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<li>pair_style multi/lucy/rx command</li>
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<div class="section" id="pair-style-multi-lucy-rx-command">
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<span id="index-0"></span><h1>pair_style multi/lucy/rx 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">pair_style</span> <span class="n">multi</span><span class="o">/</span><span class="n">lucy</span><span class="o">/</span><span class="n">rx</span> <span class="n">style</span> <span class="n">N</span> <span class="n">keyword</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>style = <em>lookup</em> or <em>linear</em> = method of interpolation</li>
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<li>N = use N values in <em>lookup</em>, <em>linear</em> tables</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">pair_style</span> <span class="n">multi</span><span class="o">/</span><span class="n">lucy</span><span class="o">/</span><span class="n">rx</span> <span class="n">linear</span> <span class="mi">1000</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">multibody</span><span class="o">.</span><span class="n">table</span> <span class="n">ENTRY1</span> <span class="n">h2o</span> <span class="n">h2o</span> <span class="mf">7.0</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">multibody</span><span class="o">.</span><span class="n">table</span> <span class="n">ENTRY1</span> <span class="n">h2o</span> <span class="mi">1</span><span class="n">fluid</span> <span class="mf">7.0</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>Style <em>multi/lucy/rx</em> is used in reaction DPD simulations, where the coarse-grained
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(CG) particles are composed of <em>m</em> species whose reaction rate kinetics are determined
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from a set of <em>n</em> reaction rate equations through the <a class="reference internal" href="fix_rx.html"><span class="doc">fix rx</span></a> command.
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The species of one CG particle can interact with a species in a neighboring CG particle
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through a site-site interaction potential model. Style <em>multi/lucy/rx</em> computes the
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site-site density-dependent force following from the many-body form described in
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<a class="reference internal" href="#moore"><span class="std std-ref">(Moore)</span></a> and <a class="reference internal" href="#warren"><span class="std std-ref">(Warren)</span></a> as</p>
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<img alt="_images/pair_multi_lucy.jpg" class="align-center" src="_images/pair_multi_lucy.jpg" />
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<p>which consists of a density-dependent function, A(rho), and a radial-dependent weight
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function, omegaDD(rij). The radial-dependent weight function, omegaDD(rij), is taken
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as the Lucy function:</p>
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<img alt="_images/pair_multi_lucy2.jpg" class="align-center" src="_images/pair_multi_lucy2.jpg" />
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<p>The density-dependent energy for a given particle is given by:</p>
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<img alt="_images/pair_multi_lucy_energy.jpg" class="align-center" src="_images/pair_multi_lucy_energy.jpg" />
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<p>See the supporting information of <a class="reference internal" href="#brennan"><span class="std std-ref">(Brennan)</span></a> or the publication by <a class="reference internal" href="#moore"><span class="std std-ref">(Moore)</span></a>
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for more details on the functional form.</p>
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<p>An interpolation table is used to evaluate the density-dependent energy (Integral(A(rho)drho) and force (A(rho)).
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Note that the pre-factor to the energy is computed after the interpolation, thus the Integral(A(rho)drho will
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have units of energy / length^4.</p>
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<p>The interpolation table is created as a pre-computation by fitting cubic splines to
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the file values and interpolating the density-dependent energy and force at each of <em>N</em> densities.
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During a simulation, the tables are used to interpolate the density-dependent energy and force as
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needed for each pair of particles separated by a distance <em>R</em>. The interpolation is done in
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one of 2 styles: <em>lookup</em> and <em>linear</em>.</p>
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<p>For the <em>lookup</em> style, the density is used to find the nearest table entry, which is the
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density-dependent energy and force.</p>
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<p>For the <em>linear</em> style, the density is used to find the 2 surrounding table values from
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which the density-dependent energy and force are computed by linear interpolation.</p>
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<p>The following coefficients must be defined for each pair of atoms
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types via the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command as in the examples
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above.</p>
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<ul class="simple">
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<li>filename</li>
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<li>keyword</li>
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<li>species1</li>
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<li>species2</li>
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<li>cutoff (distance units)</li>
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</ul>
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<p>The filename specifies a file containing the tabulated density-dependent
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energy and force. The keyword specifies a section of the file.
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The cutoff is an optional coefficient. If not specified, the outer cutoff in the
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table itself (see below) will be used to build an interpolation table
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that extend to the largest tabulated distance. If specified, only
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file values up to the cutoff are used to create the interpolation
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table. The format of this file is described below.</p>
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<p>The species tags define the site-site interaction potential between two
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species contained within two different particles.
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The species tags must either correspond to the species defined in the reaction
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kinetics files specified with the <a class="reference internal" href="fix_rx.html"><span class="doc">fix rx</span></a> command
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or they must correspond to the tag “1fluid”, signifying interaction
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with a product species mixture determined through a one-fluid approximation.
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The interaction potential is weighted by the geometric average of the
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concentrations of the two species. The coarse-grained potential
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is stored before and after the reaction kinetics solver is applied, where
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the difference is defined to be the internal chemical energy (uChem).</p>
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<hr class="docutils" />
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<p>The format of a tabulated file is a series of one or more sections,
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defined as follows (without the parenthesized comments):</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Density-dependent function (one or more comment or blank lines)</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="n">DD</span><span class="o">-</span><span class="n">FUNCTION</span> <span class="p">(</span><span class="n">keyword</span> <span class="ow">is</span> <span class="n">first</span> <span class="n">text</span> <span class="n">on</span> <span class="n">line</span><span class="p">)</span>
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<span class="n">N</span> <span class="mi">500</span> <span class="n">R</span> <span class="mf">1.0</span> <span class="mf">10.0</span> <span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">RSQ</span> <span class="n">parameters</span><span class="p">)</span>
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<span class="p">(</span><span class="n">blank</span><span class="p">)</span>
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<span class="mi">1</span> <span class="mf">1.0</span> <span class="mf">25.5</span> <span class="mf">102.34</span> <span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="n">density</span><span class="p">,</span> <span class="n">energy</span><span class="o">/</span><span class="n">r</span><span class="o">^</span><span class="mi">4</span><span class="p">,</span> <span class="n">force</span><span class="p">)</span>
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<span class="mi">2</span> <span class="mf">1.02</span> <span class="mf">23.4</span> <span class="mf">98.5</span>
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<span class="o">...</span>
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<span class="mi">500</span> <span class="mf">10.0</span> <span class="mf">0.001</span> <span class="mf">0.003</span>
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</pre></div>
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</div>
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<p>A section begins with a non-blank line whose 1st character is not a
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“#”; blank lines or lines starting with “#” can be used as comments
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between sections. The first line begins with a keyword which
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identifies the section. The line can contain additional text, but the
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initial text must match the argument specified in the pair_coeff
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command. The next line lists (in any order) one or more parameters
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for the table. Each parameter is a keyword followed by one or more
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numeric values.</p>
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<p>The parameter “N” is required and its value is the number of table
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entries that follow. Note that this may be different than the <em>N</em>
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specified in the <a class="reference internal" href="#"><span class="doc">pair_style multi/lucy/rx</span></a> command. Let
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Ntable = <em>N</em> in the pair_style command, and Nfile = “N” in the
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tabulated file. What LAMMPS does is a preliminary interpolation by
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creating splines using the Nfile tabulated values as nodal points. It
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uses these to interpolate the density-dependent energy and force at Ntable different
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points. The resulting tables of length Ntable are then used as
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described above, when computing the density-dependent energy and force.
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This means that if you want the interpolation tables of
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length Ntable to match exactly what is in the tabulated file (with
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effectively no preliminary interpolation), you should set Ntable =
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Nfile, and use the “RSQ” parameter. This is because the
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internal table abscissa is always RSQ (separation distance squared),
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for efficient lookup.</p>
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<p>All other parameters are optional. If “R” or “RSQ” does
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not appear, then the distances in each line of the table are used
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as-is to perform spline interpolation. In this case, the table values
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can be spaced in <em>density</em> uniformly or however you wish to position table
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values in regions of large gradients.</p>
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<p>If used, the parameters “R” or “RSQ” are followed by 2 values <em>rlo</em>
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and <em>rhi</em>. If specified, the density associated with each density-dependent
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energy and force value is computed from these 2 values (at high accuracy), rather
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than using the (low-accuracy) value listed in each line of the table.
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The density values in the table file are ignored in this case.
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For “R”, distances uniformly spaced between <em>rlo</em> and <em>rhi</em> are
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computed; for “RSQ”, squared distances uniformly spaced between
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<em>rlo*rlo</em> and <em>rhi*rhi</em> are computed.</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 you use “R” or “RSQ”, the tabulated distance values in the
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file are effectively ignored, and replaced by new values as described
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in the previous paragraph. If the density value in the table is not
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very close to the new value (i.e. round-off difference), then you will
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be assigning density-dependent energy and force values to a different density,
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which is probably not what you want. LAMMPS will warn if this is occurring.</p>
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</div>
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<p>Following a blank line, the next N lines list the tabulated values.
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On each line, the 1st value is the index from 1 to N, the 2nd value is
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r (in density units), the 3rd value is the density-dependent function value
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(in energy units / length^4), and the 4th is the force (in force units). The
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density values must increase from one line to the next.</p>
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<p>Note that one file can contain many sections, each with a tabulated
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potential. LAMMPS reads the file section by section until it finds
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one that matches the specified keyword.</p>
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<hr class="docutils" />
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<p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
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<p>This pair style does not support mixing. Thus, coefficients for all
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I,J pairs must be specified explicitly.</p>
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<p>The <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a> shift, table, and tail options are
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not relevant for this pair style.</p>
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<p>This pair style writes the settings for the “pair_style multi/lucy/rx” command
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to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>, so a pair_style command does
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not need to specified in an input script that reads a restart file.
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However, the coefficient information is not stored in the restart
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file, since it is tabulated in the potential files. Thus, pair_coeff
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commands do need to be specified in the restart input script.</p>
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<p>This pair style can only be used via the <em>pair</em> keyword of the
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<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does not support the
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<em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
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</div>
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<hr class="docutils" />
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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="pair_coeff.html"><span class="doc">pair_coeff</span></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<p id="warren"><strong>(Warren)</strong> Warren, Phys Rev E, 68, 066702 (2003).</p>
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<p id="brennan"><strong>(Brennan)</strong> Brennan, J Chem Phys Lett, 5, 2144-2149 (2014).</p>
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<p id="moore"><strong>(Moore)</strong> Moore, J Chem Phys, 144, 104501 (2016).</p>
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