<p>Here v_r1 specifies a per-type radius of 0.1 units for type 1 atoms
and 0.4 units for type 2 atoms, and v_r2 accesses the radius property
present in atom_style sphere for granular models.</p>
<p>The <em>edge_histo</em> keyword activates the compilation of a histogram of
number of edges on the faces of the Voronoi cells in the compute
group. The argument <em>maxedge</em> of the this keyword is the largest number
of edges on a single Voronoi cell face expected to occur in the
sample. This keyword adds the generation of a global vector with
<em>maxedge</em>+1 entries. The last entry in the vector contains the number of
faces with with more than <em>maxedge</em> edges. Since the polygon with the
smallest amount of edges is a triangle, entries 1 and 2 of the vector
will always be zero.</p>
<p>The <em>edge_threshold</em> and <em>face_threshold</em> keywords allow the
suppression of edges below a given minimum length and faces below a
given minimum area. Ultra short edges and ultra small faces can occur
as artifacts of the Voronoi tessellation. These keywords will affect
the neighbor count and edge histogram outputs.</p>
<p>If the <em>occupation</em> keyword is specified the tessellation is only
performed for the first invocation of the compute and then stored.
For all following invocations of the compute the number of atoms in
each Voronoi cell in the stored tessellation is counted. In this mode
the compute returns a per-atom array with 2 columns. The first column
is the number of atoms currently in the Voronoi volume defined by this
atom at the time of the first invocation of the compute (note that the
atom may have moved significantly). The second column contains the
total number of atoms sharing the Voronoi cell of the stored
tessellation at the location of the current atom. Numbers in column
one can be any positive integer including zero, while column two
values will always be greater than zero. Column one data can be used
to locate vacancies (the coordinates are given by the atom coordinates
at the time step when the compute was first invoked), while column two
data can be used to identify interstitial atoms.</p>
<p>If the <em>neighbors</em> value is set to yes, then
this compute creates a local array with 3 columns. There
is one row for each face of each Voronoi cell. The
3 columns are the atom ID of the atom that owns the cell,
the atom ID of the atom in the neighboring cell
(or zero if the face is external), and the area of the face.
The array can be accessed by any command that
uses local values from a compute as input. See <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">this section</span></a> for an overview of LAMMPS output
options. More specifically, the array can be accessed by a
<aclass="reference internal"href="dump.html"><spanclass="doc">dump local</span></a> command to write a file containing
<p>If the <em>face_threshold</em> keyword is used, then only faces
with areas greater than the threshold are stored.</p>
<hrclass="docutils"/>
<p>The Voronoi calculation is performed by the freely available <aclass="reference external"href="http://math.lbl.gov/voro++/">Voro++ package</a>, written by Chris Rycroft at UC Berkeley and LBL,
which must be installed on your system when building LAMMPS for use
with this compute. See instructions on obtaining and installing the
Voro++ software in the src/VORONOI/README file.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">The calculation of Voronoi volumes is performed by each
processor for the atoms it owns, and includes the effect of ghost
atoms stored by the processor. This assumes that the Voronoi cells of
owned atoms are not affected by atoms beyond the ghost atom cut-off
distance. This is usually a good assumption for liquid and solid
systems, but may lead to underestimation of Voronoi volumes in low
density systems. By default, the set of ghost atoms stored by each
processor is determined by the cutoff used for
<aclass="reference internal"href="pair_style.html"><spanclass="doc">pair_style</span></a> interactions. The cutoff can be set
explicitly via the <aclass="reference internal"href="comm_modify.html"><spanclass="doc">comm_modify cutoff</span></a> command. The
Voronoi cells for atoms adjacent to empty regions will extend into
those regions up to the communication cutoff in x, y, or z. In that
situation, an exterior face is created at the cutoff distance normal
to the x, y, or z direction. For triclinic systems, the exterior face
is parallel to the corresponding reciprocal lattice vector.</p>
</div>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">The Voro++ package performs its calculation in 3d. This will
still work for a 2d LAMMPS simulation, provided all the atoms have the
same z coordinate. The Voronoi cell of each atom will be a columnar
polyhedron with constant cross-sectional area along the z direction
and two exterior faces at the top and bottom of the simulation box. If
the atoms do not all have the same z coordinate, then the columnar
cells will be accordingly distorted. The cross-sectional area of each
Voronoi cell can be obtained by dividing its volume by the z extent of
the simulation box. Note that you define the z extent of the
simulation box for 2d simulations when using the
<aclass="reference internal"href="create_box.html"><spanclass="doc">create_box</span></a> or <aclass="reference internal"href="read_data.html"><spanclass="doc">read_data</span></a> commands.</p>
</div>
<p><strong>Output info:</strong></p>
<p>By default, this compute calculates a per-atom array with 2
columns. In regular dynamic tessellation mode the first column is the
Voronoi volume, the second is the neighbor count, as described above
(read above for the output data in case the <em>occupation</em> keyword is
specified). These values can be accessed by any command that uses
per-atom values from a compute as input. See <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">Section_howto 15</span></a> for an overview of LAMMPS output
options. If the <em>peratom</em> keyword is set to “no”, the per-atom array
is still created, but it is not accessible.</p>
<p>If the <em>edge_histo</em> keyword is used, then this compute generates a
global vector of length <em>maxedge</em>+1, containing a histogram of the
number of edges per face.</p>
<p>If the <em>neighbors</em> value is set to yes, then this compute calculates a
local array with 3 columns. There is one row for each face of each
Voronoi cell.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">Some LAMMPS commands such as the <aclass="reference internal"href="compute_reduce.html"><spanclass="doc">compute reduce</span></a> command can accept either a per-atom or
local quantity. If this compute produces both quantities, the command
may access the per-atom quantity, even if you want to access the local
quantity. This effect can be eliminated by using the <em>peratom</em>
keyword to turn off the production of the per-atom quantities. For
the default value <em>yes</em> both quantities are produced. For the value
<em>no</em>, only the local array is produced.</p>
</div>
<p>The Voronoi cell volume will be in distance <spanclass="xref doc">units</span> cubed.
The Voronoi face area will be in distance <spanclass="xref doc">units</span> squared.</p>
</div>
<divclass="section"id="restrictions">
<h2>Restrictions</h2>
<p>This compute is part of the VORONOI package. It is only enabled if
LAMMPS was built with that package. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
Built with <ahref="http://sphinx-doc.org/">Sphinx</a> using a <ahref="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <ahref="https://readthedocs.org">Read the Docs</a>.