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<div class="section" id="fix-thermal-conductivity-command">
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<span id="index-0"></span><h1>fix thermal/conductivity 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">thermal</span><span class="o">/</span><span class="n">conductivity</span> <span class="n">N</span> <span class="n">edim</span> <span class="n">Nbin</span> <span class="n">keyword</span> <span class="n">value</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>thermal/conductivity = style name of this fix command</li>
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<li>N = perform kinetic energy exchange every N steps</li>
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<li>edim = <em>x</em> or <em>y</em> or <em>z</em> = direction of kinetic energy transfer</li>
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<li>Nbin = # of layers in edim direction (must be even number)</li>
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>swap</em></li>
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</ul>
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<pre class="literal-block">
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<em>swap</em> value = Nswap = number of swaps to perform every N steps
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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">thermal</span><span class="o">/</span><span class="n">conductivity</span> <span class="mi">100</span> <span class="n">z</span> <span class="mi">20</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">thermal</span><span class="o">/</span><span class="n">conductivity</span> <span class="mi">50</span> <span class="n">z</span> <span class="mi">20</span> <span class="n">swap</span> <span class="mi">2</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>Use the Muller-Plathe algorithm described in <a class="reference internal" href="fix_viscosity.html#muller-plathe"><span class="std std-ref">this paper</span></a> to exchange kinetic energy between two particles
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in different regions of the simulation box every N steps. This
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induces a temperature gradient in the system. As described below this
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enables the thermal conductivity of a material to be calculated. This
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algorithm is sometimes called a reverse non-equilibrium MD (reverse
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NEMD) approach to computing thermal conductivity. This is because the
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usual NEMD approach is to impose a temperature gradient on the system
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and measure the response as the resulting heat flux. In the
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Muller-Plathe method, the heat flux is imposed, and the temperature
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gradient is the system’s response.</p>
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<p>See the <a class="reference internal" href="compute_heat_flux.html"><span class="doc">compute heat/flux</span></a> command for details
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on how to compute thermal conductivity in an alternate way, via the
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Green-Kubo formalism.</p>
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<p>The simulation box is divided into <em>Nbin</em> layers in the <em>edim</em>
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direction, where the layer 1 is at the low end of that dimension and
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the layer <em>Nbin</em> is at the high end. Every N steps, Nswap pairs of
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atoms are chosen in the following manner. Only atoms in the fix group
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are considered. The hottest Nswap atoms in layer 1 are selected.
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Similarly, the coldest Nswap atoms in the “middle” layer (see below)
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are selected. The two sets of Nswap atoms are paired up and their
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velocities are exchanged. This effectively swaps their kinetic
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energies, assuming their masses are the same. If the masses are
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different, an exchange of velocities relative to center of mass motion
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of the 2 atoms is performed, to conserve kinetic energy. Over time,
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this induces a temperature gradient in the system which can be
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measured using commands such as the following, which writes the
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temperature profile (assuming z = edim) to the file tmp.profile:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="n">ke</span> <span class="nb">all</span> <span class="n">ke</span><span class="o">/</span><span class="n">atom</span>
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<span class="n">variable</span> <span class="n">temp</span> <span class="n">atom</span> <span class="n">c_ke</span><span class="o">/</span><span class="mf">1.5</span>
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<span class="n">fix</span> <span class="mi">3</span> <span class="nb">all</span> <span class="n">ave</span><span class="o">/</span><span class="n">spatial</span> <span class="mi">10</span> <span class="mi">100</span> <span class="mi">1000</span> <span class="n">z</span> <span class="n">lower</span> <span class="mf">0.05</span> <span class="n">v_temp</span> <span class="o">&</span>
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<span class="n">file</span> <span class="n">tmp</span><span class="o">.</span><span class="n">profile</span> <span class="n">units</span> <span class="n">reduced</span>
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</pre></div>
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</div>
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<p>Note that by default, Nswap = 1, though this can be changed by the
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optional <em>swap</em> keyword. Setting this parameter appropriately, in
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conjunction with the swap rate N, allows the heat flux to be adjusted
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across a wide range of values, and the kinetic energy to be exchanged
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in large chunks or more smoothly.</p>
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<p>The “middle” layer for velocity swapping is defined as the <em>Nbin</em>/2 +
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1 layer. Thus if <em>Nbin</em> = 20, the two swapping layers are 1 and 11.
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This should lead to a symmetric temperature profile since the two
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layers are separated by the same distance in both directions in a
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periodic sense. This is why <em>Nbin</em> is restricted to being an even
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number.</p>
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<p>As described below, the total kinetic energy transferred by these
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swaps is computed by the fix and can be output. Dividing this
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quantity by time and the cross-sectional area of the simulation box
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yields a heat flux. The ratio of heat flux to the slope of the
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temperature profile is proportional to the thermal conductivity of the
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fluid, in appropriate units. See the <a class="reference internal" href="fix_viscosity.html#muller-plathe"><span class="std std-ref">Muller-Plathe paper</span></a> for details.</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">If your system is periodic in the direction of the heat flux,
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then the flux is going in 2 directions. This means the effective heat
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flux in one direction is reduced by a factor of 2. You will see this
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in the equations for thermal conductivity (kappa) in the Muller-Plathe
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paper. LAMMPS is simply tallying kinetic energy which does not
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account for whether or not your system is periodic; you must use the
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value appropriately to yield a kappa for your system.</p>
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</div>
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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">After equilibration, if the temperature gradient you observe is
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not linear, then you are likely swapping energy too frequently and are
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not in a regime of linear response. In this case you cannot
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accurately infer a thermal conductivity and should try increasing the
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Nevery parameter.</p>
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</div>
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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</h2>
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<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options
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are relevant to this fix.</p>
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<p>This fix computes a global scalar which can be accessed by various
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<a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. The scalar is the
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cummulative kinetic energy transferred between the bottom and middle
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of the simulation box (in the <em>edim</em> direction) is stored as a scalar
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quantity by this fix. This quantity is zeroed when the fix is defined
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and accumlates thereafter, once every N steps. The units of the
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quantity are energy; see the <a class="reference internal" href="units.html"><span class="doc">units</span></a> command for details.
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The scalar value calculated by this fix is “intensive”.</p>
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<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
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the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. 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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<p>Swaps conserve both momentum and kinetic energy, even if the masses of
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the swapped atoms are not equal. Thus you should not need to
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thermostat the system. If you do use a thermostat, you may want to
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apply it only to the non-swapped dimensions (other than <em>vdim</em>).</p>
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<p>LAMMPS does not check, but you should not use this fix to swap the
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kinetic energy of atoms that are in constrained molecules, e.g. via
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<a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> or <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a>. This is
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because application of the constraints will alter the amount of
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transferred momentum. You should, however, be able to use flexible
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molecules. See the <a class="reference internal" href="pair_gran.html#zhang"><span class="std std-ref">Zhang paper</span></a> for a discussion and results
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of this idea.</p>
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<p>When running a simulation with large, massive particles or molecules
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in a background solvent, you may want to only exchange kinetic energy
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bewteen solvent particles.</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_ave_spatial.html"><span class="doc">fix ave/spatial</span></a>, <a class="reference internal" href="fix_viscosity.html"><span class="doc">fix viscosity</span></a>, <a class="reference internal" href="compute_heat_flux.html"><span class="doc">compute heat/flux</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 swap = 1.</p>
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<hr class="docutils" />
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<p id="muller-plathe"><strong>(Muller-Plathe)</strong> Muller-Plathe, J Chem Phys, 106, 6082 (1997).</p>
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<p id="zhang"><strong>(Zhang)</strong> Zhang, Lussetti, de Souza, Muller-Plathe, J Phys Chem B,
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109, 15060-15067 (2005).</p>
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