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<li class="toctree-l2"><a class="reference internal" href="bond_class2.html">bond_style class2 command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_fene.html">bond_style fene command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_fene.html#bond-style-fene-nm-command">bond_style fene/nm command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_fene_expand.html">bond_style fene/expand command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_gaussian.html">bond_style gaussian command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_gromos.html">bond_style gromos command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_harmonic.html">bond_style harmonic command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_harmonic_restrain.html">bond_style harmonic/restrain command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_harmonic_shift_cut.html">bond_style harmonic/shift/cut command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_hybrid.html">bond_style hybrid command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_lepton.html">bond_style lepton command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_mesocnt.html">bond_style mesocnt command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_mm3.html">bond_style mm3 command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_morse.html">bond_style morse command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_none.html">bond_style none command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_nonlinear.html">bond_style nonlinear command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_oxdna.html">bond_style oxdna/fene command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_oxdna.html#bond-style-oxdna2-fene-command">bond_style oxdna2/fene command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_oxdna.html#bond-style-oxrna2-fene-command">bond_style oxrna2/fene command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_quartic.html">bond_style quartic command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_rheo_shell.html">bond_style rheo/shell command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_special.html">bond_style special command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_table.html">bond_style table command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="bond_zero.html">bond_style zero command</a></li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="bond-style-bpm-spring-command">
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<span id="index-0"></span><h1>bond_style bpm/spring command<a class="headerlink" href="#bond-style-bpm-spring-command" title="Link to this heading"></a></h1>
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<section id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Link to this heading"></a></h2>
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<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">bond_style</span><span class="w"> </span><span class="n">bpm</span><span class="o">/</span><span class="n">spring</span><span class="w"> </span><span class="n">keyword</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="n">attribute1</span><span class="w"> </span><span class="n">attribute2</span><span class="w"> </span><span class="n">...</span>
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</pre></div>
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</div>
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<ul>
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<li><p>optional keyword = <em>overlay/pair</em> or <em>store/local</em> or <em>smooth</em> or <em>break</em> or <em>volume/factor</em></p>
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<pre class="literal-block"><em>store/local</em> values = fix_ID N attributes ...
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* fix_ID = ID of associated internal fix to store data
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* N = prepare data for output every this many timesteps
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* attributes = zero or more of the below attributes may be appended
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<em>id1, id2</em> = IDs of two atoms in the bond
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<em>time</em> = the timestep the bond broke
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<em>x, y, z</em> = the center of mass position of the two atoms when the bond broke (distance units)
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<em>x/ref, y/ref, z/ref</em> = the initial center of mass position of the two atoms (distance units)
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<em>overlay/pair</em> value = <em>yes</em> or <em>no</em>
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bonded particles will still interact with pair forces
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<em>smooth</em> value = <em>yes</em> or <em>no</em>
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smooths bond forces near the breaking point
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<em>normalize</em> value = <em>yes</em> or <em>no</em>
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normalizes bond forces by the reference length
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<em>break</em> value = <em>yes</em> or <em>no</em>
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indicates whether bonds break during a run
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<em>volume/factor</em> value = <em>yes</em> or <em>no</em>
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indicates whether forces include the volumetric contribution</pre>
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</li>
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</ul>
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</section>
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<section id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h2>
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<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">bond_style</span><span class="w"> </span><span class="n">bpm</span><span class="o">/</span><span class="n">spring</span>
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<span class="k">bond_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1.0</span><span class="w"> </span><span class="m">0.05</span><span class="w"> </span><span class="m">0.1</span>
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<span class="k">bond_style</span><span class="w"> </span><span class="n">bpm</span><span class="o">/</span><span class="n">spring</span><span class="w"> </span><span class="n">volume</span><span class="o">/</span><span class="n">factor</span><span class="w"> </span><span class="n">yes</span>
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<span class="k">bond_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1.0</span><span class="w"> </span><span class="m">0.05</span><span class="w"> </span><span class="m">0.1</span><span class="w"> </span><span class="m">0.5</span>
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<span class="k">bond_style</span><span class="w"> </span><span class="n">bpm</span><span class="o">/</span><span class="n">spring</span><span class="w"> </span><span class="n">myfix</span><span class="w"> </span><span class="m">1000</span><span class="w"> </span><span class="n">time</span><span class="w"> </span><span class="n">id1</span><span class="w"> </span><span class="n">id2</span>
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<span class="k">dump </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">local</span><span class="w"> </span><span class="m">1000</span><span class="w"> </span><span class="n">dump.broken</span><span class="w"> </span><span class="n">f_myfix[1]</span><span class="w"> </span><span class="n">f_myfix[2]</span><span class="w"> </span><span class="n">f_myfix[3]</span>
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<span class="k">dump_modify </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="n">write_header</span><span class="w"> </span><span class="n">no</span>
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</pre></div>
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</div>
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</section>
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<section id="description">
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<h2>Description<a class="headerlink" href="#description" title="Link to this heading"></a></h2>
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<div class="versionadded">
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<p><span class="versionmodified added">Added in version 4May2022.</span></p>
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</div>
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<p>The <em>bpm/spring</em> bond style computes forces based on
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deviations from the initial reference state of the two atoms. The
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reference state is stored by each bond when it is first computed in
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the setup of a run. Data is then preserved across run commands and is
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written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a> such that restarting
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the system will not reset the reference state of a bond.</p>
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<p>This bond style only applies central-body forces which conserve the
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translational and rotational degrees of freedom of a bonded set of
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particles based on a model described by Clemmer and Robbins
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<a class="reference internal" href="#fragment-clemmer"><span class="std std-ref">(Clemmer)</span></a>. The force has a magnitude of</p>
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<div class="math notranslate nohighlight">
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\[F = k (r - r_0) w\]</div>
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<p>where <span class="math notranslate nohighlight">\(k\)</span> is a stiffness, <span class="math notranslate nohighlight">\(r\)</span> is the current distance
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and <span class="math notranslate nohighlight">\(r_0\)</span> is the initial distance between the two particles, and
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<span class="math notranslate nohighlight">\(w\)</span> is an optional smoothing factor discussed below. Bonds will
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break at a strain of <span class="math notranslate nohighlight">\(\epsilon_c\)</span>. This is done by setting
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the bond type to 0 such that forces are no longer computed.</p>
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<p>An additional damping force is applied to the bonded
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particles. This forces is proportional to the difference in the
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normal velocity of particles using a similar construction as
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dissipative particle dynamics <a class="reference internal" href="#groot4"><span class="std std-ref">(Groot)</span></a>:</p>
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<div class="math notranslate nohighlight">
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\[F_D = - \gamma w (\hat{r} \bullet \vec{v})\]</div>
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<p>where <span class="math notranslate nohighlight">\(\gamma\)</span> is the damping strength, <span class="math notranslate nohighlight">\(\hat{r}\)</span> is the
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radial normal vector, and <span class="math notranslate nohighlight">\(\vec{v}\)</span> is the velocity difference
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between the two particles.</p>
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<p>The smoothing factor <span class="math notranslate nohighlight">\(w\)</span> can be added or removed by setting the
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<em>smooth</em> keyword to <em>yes</em> or <em>no</em>, respectively. It is constructed such
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that forces smoothly go to zero, avoiding discontinuities, as bonds
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approach the critical strain</p>
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<div class="math notranslate nohighlight">
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\[w = 1.0 - \left( \frac{r - r_0}{r_0 \epsilon_c} \right)^8 .\]</div>
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<p>If the <em>normalize</em> keyword is set to <em>yes</em>, the elastic bond force will be
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normalized by <span class="math notranslate nohighlight">\(r_0\)</span> such that <span class="math notranslate nohighlight">\(k\)</span> must be given in force units.</p>
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<p>By default, pair forces are not calculated between bonded particles.
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Pair forces can alternatively be overlaid on top of bond forces by setting
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the <em>overlay/pair</em> keyword to <em>yes</em>. These settings require specific
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<a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a> settings described in the
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restrictions. Further details can be found in the <a class="reference internal" href="Howto_bpm.html"><span class="doc">how to</span></a>
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page on BPMs.</p>
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<div class="versionadded">
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<p><span class="versionmodified added">Added in version 28Mar2023.</span></p>
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</div>
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<p>If the <em>break</em> keyword is set to <em>no</em>, LAMMPS assumes bonds should not break
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during a simulation run. This will prevent some unnecessary calculation.
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The recommended bond communication distance no longer depends on the value of
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<span class="math notranslate nohighlight">\(\epsilon_c\)</span> (which is ignored) but instead corresponds to the typical
|
||
heuristic maximum strain used by typical non-bpm bond styles. Similar behavior
|
||
to <em>break no</em> can also be attained by setting an arbitrarily high value of
|
||
<span class="math notranslate nohighlight">\(\epsilon_c\)</span>. One cannot use <em>break no</em> with <em>smooth yes</em>.</p>
|
||
<div class="versionadded">
|
||
<p><span class="versionmodified added">Added in version TBD.</span></p>
|
||
</div>
|
||
<p>The <em>volume/factor</em> keyword toggles whether an additional multibody
|
||
contribution is added to he force using the formulation in
|
||
<a class="reference internal" href="#multibody-clemmer"><span class="std std-ref">(Clemmer2)</span></a>,</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[\alpha_v \left(\left[\frac{V_i + V_j}{V_{0,i} + V_{0,j}}\right]^{1/3} - \frac{r_{ij}}{r_{0,ij}}\right)\]</div>
|
||
<p>where <span class="math notranslate nohighlight">\(\alpha_v\)</span> is a user specified coefficient and <span class="math notranslate nohighlight">\(V_i\)</span>
|
||
and <span class="math notranslate nohighlight">\(V_{0,i}\)</span> are estimates of the current and local volume
|
||
of atom <span class="math notranslate nohighlight">\(i\)</span>. These volumes are calculated as the sum of current
|
||
or initial bond lengths cubed. In 2D, the volume is replaced with an area
|
||
calculated using bond lengths squared and the cube root in the above equation
|
||
is accordingly replaced with a square root. This approximation assumes bonds
|
||
are evenly distributed on a spherical surface and neglects constant prefactors
|
||
which are irrelevant since only the ratio of volumes matters. This term may be
|
||
used to adjust the Poisson’s ratio.</p>
|
||
<p>If a bond is broken (or created), <span class="math notranslate nohighlight">\(V_{0,i}\)</span> is updated by subtracting
|
||
(or adding) that bond’s contribution.</p>
|
||
<p>The following coefficients must be defined for each bond type via the
|
||
<a class="reference internal" href="bond_coeff.html"><span class="doc">bond_coeff</span></a> command as in the example above, or in
|
||
the data file or restart files read by the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> or <a class="reference internal" href="read_restart.html"><span class="doc">read_restart</span></a> commands:</p>
|
||
<ul class="simple">
|
||
<li><p><span class="math notranslate nohighlight">\(k\)</span> (force/distance units)</p></li>
|
||
<li><p><span class="math notranslate nohighlight">\(\epsilon_c\)</span> (unit less)</p></li>
|
||
<li><p><span class="math notranslate nohighlight">\(\gamma\)</span> (force/velocity units)</p></li>
|
||
</ul>
|
||
<p>Additionally, if <em>volume/factor</em> is set to <em>yes</em>, a fourth coefficient
|
||
must be provided:</p>
|
||
<ul class="simple">
|
||
<li><p><span class="math notranslate nohighlight">\(a_v\)</span> (force units)</p></li>
|
||
</ul>
|
||
<p>If the <em>store/local</em> keyword is used, an internal fix will track bonds that
|
||
break during the simulation. Whenever a bond breaks, data is processed
|
||
and transferred to an internal fix labeled <em>fix_ID</em>. This allows the
|
||
local data to be accessed by other LAMMPS commands. Following this optional
|
||
keyword, a list of one or more attributes is specified. These include the
|
||
IDs of the two atoms in the bond. The other attributes for the two atoms
|
||
include the timestep during which the bond broke and the current/initial
|
||
center of mass position of the two atoms.</p>
|
||
<p>Data is continuously accumulated over intervals of <em>N</em>
|
||
timesteps. At the end of each interval, all of the saved accumulated
|
||
data is deleted to make room for new data. Individual datum may
|
||
therefore persist anywhere between <em>1</em> to <em>N</em> timesteps depending on
|
||
when they are saved. This data can be accessed using the <em>fix_ID</em> and a
|
||
<a class="reference internal" href="dump.html"><span class="doc">dump local</span></a> command. To ensure all data is output,
|
||
the dump frequency should correspond to the same interval of <em>N</em>
|
||
timesteps. A dump frequency of an integer multiple of <em>N</em> can be used
|
||
to regularly output a sample of the accumulated data.</p>
|
||
<p>Note that when unbroken bonds are dumped to a file via the
|
||
<a class="reference internal" href="dump.html"><span class="doc">dump local</span></a> command, bonds with type 0 (broken bonds)
|
||
are not included.
|
||
The <a class="reference internal" href="delete_bonds.html"><span class="doc">delete_bonds</span></a> command can also be used to
|
||
query the status of broken bonds or permanently delete them, e.g.:</p>
|
||
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">delete_bonds </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">stats</span>
|
||
<span class="k">delete_bonds </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">bond</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="n">remove</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<hr class="docutils" />
|
||
<section id="restart-and-other-info">
|
||
<h2>Restart and other info<a class="headerlink" href="#restart-and-other-info" title="Link to this heading"></a></h2>
|
||
<p>This bond style writes the reference state of each bond to
|
||
<a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. Loading a restart
|
||
file will properly restore bonds. However, the reference state is NOT
|
||
written to data files. Therefore reading a data file will not
|
||
restore bonds and will cause their reference states to be redefined.</p>
|
||
<p>If the <em>store/local</em> option is used, an internal fix will calculate
|
||
a local vector or local array depending on the number of input values.
|
||
The length of the vector or number of rows in the array is the number
|
||
of recorded, broken bonds. If a single input is specified, a local
|
||
vector is produced. If two or more inputs are specified, a local array
|
||
is produced where the number of columns = the number of inputs. The
|
||
vector or array can be accessed by any command that uses local values
|
||
from a compute as input. See the <a class="reference internal" href="Howto_output.html"><span class="doc">Howto output</span></a> page
|
||
for an overview of LAMMPS output options.</p>
|
||
<p>The vector or array will be floating point values that correspond to
|
||
the specified attribute.</p>
|
||
<p>The single() function of this bond style returns 0.0 for the energy
|
||
of a bonded interaction, since energy is not conserved in these
|
||
dissipative potentials. The single() function also calculates an
|
||
extra bond quantity, the initial distance <span class="math notranslate nohighlight">\(r_0\)</span>. This
|
||
extra quantity can be accessed by the
|
||
<a class="reference internal" href="compute_bond_local.html"><span class="doc">compute bond/local</span></a> command as <em>b1</em>.</p>
|
||
</section>
|
||
<section id="restrictions">
|
||
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Link to this heading"></a></h2>
|
||
<p>This bond style is part of the BPM package. It is only enabled if
|
||
LAMMPS was built with that package. See the <a class="reference internal" href="Build_package.html"><span class="doc">Build package</span></a> page for more info.</p>
|
||
<p>By default if pair interactions between bonded atoms are to be disabled,
|
||
this bond style requires setting</p>
|
||
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">special_bonds</span><span class="w"> </span><span class="n">lj</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">coul</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>and <a class="reference internal" href="newton.html"><span class="doc">newton</span></a> must be set to bond off. If the <em>overlay/pair</em>
|
||
keyword is set to <em>yes</em>, this bond style alternatively requires setting</p>
|
||
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">special_bonds</span><span class="w"> </span><span class="n">lj</span><span class="o">/</span><span class="n">coul</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="related-commands">
|
||
<h2>Related commands<a class="headerlink" href="#related-commands" title="Link to this heading"></a></h2>
|
||
<p><a class="reference internal" href="bond_coeff.html"><span class="doc">bond_coeff</span></a>, <a class="reference internal" href="pair_bpm_spring.html"><span class="doc">pair bpm/spring</span></a></p>
|
||
</section>
|
||
<section id="default">
|
||
<h2>Default<a class="headerlink" href="#default" title="Link to this heading"></a></h2>
|
||
<p>The option defaults are <em>overlay/pair</em> = <em>no</em>, <em>smooth</em> = <em>yes</em>, <em>normalize</em> = <em>no</em>, <em>break</em> = <em>yes</em>, and <em>volume/factor</em> = <em>no</em></p>
|
||
<hr class="docutils" />
|
||
<p id="fragment-clemmer"><strong>(Clemmer)</strong> Clemmer and Robbins, Phys. Rev. Lett. (2022).</p>
|
||
<p id="groot4"><strong>(Groot)</strong> Groot and Warren, J Chem Phys, 107, 4423-35 (1997).</p>
|
||
<p id="multibody-clemmer"><strong>(Clemmer2)</strong> Clemmer, Monti, Lechman, Soft Matter, 20, 1702 (2024).</p>
|
||
</section>
|
||
</section>
|
||
|
||
|
||
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|
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