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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li>compute heat/flux command</li>
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<div class="section" id="compute-heat-flux-command">
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<span id="index-0"></span><h1>compute heat/flux 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">compute</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">heat</span><span class="o">/</span><span class="n">flux</span> <span class="n">ke</span><span class="o">-</span><span class="n">ID</span> <span class="n">pe</span><span class="o">-</span><span class="n">ID</span> <span class="n">stress</span><span class="o">-</span><span class="n">ID</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="compute.html"><span class="doc">compute</span></a> command</li>
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<li>heat/flux = style name of this compute command</li>
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<li>ke-ID = ID of a compute that calculates per-atom kinetic energy</li>
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<li>pe-ID = ID of a compute that calculates per-atom potential energy</li>
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<li>stress-ID = ID of a compute that calculates per-atom stress</li>
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</ul>
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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">compute</span> <span class="n">myFlux</span> <span class="nb">all</span> <span class="n">heat</span><span class="o">/</span><span class="n">flux</span> <span class="n">myKE</span> <span class="n">myPE</span> <span class="n">myStress</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>Define a computation that calculates the heat flux vector based on
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contributions from atoms in the specified group. This can be used by
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itself to measure the heat flux into or out of a reservoir of atoms,
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or to calculate a thermal conductivity using the Green-Kubo formalism.</p>
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<p>See the <a class="reference internal" href="fix_thermal_conductivity.html"><span class="doc">fix thermal/conductivity</span></a>
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command for details on how to compute thermal conductivity in an
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alternate way, via the Muller-Plathe method. See the <a class="reference internal" href="fix_heat.html"><span class="doc">fix heat</span></a> command for a way to control the heat added or
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subtracted to a group of atoms.</p>
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<p>The compute takes three arguments which are IDs of other
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<a class="reference internal" href="compute.html"><span class="doc">computes</span></a>. One calculates per-atom kinetic energy
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(<em>ke-ID</em>), one calculates per-atom potential energy (<em>pe-ID)</em>, and the
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third calcualtes per-atom stress (<em>stress-ID</em>). These should be
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defined for the same group used by compute heat/flux, though LAMMPS
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does not check for this.</p>
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<p>The Green-Kubo formulas relate the ensemble average of the
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auto-correlation of the heat flux J to the thermal conductivity kappa:</p>
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<img alt="_images/heat_flux_J.jpg" class="align-center" src="_images/heat_flux_J.jpg" />
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<img alt="_images/heat_flux_k.jpg" class="align-center" src="_images/heat_flux_k.jpg" />
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<p>Ei in the first term of the equation for J is the per-atom energy
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(potential and kinetic). This is calculated by the computes <em>ke-ID</em>
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and <em>pe-ID</em>. Si in the second term of the equation for J is the
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per-atom stress tensor calculated by the compute <em>stress-ID</em>. The
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tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a
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vector. Note that as discussed below, the 1/V scaling factor in the
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equation for J is NOT included in the calculation performed by this
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compute; you need to add it for a volume appropriate to the atoms
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included in the calculation.</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">The <a class="reference internal" href="compute_pe_atom.html"><span class="doc">compute pe/atom</span></a> and <a class="reference internal" href="compute_stress_atom.html"><span class="doc">compute stress/atom</span></a> commands have options for which
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terms to include in their calculation (pair, bond, etc). The heat
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flux calculation will thus include exactly the same terms. Normally
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you should use <a class="reference internal" href="compute_stress_atom.html"><span class="doc">compute stress/atom virial</span></a>
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so as not to include a kinetic energy term in the heat flux.</p>
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</div>
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<p>This compute calculates 6 quantities and stores them in a 6-component
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vector. The first 3 components are the x, y, z components of the full
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heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x,
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y, z components of just the convective portion of the flux, i.e. the
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first term in the equation for J above.</p>
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<hr class="docutils" />
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<p>The heat flux can be output every so many timesteps (e.g. via the
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<a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style custom</span></a> command). Then as a
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post-processing operation, an autocorrelation can be performed, its
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integral estimated, and the Green-Kubo formula above evaluated.</p>
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<p>The <a class="reference internal" href="fix_ave_correlate.html"><span class="doc">fix ave/correlate</span></a> command can calclate
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the autocorrelation. The trap() function in the
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<a class="reference internal" href="variable.html"><span class="doc">variable</span></a> command can calculate the integral.</p>
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<p>An example LAMMPS input script for solid Ar is appended below. The
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result should be: average conductivity ~0.29 in W/mK.</p>
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<hr class="docutils" />
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<p><strong>Output info:</strong></p>
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<p>This compute calculates a global vector of length 6 (total heat flux
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vector, followed by convective heat flux vector), which can be
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accessed by indices 1-6. These values can be used by any command that
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uses global vector values from a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">this section</span></a> for an overview of LAMMPS output
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options.</p>
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<p>The vector values calculated by this compute are “extensive”, meaning
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they scale with the number of atoms in the simulation. They can be
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divided by the appropriate volume to get a flux, which would then be
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an “intensive” value, meaning independent of the number of atoms in
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the simulation. Note that if the compute is “all”, then the
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appropriate volume to divide by is the simulation box volume.
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However, if a sub-group is used, it should be the volume containing
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those atoms.</p>
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<p>The vector values will be in energy*velocity <a class="reference internal" href="units.html"><span class="doc">units</span></a>. Once
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divided by a volume the units will be that of flux, namely
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energy/area/time <a class="reference internal" href="units.html"><span class="doc">units</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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<blockquote>
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<div>none</div></blockquote>
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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_thermal_conductivity.html"><span class="doc">fix thermal/conductivity</span></a>,
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<a class="reference internal" href="fix_ave_correlate.html"><span class="doc">fix ave/correlate</span></a>,
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<a class="reference internal" href="variable.html"><span class="doc">variable</span></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Sample LAMMPS input script for thermal conductivity of solid Ar</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>units real
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variable T equal 70
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variable V equal vol
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variable dt equal 4.0
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variable p equal 200 # correlation length
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variable s equal 10 # sample interval
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variable d equal $p*$s # dump interval
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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"># convert from LAMMPS real units to SI</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>variable kB equal 1.3806504e-23 # [J/K] Boltzmann
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variable kCal2J equal 4186.0/6.02214e23
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variable A2m equal 1.0e-10
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variable fs2s equal 1.0e-15
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variable convert equal ${kCal2J}*${kCal2J}/${fs2s}/${A2m}
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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"># setup problem</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>dimension 3
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boundary p p p
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lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
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region box block 0 4 0 4 0 4
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create_box 1 box
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create_atoms 1 box
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mass 1 39.948
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pair_style lj/cut 13.0
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pair_coeff * * 0.2381 3.405
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timestep ${dt}
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thermo $d
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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"># equilibration and thermalization</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>velocity all create $T 102486 mom yes rot yes dist gaussian
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fix NVT all nvt temp $T $T 10 drag 0.2
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run 8000
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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"># thermal conductivity calculation, switch to NVE if desired</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">#unfix NVT</span>
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<span class="c1">#fix NVE all nve</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>reset_timestep 0
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compute myKE all ke/atom
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compute myPE all pe/atom
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compute myStress all stress/atom NULL virial
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compute flux all heat/flux myKE myPE myStress
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variable Jx equal c_flux[1]/vol
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variable Jy equal c_flux[2]/vol
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variable Jz equal c_flux[3]/vol
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fix JJ all ave/correlate $s $p $d &
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c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
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variable scale equal ${convert}/${kB}/$T/$T/$V*$s*${dt}
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variable k11 equal trap(f_JJ[3])*${scale}
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variable k22 equal trap(f_JJ[4])*${scale}
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variable k33 equal trap(f_JJ[5])*${scale}
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thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
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run 100000
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variable k equal (v_k11+v_k22+v_k33)/3.0
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variable ndens equal count(all)/vol
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print "average conductivity: $k[W/mK] @ $T K, ${ndens} /A^3"
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</pre></div>
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</div>
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