma-point will/can be evaluated. Please keep in
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mind that fix-phonon is designed for cyrstals, it will be inefficient and
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even degrade the performance of lammps in case the unit cell is too large.</p>
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<p>The calculated dynamical matrix elements are written out in
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<a class="reference internal" href="units.html"><em>energy/distance^2/mass</em></a> units. The coordinates for <em>q</em>
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points in the log file is in the units of the basis vectors of the
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corresponding reciprocal lattice.</p>
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</div>
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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<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
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<p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
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<p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
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fix. You can use it to change the temperature compute from thermo_temp
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to the one that reflects the true temperature of atoms in the group.</p>
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<p>No global scalar or vector or per-atom quantities are stored by this
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fix for access by various <span class="xref std std-ref">output commands</span>.</p>
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<p>Instead, this fix outputs its initialization information (including
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mapping information) and the calculated dynamical matrices to the file
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<em>prefix</em>.log, with the specified <em>prefix</em>. The dynamical matrices are
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also written to files <em>prefix</em>.bin.timestep in binary format. These
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can be read by the post-processing tool in tools/phonon to compute the
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phonon density of states and/or phonon dispersion curves.</p>
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<p>No parameter of this fix can be used with the <em>start/stop</em> keywords
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of the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
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<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<p>This fix assumes a crystalline system with periodical lattice. The
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temperature of the system should not exceed the melting temperature to
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keep the system in its solid state.</p>
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<p>This fix is part of the USER-PHONON package. It is only enabled if
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LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
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<p>This fix requires LAMMPS be built with an FFT library. See the
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<a class="reference internal" href="Section_start.html#start-2"><span>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<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
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<p><a class="reference internal" href="compute_msd.html"><em>compute msd</em></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
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<p>The option defaults are sysdim = the same dimemsion as specified by
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the <a class="reference external" href="dimension">dimension</a> command, and nasr = 20.</p>
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<hr class="docutils" />
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<p id="campana"><strong>(Campa&ntilde;&aacute;)</strong> C. Campa&ntilde;&aacute; and
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M. H. M&uuml;ser, <em>Practical Green’s function approach to the
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simulation of elastic semi-infinite solids</em>, <a class="reference external" href="http://dx.doi.org/10.1103/PhysRevB.74.075420">Phys. Rev. B [74], 075420 (2006)</a></p>
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<p id="kong"><strong>(Kong)</strong> L.T. Kong, G. Bartels, C. Campa&ntilde;&aacute;,
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C. Denniston, and Martin H. M&uuml;ser, <em>Implementation of Green’s
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function molecular dynamics: An extension to LAMMPS</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2008.12.035">Computer Physics Communications [180](6):1004-1010 (2009).</a></p>
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<p>L.T. Kong, C. Denniston, and Martin H. M&uuml;ser,
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<em>An improved version of the Green’s function molecular dynamics
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method</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2010.10.006">Computer Physics Communications [182](2):540-541 (2011).</a></p>
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<p id="kong2011"><strong>(Kong2011)</strong> L.T. Kong, <em>Phonon dispersion measured directly from
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molecular dynamics simulations</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2011.04.019">Computer Physics Communications [182](10):2201-2207, (2011).</a></p>
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