a point particle.  If it is an ellipsoid, it also stores a shape

vector with the 3 diamters of the ellipsoid and a quaternion 4-vector

with its orientation.</p>

<p>For the <em>dipole</em> style, a point dipole is defined for each point

particle.  Note that if you wish the particles to be finite-size

spheres as in a Stockmayer potential for a dipolar fluid, so that the

particles can rotate due to dipole-dipole interactions, then you need

to use atom_style hybrid sphere dipole, which will assign both a

diameter and dipole moment to each particle.</p>

<p>For the <em>electron</em> style, the particles representing electrons are 3d

Gaussians with a specified position and bandwidth or uncertainty in

position, which is represented by the eradius = electron size.</p>

If some atoms have bonds, but others do not, use the <em>bond</em> style.</p>

<p>The only scenario where the <em>hybrid</em> style is needed is if there is no

single style which defines all needed properties of all atoms.  For

example, if you want dipolar particles which will rotate due to

torque, you would need to use “atom_style hybrid sphere dipole”.  When

a hybrid style is used, atoms store and communicate the union of all

quantities implied by the individual styles.</p>

example, as mentioned above, if you want dipolar particles which will

rotate due to torque, you need to use “atom_style hybrid sphere

dipole”.  When a hybrid style is used, atoms store and communicate the

union of all quantities implied by the individual styles.</p>

<p>When using the <em>hybrid</em> style, you cannot combine the <em>template</em> style

with another molecular style that stores bond,angle,etc info on a

per-atom basis.</p>

vector with the 3 diamters of the ellipsoid and a quaternion 4-vector

with its orientation.

For the {dipole} style, a point dipole is defined for each point

particle.  Note that if you wish the particles to be finite-size

spheres as in a Stockmayer potential for a dipolar fluid, so that the

particles can rotate due to dipole-dipole interactions, then you need

to use atom_style hybrid sphere dipole, which will assign both a

diameter and dipole moment to each particle.

For the {electron} style, the particles representing electrons are 3d

Gaussians with a specified position and bandwidth or uncertainty in

position, which is represented by the eradius = electron size.

The only scenario where the {hybrid} style is needed is if there is no

single style which defines all needed properties of all atoms.  For

example, if you want dipolar particles which will rotate due to

torque, you would need to use "atom_style hybrid sphere dipole".  When

a hybrid style is used, atoms store and communicate the union of all

quantities implied by the individual styles.

example, as mentioned above, if you want dipolar particles which will

rotate due to torque, you need to use "atom_style hybrid sphere

dipole".  When a hybrid style is used, atoms store and communicate the

union of all quantities implied by the individual styles.

When using the {hybrid} style, you cannot combine the {template} style

with another molecular style that stores bond,angle,etc info on a

<p>The <em>rounded/polygon</em> body style represents body particles as a convex

polygon with a variable number N > 2 of vertices, which can only be

used for 2d models.  One example use of this body style is for 2d

discrete element models, as described in <a class="reference internal" href="#fraige"><span>Fraige</span></a>.  Similar to

discrete element models, as described in <a class="reference internal" href="pair_body_rounded_polygon.html#fraige"><span>Fraige</span></a>.  Similar to

body style <em>nparticle</em>, the atom_style body command for this body

style takes two additional arguments:</p>

<div class="highlight-python"><div class="highlight"><pre>atom_style body rounded/polygon Nmin Nmax

<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>

<li>voronoi/atom = style name of this compute command</li>

<li>zero or more keyword/value pairs may be appended</li>

<li>keyword = <em>only_group</em> or <em>surface</em> or <em>radius</em> or <em>edge_histo</em> or <em>edge_threshold</em> or <em>face_threshold</em></li>

<li>keyword = <em>only_group</em> or <em>surface</em> or <em>radius</em> or <em>edge_histo</em> or <em>edge_threshold</em>

or <em>face_threshold</em> or <em>neighbors</em> or <em>peratom</em></li>

</ul>

<pre class="literal-block">

<em>only_group</em> = no arg

  minlength = minimum length for an edge to be counted

<em>face_threshold</em> arg = minarea

  minarea = minimum area for a face to be counted

<em>neighbors</em> value = <em>yes</em> or <em>no</em> = store list of all neighbors or no

<em>peratom</em> value = <em>yes</em> or <em>no</em> = per-atom quantities accessible or no

</pre>

</div>

<div class="section" id="examples">

<div class="highlight-python"><div class="highlight"><pre>compute 5 defects voronoi/atom occupation

</pre></div>

</div>

<p>compute 6 all voronoi/atom neighbors yes</p>

</div>

<div class="section" id="description">

<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>

atoms in the simulation box.  The tessellation is calculated using all

atoms in the simulation, but non-zero values are only stored for atoms

in the group.</p>

<p>By default two quantities per atom are calculated by this compute.

<p>By default two per-atom quantities are calculated by this compute.

The first is the volume of the Voronoi cell around each atom.  Any

point in an atom’s Voronoi cell is closer to that atom than any other.

The second is the number of faces of the Voronoi cell, which is also

the number of nearest neighbors of the atom in the middle of the cell.</p>

The second is the number of faces of the Voronoi cell. This is

equal to the number of nearest neighbors of the central atom,

plus any exterior faces (see note below). If the <em>peratom</em> keyword

is set to “no”, the per-atom quantities are still calculated,

but they are not accessible.</p>

<hr class="docutils" />

<p>If the <em>only_group</em> keyword is specified the tessellation is performed

only with respect to the atoms contained in the compute group. This is

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 maxedge of the this keyword is the largest number

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

maxedge+1 entries. The last entry in the vector contains the number of

faces with with more than maxedge edges. Since the polygon with the

<em>maxedge*+1 entries. The last entry in the vector contains the number of

faces with with more than *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

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 <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output

options. More specifically, the array can be accessed by a

<a class="reference internal" href="dump.html"><em>dump local</em></a> command to write a file containing

all the Voronoi neighbors in a system:</p>

<div class="highlight-python"><div class="highlight"><pre>compute 6 all voronoi/atom neighbors yes

dump d2 all local 1 dump.neighbors index c_6[1] c_6[2] c_6[3]

</pre></div>

</div>

<p>If the <em>face_threshold</em> keyword is used, then only faces

with areas greater than the threshold are stored.</p>

<hr class="docutils" />

<p>The Voronoi calculation is performed by the freely available <a class="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

density systems.  By default, the set of ghost atoms stored by each

processor is determined by the cutoff used for

<a class="reference internal" href="pair_style.html"><em>pair_style</em></a> interactions.  The cutoff can be set

explicitly via the <a class="reference internal" href="comm_modify.html"><em>comm_modify cutoff</em></a> command.</p>

explicitly via the <a class="reference internal" href="comm_modify.html"><em>comm_modify cutoff</em></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>

<div class="admonition note">

<p class="first admonition-title">Note</p>

<p class="last">The Voro++ package performs its calculation in 3d.  This should

still work for a 2d LAMMPS simulation, to effectively compute Voronoi

“areas”, so long as the z-dimension of the box is roughly the same (or

smaller) compared to the separation of the atoms.  Typical values for

the z box dimensions in a 2d LAMMPS model are -0.5 to 0.5, which

satisfies the criterion for most <a class="reference internal" href="units.html"><em>units</em></a> systems.  Note

<p class="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 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or

<a class="reference internal" href="read_data.html"><em>read_data</em></a> commands.</p>

</div>

<p><strong>Output info:</strong></p>

<p>This compute calculates a per-atom array with 2 columns. In regular

<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 <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output

options.</p>

<p>The Voronoi cell volume will be in distance <a class="reference internal" href="units.html"><em>units</em></a> cubed.</p>

options. If the <em>peratom</em> keyword is set to &#8220;no&#8221;, 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 <a href="#id1"><span class="problematic" id="id2">*</span></a>maxedge*+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>

<p>In LAMMPS contexts such as <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> that can

accept either a per-atom vector quantity or a local vector

quantity, the behavior depends on the value gives for the <em>peratom</em>

keyword: for the default value “yes” the per-atom array is accessed,

for the value <em>no</em> the local array is accessed.</p>

<p>The Voronoi cell volume will be in distance <a class="reference internal" href="units.html"><em>units</em></a> cubed.

The Voronoi face area  will be in distance <a class="reference internal" href="units.html"><em>units</em></a> squared.</p>

</div>

<div class="section" id="restrictions">

<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>

</div>

<div class="section" id="related-commands">

<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>

<p><a class="reference internal" href="dump.html"><em>dump custom</em></a></p>

<p><strong>Default:</strong> none</p>

<p><a class="reference internal" href="dump.html"><em>dump custom</em></a>, <a class="reference internal" href="dump.html"><em>dump local</em></a></p>

<p><strong>Default:</strong> <em>neighbors</em> no, <em>peratom</em> yes</p>

</div>

</div>

</div>

<div class="section" id="restrictions">

<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>

<p>This command requires inter-processor communication to coordinate the

deleting of bonds.  This means that your system must be ready to

perform a simulation before using this command (force fields setup,

atom masses set, etc).</p>

<p>This command requires inter-processor communication to acquire ghost

atoms, to coordinate the deleting of bonds, angles, etc between atoms

shared by multiple processors.  This means that your system must be

ready to perform a simulation before using this command (force fields

setup, atom masses set, etc).  Just as would be needed to run

dynamics, the force field you define should define a cutoff

(e.g. through a <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command) which is long

enough for a processor to acquire the ghost atoms its needs to compute

bond, angle, etc interactions.</p>

<p>If deleted bonds (angles, etc) are removed but the 1-2, 1-3, 1-4

weighting list is not recomputed, this can cause a later <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command to fail due to an atom&#8217;s bonds being

inconsistent with the weighting list.  This should only happen if the