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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 <span class="math">\(N\)</span> unit cells in three dimensions labelled <span class="math">\(l = (l_1, l_2, l_3)\)</span> where <span class="math">\(l_i\)</span>
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are integers. Each unit cell is defined by three linearly independent
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vectors <span class="math">\(\mathbf{a}_1\)</span>, <span class="math">\(\mathbf{a}_2\)</span>, <span class="math">\(\mathbf{a}_3\)</span> forming a
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parallelipiped, containing <span class="math">\(K\)</span> basis atoms labeled <span class="math">\(k\)</span>.</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>Campana</span></a> , <a class="reference internal" href="#kong"><span>Kong</span></a>)</p>
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<div class="math">
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\[\begin{equation}\mathbf{\Phi}_{k\alpha,k^\prime \beta}(\mathbf{q}) = k_B T \mathbf{G}^{-1}_{k\alpha,k^\prime \beta}(\mathbf{q})\end{equation}\]</div>
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<p>where <span class="math">\(\mathbf{G}\)</span> is the Green’s functions coefficients given by</p>
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<div class="math">
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\[\begin{split}\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) = \left< \mathbf{u}_{k\alpha}(\mathbf{q}) \bullet \mathbf{u}_{k^\prime \beta}^*(\mathbf{q}) \right>\end{equation}\end{split}\]</div>
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<p>where <span class="math">\(\left< \ldots \right>\)</span> denotes the ensemble average, and</p>
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<div class="math">
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\[\begin{equation}\mathbf{u}_{k\alpha}(\mathbf{q}) = \sum_l \mathbf{u}_{l k \alpha} \exp{(i\mathbf{qr}_l)}\end{equation}\]</div>
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<p>is the <span class="math">\(\alpha\)</span> component of the atomic displacement for the <span class="math">\(k\)</span> th atom
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in the unit cell in reciprocal space at <span class="math">\(\mathbf{q}\)</span>. 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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<div class="math">
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\[\begin{split}\begin{equation}\mathbf{G}_{k\alpha,k^\prime \beta}(\mathbf{q}) =
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\left< \mathbf{R}_{k \alpha}(\mathbf{q}) \bullet \mathbf{R}^*_{k^\prime \beta}(\mathbf{q}) \right>
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- \left<\mathbf{R}\right>_{k \alpha}(\mathbf{q}) \bullet \left<\mathbf{R}\right>^*_{k^\prime \beta}(\mathbf{q})\end{equation}\end{split}\]</div>
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<p>where <span class="math">\(\mathbf{R}\)</span> is the instantaneous positions of atoms, and <span class="math">\(\left<\mathbf{R}\right>\)</span> 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 <span class="math">\(\mathbf{D}\)</span> can
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then be obtained by</p>
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<div class="math">
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\[\begin{equation}\mathbf{D}_{k\alpha, k^\prime\beta}(\mathbf{q}) =
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(m_k m_{k^\prime})^{-\frac{1}{2}} \mathbf{\Phi}_{k \alpha, k^\prime \beta}(\mathbf{q})\end{equation}\]</div>
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<p>whose eigenvalues are exactly the phonon frequencies at <span class="math">\(\mathbf{q}\)</span>.</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 <span class="math">\(\mathbf{G}(\mathbf{q})\)</span> 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 <span class="math">\(\mathbf{q}\)</span>.</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 <span class="math">\(\Phi\)</span> at <span class="math">\(\Gamma\)</span>, 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>(Campana)</strong> C. Campana and
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M. H. Muser, <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. Campana,
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C. Denniston, and Martin H. Muser, <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. Muser,
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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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