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<title>pair_style gran/hooke command — LAMMPS 15 May 2015 version documentation</title>
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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>pair_style gran/hooke command</li>
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<div class="section" id="pair-style-gran-hooke-command">
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<span id="index-0"></span><h1>pair_style gran/hooke command<a class="headerlink" href="#pair-style-gran-hooke-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-cuda-command">
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<h1>pair_style gran/cuda command<a class="headerlink" href="#pair-style-gran-cuda-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-omp-command">
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<h1>pair_style gran/omp command<a class="headerlink" href="#pair-style-gran-omp-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-hooke-history-command">
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<h1>pair_style gran/hooke/history command<a class="headerlink" href="#pair-style-gran-hooke-history-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-hooke-history-omp-command">
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<h1>pair_style gran/hooke/history/omp command<a class="headerlink" href="#pair-style-gran-hooke-history-omp-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-hertz-history-command">
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<h1>pair_style gran/hertz/history command<a class="headerlink" href="#pair-style-gran-hertz-history-command" title="Permalink to this headline">¶</a></h1>
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</div>
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<div class="section" id="pair-style-gran-hertz-history-omp-command">
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<h1>pair_style gran/hertz/history/omp command<a class="headerlink" href="#pair-style-gran-hertz-history-omp-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>pair_style style Kn Kt gamma_n gamma_t xmu dampflag
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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>gran/hooke</em> or <em>gran/hooke/history</em> or <em>gran/hertz/history</em></li>
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<li>Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below)</li>
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<li>Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below)</li>
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<li>gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below)</li>
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<li>gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below)</li>
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<li>xmu = static yield criterion (unitless value between 0.0 and 1.0e4)</li>
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<li>dampflag = 0 or 1 if tangential damping force is excluded or included</li>
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</ul>
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<div class="admonition warning">
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<p class="first admonition-title">Warning</p>
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<p class="last">Versions of LAMMPS before 9Jan09 had different style
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names for granular force fields. This is to emphasize the fact that
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the Hertzian equation has changed to model polydispersity more
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accurately. A side effect of the change is that the Kn, Kt, gamma_n,
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and gamma_t coefficients in the pair_style command must be specified
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with different values in order to reproduce calculations made with
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earlier versions of LAMMPS, even for monodisperse systems. See the
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NOTE below for details.</p>
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</div>
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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>pair_style gran/hooke/history 200000.0 NULL 50.0 NULL 0.5 1
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pair_style gran/hooke 200000.0 70000.0 50.0 30.0 0.5 0
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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>The <em>gran</em> styles use the following formulas for the frictional force
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between two granular particles, as described in
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<a class="reference internal" href="#brilliantov"><span>(Brilliantov)</span></a>, <a class="reference internal" href="#silbert"><span>(Silbert)</span></a>, and
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<a class="reference internal" href="#zhang"><span>(Zhang)</span></a>, when the distance r between two particles of radii
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Ri and Rj is less than their contact distance d = Ri + Rj. There is
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no force between the particles when r > d.</p>
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<p>The two Hookean styles use this formula:</p>
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<img alt="_images/pair_gran_hooke.jpg" class="align-center" src="_images/pair_gran_hooke.jpg" />
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<p>The Hertzian style uses this formula:</p>
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<img alt="_images/pair_gran_hertz.jpg" class="align-center" src="_images/pair_gran_hertz.jpg" />
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<p>In both equations the first parenthesized term is the normal force
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between the two particles and the second parenthesized term is the
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tangential force. The normal force has 2 terms, a contact force and a
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damping force. The tangential force also has 2 terms: a shear force
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and a damping force. The shear force is a “history” effect that
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accounts for the tangential displacement between the particles for the
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duration of the time they are in contact. This term is included in
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pair styles <em>hooke/history</em> and <em>hertz/history</em>, but is not included
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in pair style <em>hooke</em>. The tangential damping force term is included
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in all three pair styles if <em>dampflag</em> is set to 1; it is not included
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if <em>dampflag</em> is set to 0.</p>
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<p>The other quantities in the equations are as follows:</p>
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<ul class="simple">
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<li>delta = d - r = overlap distance of 2 particles</li>
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<li>Kn = elastic constant for normal contact</li>
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<li>Kt = elastic constant for tangential contact</li>
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<li>gamma_n = viscoelastic damping constant for normal contact</li>
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<li>gamma_t = viscoelastic damping constant for tangential contact</li>
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<li>m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj</li>
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<li>Delta St = tangential displacement vector between 2 spherical particles which is truncated to satisfy a frictional yield criterion</li>
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<li>n_ij = unit vector along the line connecting the centers of the 2 particles</li>
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<li>Vn = normal component of the relative velocity of the 2 particles</li>
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<li>Vt = tangential component of the relative velocity of the 2 particles</li>
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</ul>
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<p>The Kn, Kt, gamma_n, and gamma_t coefficients are specified as
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parameters to the pair_style command. If a NULL is used for Kt, then
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a default value is used where Kt = 2/7 Kn. If a NULL is used for
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gamma_t, then a default value is used where gamma_t = 1/2 gamma_n.</p>
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<p>The interpretation and units for these 4 coefficients are different in
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the Hookean versus Hertzian equations.</p>
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<p>The Hookean model is one where the normal push-back force for two
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overlapping particles is a linear function of the overlap distance.
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Thus the specified Kn is in units of (force/distance). Note that this
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push-back force is independent of absolute particle size (in the
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monodisperse case) and of the relative sizes of the two particles (in
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the polydisperse case). This model also applies to the other terms in
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the force equation so that the specified gamma_n is in units of
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(1/time), Kt is in units of (force/distance), and gamma_t is in units
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of (1/time).</p>
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<p>The Hertzian model is one where the normal push-back force for two
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overlapping particles is proportional to the area of overlap of the
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two particles, and is thus a non-linear function of overlap distance.
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Thus Kn has units of force per area and is thus specified in units of
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(pressure). The effects of absolute particle size (monodispersity)
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and relative size (polydispersity) are captured in the radii-dependent
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pre-factors. When these pre-factors are carried through to the other
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terms in the force equation it means that the specified gamma_n is in
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units of (1/(time*distance)), Kt is in units of (pressure), and
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gamma_t is in units of (1/(time*distance)).</p>
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<p>Note that in the Hookean case, Kn can be thought of as a linear spring
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constant with units of force/distance. In the Hertzian case, Kn is
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like a non-linear spring constant with units of force/area or
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pressure, and as shown in the <a class="reference internal" href="#zhang"><span>(Zhang)</span></a> paper, Kn = 4G /
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(3(1-nu)) where nu = the Poisson ratio, G = shear modulus = E /
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(2(1+nu)), and E = Young’s modulus. Similarly, Kt = 4G / (2-nu).
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(NOTE: in an earlier version of the manual, we incorrectly stated that
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Kt = 8G / (2-nu).)</p>
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<p>Thus in the Hertzian case Kn and Kt can be set to values that
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corresponds to properties of the material being modeled. This is also
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true in the Hookean case, except that a spring constant must be chosen
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that is appropriate for the absolute size of particles in the model.
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Since relative particle sizes are not accounted for, the Hookean
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styles may not be a suitable model for polydisperse systems.</p>
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<div class="admonition warning">
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<p class="first admonition-title">Warning</p>
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<p class="last">In versions of LAMMPS before 9Jan09, the equation for
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Hertzian interactions did not include the sqrt(RiRj/Ri+Rj) term and
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thus was not as accurate for polydisperse systems. For monodisperse
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systems, sqrt(RiRj/Ri+Rj) is a constant factor that effectively scales
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all 4 coefficients: Kn, Kt, gamma_n, gamma_t. Thus you can set the
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values of these 4 coefficients appropriately in the current code to
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reproduce the results of a previous Hertzian monodisperse calculation.
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For example, for the common case of a monodisperse system with
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particles of diameter 1, all 4 of these coefficients should now be set
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2x larger than they were previously.</p>
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</div>
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<p>Xmu is also specified in the pair_style command and is the upper limit
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of the tangential force through the Coulomb criterion Ft = xmu*Fn,
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where Ft and Fn are the total tangential and normal force components
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in the formulas above. Thus in the Hookean case, the tangential force
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between 2 particles grows according to a tangential spring and
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dash-pot model until Ft/Fn = xmu and is then held at Ft = Fn*xmu until
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the particles lose contact. In the Hertzian case, a similar analogy
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holds, though the spring is no longer linear.</p>
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<div class="admonition warning">
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<p class="first admonition-title">Warning</p>
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<p class="last">Normally, xmu should be specified as a fractional
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value between 0.0 and 1.0, however LAMMPS allows large values (up to
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1.0e4) to allow for modeling of systems which can sustain very large
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tangential forces.</p>
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</div>
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<p>For granular styles there are no additional coefficients to set for
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each pair of atom types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command.
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All settings are global and are made via the pair_style command.
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However you must still use the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> for all
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pairs of granular atom types. For example the command</p>
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<div class="highlight-python"><div class="highlight"><pre>pair_coeff * *
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</pre></div>
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</div>
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<p>should be used if all atoms in the simulation interact via a granular
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potential (i.e. one of the pair styles above is used). If a granular
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potential is used as a sub-style of <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid</em></a>, then specific atom types can be used in the
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pair_coeff command to determine which atoms interact via a granular
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potential.</p>
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<hr class="docutils" />
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<p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
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functionally the same as the corresponding style without the suffix.
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They have been optimized to run faster, depending on your available
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hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
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of the manual. The accelerated styles take the same arguments and
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should produce the same results, except for round-off and precision
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issues.</p>
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<p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
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KOKKOS, USER-OMP and OPT packages, respectively. They are only
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enabled if LAMMPS was built with those packages. 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>You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
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use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
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<p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
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more instructions on how to use the accelerated styles effectively.</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>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> mix, shift, table, and tail options
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are not relevant for granular pair styles.</p>
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<p>These pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so a pair_style command does not need to be
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specified in an input script that reads a restart file.</p>
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<p>These pair styles can only be used via the <em>pair</em> keyword of the
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<a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command. They do not support the
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<em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
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<p>The single() function of these pair styles returns 0.0 for the energy
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of a pairwise interaction, since energy is not conserved in these
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dissipative potentials. It also returns only the normal component of
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the pairwise interaction force. However, the single() function also
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calculates 4 extra pairwise quantities. The first 3 are the
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components of the tangential force between particles I and J, acting
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on particle I. <em>P4</em> is the magnitude of this tangential force. These
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extra quantites can be accessed by the <a class="reference internal" href="compute_pair_local.html"><em>compute pair/local</em></a> command, as <em>p1</em>, <em>p2</em>, <em>p3</em>,
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<em>p4</em>.</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<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<blockquote>
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<div>none</div></blockquote>
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<p>All the granular pair styles are part of the GRANULAR package. It is
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only enabled if 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>These pair styles require that atoms store torque and angular velocity
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(omega) as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a>. They also
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require a per-particle radius is stored. The <em>sphere</em> atom style does
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all of this.</p>
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<p>This pair style requires you to use the <a class="reference internal" href="comm_modify.html"><em>comm_modify vel yes</em></a> command so that velocites are stored by ghost
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atoms.</p>
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<p>These pair styles will not restart exactly when using the
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<a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command, though they should provide
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statistically similar results. This is because the forces they
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compute depend on atom velocities. See the
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<a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for more details.</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="pair_coeff.html"><em>pair_coeff</em></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="brilliantov"><strong>(Brilliantov)</strong> Brilliantov, Spahn, Hertzsch, Poschel, Phys Rev E, 53,
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p 5382-5392 (1996).</p>
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<p id="silbert"><strong>(Silbert)</strong> Silbert, Ertas, Grest, Halsey, Levine, Plimpton, Phys Rev
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E, 64, p 051302 (2001).</p>
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<p id="zhang"><strong>(Zhang)</strong> Zhang and Makse, Phys Rev E, 72, p 011301 (2005).</p>
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