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<li class="breadcrumb-item active"><span class="section-number">8.5.1. </span>Finite-size spherical and aspherical particles</li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="finite-size-spherical-and-aspherical-particles">
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<h1><span class="section-number">8.5.1. </span>Finite-size spherical and aspherical particles<a class="headerlink" href="#finite-size-spherical-and-aspherical-particles" title="Link to this heading"></a></h1>
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<p>Typical MD models treat atoms or particles as point masses. Sometimes
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it is desirable to have a model with finite-size particles such as
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spheroids or ellipsoids or generalized aspherical bodies. The
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difference is that such particles have a moment of inertia, rotational
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energy, and angular momentum. Rotation is induced by torque coming
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from interactions with other particles.</p>
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<p>LAMMPS has several options for running simulations with these kinds of
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particles. The following aspects are discussed in turn:</p>
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<ul class="simple">
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<li><p>atom styles</p></li>
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<li><p>pair potentials</p></li>
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<li><p>time integration</p></li>
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<li><p>computes, thermodynamics, and dump output</p></li>
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<li><p>rigid bodies composed of finite-size particles</p></li>
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</ul>
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<p>Example input scripts for these kinds of models are in the body,
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colloid, dipole, ellipse, line, peri, pour, and tri directories of the
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<a class="reference internal" href="Examples.html"><span class="doc">examples directory</span></a> in the LAMMPS distribution.</p>
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<section id="atom-styles">
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<h2>Atom styles<a class="headerlink" href="#atom-styles" title="Link to this heading"></a></h2>
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<p>There are several <a class="reference internal" href="atom_style.html"><span class="doc">atom styles</span></a> that allow for
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definition of finite-size particles: sphere, dipole, ellipsoid, line,
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tri, peri, and body.</p>
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<p>The sphere style defines particles that are spheroids and each
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particle can have a unique diameter and mass (or density). These
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particles store an angular velocity (omega) and can be acted upon by
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torque. The “set” command can be used to modify the diameter and mass
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of individual particles, after then are created.</p>
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<p>The dipole style does not actually define finite-size particles, but
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is often used in conjunction with spherical particles, via a command
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like</p>
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<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">atom_style</span><span class="w"> </span><span class="n">hybrid</span><span class="w"> </span><span class="n">sphere</span><span class="w"> </span><span class="n">dipole</span>
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</pre></div>
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</div>
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<p>This is because when dipoles interact with each other, they induce
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torques, and a particle must be finite-size (i.e. have a moment of
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inertia) in order to respond and rotate. See the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style dipole</span></a> command for details. The “set” command can be
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used to modify the orientation and length of the dipole moment of
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individual particles, after then are created.</p>
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<p>The ellipsoid style defines particles that are ellipsoids and thus can
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be aspherical. Each particle has a shape, specified by 3 diameters,
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and mass (or density). These particles store an angular momentum and
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their orientation (quaternion), and can be acted upon by torque. They
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do not store an angular velocity (omega), which can be in a different
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direction than angular momentum, rather they compute it as needed.
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The “set” command can be used to modify the diameter, orientation, and
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mass of individual particles, after then are created. It also has a
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brief explanation of what quaternions are.</p>
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<p>The line style defines line segment particles with two end points and
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a mass (or density). They can be used in 2d simulations, and they can
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be joined together to form rigid bodies which represent arbitrary
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polygons.</p>
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<p>The tri style defines triangular particles with three corner points
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and a mass (or density). They can be used in 3d simulations, and they
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can be joined together to form rigid bodies which represent arbitrary
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particles with a triangulated surface.</p>
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<p>The peri style is used with <a class="reference internal" href="pair_peri.html"><span class="doc">Peridynamic models</span></a> and
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defines particles as having a volume, that is used internally in the
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<a class="reference internal" href="pair_peri.html"><span class="doc">pair_style peri</span></a> potentials.</p>
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<p>The body style allows for definition of particles which can represent
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complex entities, such as surface meshes of discrete points,
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collections of sub-particles, deformable objects, etc. The body style
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is discussed in more detail on the <a class="reference internal" href="Howto_body.html"><span class="doc">Howto body</span></a> doc
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page.</p>
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<p>Note that if one of these atom styles is used (or multiple styles via
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the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style hybrid</span></a> command), not all particles in
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the system are required to be finite-size or aspherical.</p>
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<p>For example, in the ellipsoid style, if the 3 shape parameters are set
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to the same value, the particle will be a sphere rather than an
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ellipsoid. If the 3 shape parameters are all set to 0.0 or if the
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diameter is set to 0.0, it will be a point particle. In the line or
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tri style, if the lineflag or triflag is specified as 0, then it
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will be a point particle.</p>
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<p>Some of the pair styles used to compute pairwise interactions between
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finite-size particles also compute the correct interaction with point
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particles as well, e.g. the interaction between a point particle and a
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finite-size particle or between two point particles. If necessary,
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<a class="reference internal" href="pair_hybrid.html"><span class="doc">pair_style hybrid</span></a> can be used to ensure the correct
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interactions are computed for the appropriate style of interactions.
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Likewise, using groups to partition particles (ellipsoids versus
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spheres versus point particles) will allow you to use the appropriate
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time integrators and temperature computations for each class of
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particles. See the doc pages for various commands for details.</p>
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<p>Also note that for <a class="reference internal" href="dimension.html"><span class="doc">2d simulations</span></a>, atom styles sphere
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and ellipsoid still use 3d particles, rather than as circular disks or
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ellipses. This means they have the same moment of inertia as the 3d
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object. When temperature is computed, the correct degrees of freedom
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are used for rotation in a 2d versus 3d system.</p>
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</section>
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<section id="pair-potentials">
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<h2>Pair potentials<a class="headerlink" href="#pair-potentials" title="Link to this heading"></a></h2>
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<p>When a system with finite-size particles is defined, the particles
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will only rotate and experience torque if the force field computes
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such interactions. These are the various <a class="reference internal" href="pair_style.html"><span class="doc">pair styles</span></a> that generate torque:</p>
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<ul class="simple">
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<li><p><a class="reference internal" href="pair_gran.html"><span class="doc">pair_style gran/history</span></a></p></li>
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<li><p><a class="reference internal" href="pair_gran.html"><span class="doc">pair_style gran/hertz</span></a></p></li>
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<li><p><a class="reference internal" href="pair_gran.html"><span class="doc">pair_style gran/no_history</span></a></p></li>
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<li><p><a class="reference internal" href="pair_dipole.html"><span class="doc">pair_style dipole/cut</span></a></p></li>
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<li><p><a class="reference internal" href="pair_gayberne.html"><span class="doc">pair_style gayberne</span></a></p></li>
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<li><p><a class="reference internal" href="pair_resquared.html"><span class="doc">pair_style resquared</span></a></p></li>
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<li><p><a class="reference internal" href="pair_brownian.html"><span class="doc">pair_style brownian</span></a></p></li>
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<li><p><a class="reference internal" href="pair_lubricate.html"><span class="doc">pair_style lubricate</span></a></p></li>
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<li><p><a class="reference internal" href="pair_line_lj.html"><span class="doc">pair_style line/lj</span></a></p></li>
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<li><p><a class="reference internal" href="pair_tri_lj.html"><span class="doc">pair_style tri/lj</span></a></p></li>
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<li><p><a class="reference internal" href="pair_body_nparticle.html"><span class="doc">pair_style body/nparticle</span></a></p></li>
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</ul>
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<p>The granular pair styles are used with spherical particles. The
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dipole pair style is used with the dipole atom style, which could be
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applied to spherical or ellipsoidal particles. The GayBerne and
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REsquared potentials require ellipsoidal particles, though they will
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also work if the 3 shape parameters are the same (a sphere). The
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Brownian and lubrication potentials are used with spherical particles.
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The line, tri, and body potentials are used with line segment,
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triangular, and body particles respectively.</p>
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</section>
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<section id="time-integration">
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<h2>Time integration<a class="headerlink" href="#time-integration" title="Link to this heading"></a></h2>
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<p>There are several fixes that perform time integration on finite-size
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spherical particles, meaning the integrators update the rotational
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orientation and angular velocity or angular momentum of the particles:</p>
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<ul class="simple">
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<li><p><a class="reference internal" href="fix_nve_sphere.html"><span class="doc">fix nve/sphere</span></a></p></li>
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<li><p><a class="reference internal" href="fix_nvt_sphere.html"><span class="doc">fix nvt/sphere</span></a></p></li>
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<li><p><a class="reference internal" href="fix_npt_sphere.html"><span class="doc">fix npt/sphere</span></a></p></li>
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</ul>
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<p>Likewise, there are 3 fixes that perform time integration on
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ellipsoidal particles:</p>
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<ul class="simple">
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<li><p><a class="reference internal" href="fix_nve_asphere.html"><span class="doc">fix nve/asphere</span></a></p></li>
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<li><p><a class="reference internal" href="fix_nvt_asphere.html"><span class="doc">fix nvt/asphere</span></a></p></li>
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<li><p><a class="reference internal" href="fix_npt_asphere.html"><span class="doc">fix npt/asphere</span></a></p></li>
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</ul>
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<p>The advantage of these fixes is that those which thermostat the
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particles include the rotational degrees of freedom in the temperature
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calculation and thermostatting. The <a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>
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command can also be used with its <em>omgea</em> or <em>angmom</em> options to
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thermostat the rotational degrees of freedom for spherical or
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ellipsoidal particles. Other thermostatting fixes only operate on the
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translational kinetic energy of finite-size particles.</p>
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|
<p>These fixes perform constant NVE time integration on line segment,
|
|
triangular, and body particles:</p>
|
|
<ul class="simple">
|
|
<li><p><a class="reference internal" href="fix_nve_line.html"><span class="doc">fix nve/line</span></a></p></li>
|
|
<li><p><a class="reference internal" href="fix_nve_tri.html"><span class="doc">fix nve/tri</span></a></p></li>
|
|
<li><p><a class="reference internal" href="fix_nve_body.html"><span class="doc">fix nve/body</span></a></p></li>
|
|
</ul>
|
|
<p>Note that for mixtures of point and finite-size particles, these
|
|
integration fixes can only be used with <a class="reference internal" href="group.html"><span class="doc">groups</span></a> which
|
|
contain finite-size particles.</p>
|
|
</section>
|
|
<section id="computes-thermodynamics-and-dump-output">
|
|
<h2>Computes, thermodynamics, and dump output<a class="headerlink" href="#computes-thermodynamics-and-dump-output" title="Link to this heading"></a></h2>
|
|
<p>There are several computes that calculate the temperature or
|
|
rotational energy of spherical or ellipsoidal particles:</p>
|
|
<ul class="simple">
|
|
<li><p><a class="reference internal" href="compute_temp_sphere.html"><span class="doc">compute temp/sphere</span></a></p></li>
|
|
<li><p><a class="reference internal" href="compute_temp_asphere.html"><span class="doc">compute temp/asphere</span></a></p></li>
|
|
<li><p><a class="reference internal" href="compute_erotate_sphere.html"><span class="doc">compute erotate/sphere</span></a></p></li>
|
|
<li><p><a class="reference internal" href="compute_erotate_asphere.html"><span class="doc">compute erotate/asphere</span></a></p></li>
|
|
</ul>
|
|
<p>These include rotational degrees of freedom in their computation. If
|
|
you wish the thermodynamic output of temperature or pressure to use
|
|
one of these computes (e.g. for a system entirely composed of
|
|
finite-size particles), then the compute can be defined and the
|
|
<a class="reference internal" href="thermo_modify.html"><span class="doc">thermo_modify</span></a> command used. Note that by default
|
|
thermodynamic quantities will be calculated with a temperature that
|
|
only includes translational degrees of freedom. See the
|
|
<a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command for details.</p>
|
|
<p>These commands can be used to output various attributes of finite-size
|
|
particles:</p>
|
|
<ul class="simple">
|
|
<li><p><a class="reference internal" href="dump.html"><span class="doc">dump custom</span></a></p></li>
|
|
<li><p><a class="reference internal" href="compute_property_atom.html"><span class="doc">compute property/atom</span></a></p></li>
|
|
<li><p><a class="reference internal" href="dump.html"><span class="doc">dump local</span></a></p></li>
|
|
<li><p><a class="reference internal" href="compute_body_local.html"><span class="doc">compute body/local</span></a></p></li>
|
|
</ul>
|
|
<p>Attributes include the dipole moment, the angular velocity, the
|
|
angular momentum, the quaternion, the torque, the end-point and
|
|
corner-point coordinates (for line and tri particles), and
|
|
sub-particle attributes of body particles.</p>
|
|
</section>
|
|
<section id="rigid-bodies-composed-of-finite-size-particles">
|
|
<h2>Rigid bodies composed of finite-size particles<a class="headerlink" href="#rigid-bodies-composed-of-finite-size-particles" title="Link to this heading"></a></h2>
|
|
<p>The <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command treats a collection of
|
|
particles as a rigid body, computes its inertia tensor, sums the total
|
|
force and torque on the rigid body each timestep due to forces on its
|
|
constituent particles, and integrates the motion of the rigid body.</p>
|
|
<p>If any of the constituent particles of a rigid body are finite-size
|
|
particles (spheres or ellipsoids or line segments or triangles), then
|
|
their contribution to the inertia tensor of the body is different than
|
|
if they were point particles. This means the rotational dynamics of
|
|
the rigid body will be different. Thus a model of a dimer is
|
|
different if the dimer consists of two point masses versus two
|
|
spheroids, even if the two particles have the same mass. Finite-size
|
|
particles that experience torque due to their interaction with other
|
|
particles will also impart that torque to a rigid body they are part
|
|
of.</p>
|
|
<p>See the “fix rigid” command for example of complex rigid-body models
|
|
it is possible to define in LAMMPS.</p>
|
|
<p>Note that the <a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> command can also be used to
|
|
treat 2, 3, or 4 particles as a rigid body, but it always assumes the
|
|
particles are point masses.</p>
|
|
<p>Also note that body particles cannot be modeled with the <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command. Body particles are treated by LAMMPS
|
|
as single particles, though they can store internal state, such as a
|
|
list of sub-particles. Individual body particles are typically treated
|
|
as rigid bodies, and their motion integrated with a command like <a class="reference internal" href="fix_nve_body.html"><span class="doc">fix nve/body</span></a>. Interactions between pairs of body
|
|
particles are computed via a command like <a class="reference internal" href="pair_body_nparticle.html"><span class="doc">pair_style body/nparticle</span></a>.</p>
|
|
</section>
|
|
</section>
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