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Math replacements; code-block LAMMPS; clarity and parsing-friendly edits

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2022-08-16 20:29:12 -05:00
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6
doc/src/compute_bond_local.rst
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@ -123,7 +123,7 @@ directly. The *set* keyword is used to identify the name of this
other variable associated with theta.
As an example, these commands can be added to the bench/in.rhodo
script to compute the length\^2 of every bond in the system and
script to compute the length\ :math:`^2` of every bond in the system and
output the statistics in various ways:
.. code-block:: LAMMPS
@ -141,11 +141,11 @@ output the statistics in various ways:
fix 10 all ave/histo 10 10 100 0 6 20 c_2[3] mode vector file tmp.histo
The :doc:`dump local <dump>` command will output the energy, length,
and length\^2 for every bond in the system. The
and length\ :math:`^2` for every bond in the system. The
:doc:`thermo_style <thermo_style>` command will print the average of
those quantities via the :doc:`compute reduce <compute_reduce>` command
with thermo output, and the :doc:`fix ave/histo <fix_ave_histo>`
command will histogram the length\^2 values and write them to a file.
command will histogram the length\ :math:`^2` values and write them to a file.
----------

2
doc/src/compute_chunk_atom.rst
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@ -602,7 +602,7 @@ be used. For non-orthogonal (triclinic) simulation boxes, only the
*reduced* option may be used.
A *box* value selects standard distance units as defined by the
:doc:`units <units>` command (e.g., Ångströms for units = *real* or *metal*).
:doc:`units <units>` command (e.g., Angstroms for units = *real* or *metal*).
A *lattice* value means the distance units are in lattice spacings.
The :doc:`lattice <lattice>` command must have been previously used to
define the lattice spacing. A *reduced* value means normalized

4
doc/src/compute_coord_atom.rst
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@ -11,11 +11,11 @@ Syntax
.. code-block:: LAMMPS
compute ID group-ID coord/atom cstyle args ...
compute ID group-ID coord/atom style args ...
* ID, group-ID are documented in :doc:`compute <compute>` command
* coord/atom = style name of this compute command
* cstyle = *cutoff* or *orientorder*
* style = *cutoff* or *orientorder*
.. parsed-literal::

4
doc/src/compute_entropy_atom.rst
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@ -98,13 +98,13 @@ by the corresponding volume. This option can be useful when dealing with
inhomogeneous systems such as those that have surfaces.
Here are typical input parameters for fcc aluminum (lattice
constant 4.05 Ångströms),
constant 4.05 Angstroms),
.. parsed-literal::
compute 1 all entropy/atom 0.25 5.7 avg yes 3.7
and for bcc sodium (lattice constant 4.23 Ångströms),
and for bcc sodium (lattice constant 4.23 Angstroms),
.. parsed-literal::

44
doc/src/compute_global_atom.rst
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@ -6,7 +6,7 @@ compute global/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID style index input1 input2 ...
@ -55,18 +55,20 @@ reference a global vector or array from a :doc:`compute <compute>` or
:doc:`fix <fix>` or the evaluation of an vector-style
:doc:`variable <variable>`. Details are given below.
The *index* value for an atom is used as a index I (from 1 to N) into
the vector associated with each of the input values. The Ith value
The *index* value for an atom is used as an index :math:`I` (from 1 to
:math:`N`, where :math:`N` is the number of atoms) into the vector
associated with each of the input values. The :math:`I`\ th value
from the input vector becomes one output value for that atom. If the
atom is not in the specified group, or the index I < 1 or I > M, where
M is the actual length of the input vector, then an output value of
0.0 is assigned to the atom.
atom is not in the specified group, or the index :math:`I < 1` or
:math:`I > M`, where :math:`M` is the actual length of the input vector,
then an output value of 0.0 is assigned to the atom.
An example of how this command is useful, is in the context of
"chunks" which are static or dynamic subsets of atoms. The :doc:`compute chunk/atom <compute_chunk_atom>` command assigns unique chunk IDs
to each atom. It's output can be used as the *index* parameter for
to each atom. Its output can be used as the *index* parameter for
this command. Various other computes with "chunk" in their style
name, such as :doc:`compute com/chunk <compute_com_chunk>` or :doc:`compute msd/chunk <compute_msd_chunk>`, calculate properties for each
name, such as :doc:`compute com/chunk <compute_com_chunk>` or
:doc:`compute msd/chunk <compute_msd_chunk>`, calculate properties for each
chunk. The output of these commands are global vectors or arrays,
with one or more values per chunk, and can be used as input values for
this command. This command will then assign the global chunk value to
@ -102,17 +104,18 @@ they work.
Note that for input values from a compute or fix, the bracketed index
I can be specified using a wildcard asterisk with the index to
effectively specify multiple values. This takes the form "\*" or "\*n"
or "n\*" or "m\*n". If N = the size of the vector (for *mode* = scalar)
or "m\*" or "m\*n". If :math:`N` is the size of the vector
(for *mode* = scalar)
or the number of columns in the array (for *mode* = vector), then an
asterisk with no numeric values means all indices from 1 to N. A
leading asterisk means all indices from 1 to n (inclusive). A
trailing asterisk means all indices from n to N (inclusive). A middle
asterisk means all indices from m to n (inclusive).
asterisk with no numeric values means all indices from 1 to :math:`N`.
A leading asterisk means all indices from 1 to n (inclusive). A
trailing asterisk means all indices from m to :math:`N` (inclusive).
A middle asterisk means all indices from m to n (inclusive).
Using a wildcard is the same as if the individual columns of the array
had been listed one by one. E.g. these 2 compute global/atom commands
are equivalent, since the :doc:`compute com/chunk <compute_com_chunk>`
command creates a global array with 3 columns:
had been listed one by one. For example, the following two compute global/atom
commands are equivalent, since the :doc:`compute com/chunk <compute_com_chunk>`
command creates a global array with three columns:
.. code-block:: LAMMPS
@ -124,14 +127,14 @@ command creates a global array with 3 columns:
----------
This section explains the *index* parameter. Note that it must
reference per-atom values, as contrasted with the *input* values which
reference per-atom values, as contrasted with the *input* values, which
must reference global values.
Note that all of these options generate floating point values. When
they are used as an index into the specified input vectors, they
simple rounded down to convert the value to integer indices. The
final values should range from 1 to N (inclusive), since they are used
to access values from N-length vectors.
final values should range from 1 to :math:`N` (inclusive), since they are used
to access values from :math:`N`-length vectors.
If *index* begins with "c\_", a compute ID must follow which has been
previously defined in the input script. The compute must generate
@ -177,7 +180,8 @@ global vector or array. See the individual :doc:`compute <compute>` doc
page for details. If no bracketed integer is appended, the vector
calculated by the compute is used. If a bracketed integer is
appended, the Ith column of the array calculated by the compute is
used. Users can also write code for their own compute styles and :doc:`add them to LAMMPS <Modify>`. See the discussion above for how
used. Users can also write code for their own compute styles and
:doc:`add them to LAMMPS <Modify>`. See the discussion above for how
I can be specified with a wildcard asterisk to effectively specify
multiple values.

38
doc/src/compute_group_group.rst
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@ -6,7 +6,7 @@ compute group/group command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID group/group group2-ID keyword value ...
@ -102,19 +102,20 @@ frequently.
If you have a bonded system, then the settings of
:doc:`special_bonds <special_bonds>` command can remove pairwise
interactions between atoms in the same bond, angle, or dihedral. This
is the default setting for the :doc:`special_bonds <special_bonds>`
command, and means those pairwise interactions do not appear in the
neighbor list. Because this compute uses a neighbor list, it also
means those pairs will not be included in the group/group interaction.
This does not apply when using long-range coulomb interactions
(\ *coul/long*, *coul/msm*, *coul/wolf* or similar. One way to get
around this would be to set special_bond scaling factors to very tiny
numbers that are not exactly zero (e.g. 1.0e-50). Another workaround
is to write a dump file, and use the :doc:`rerun <rerun>` command to
compute the group/group interactions for snapshots in the dump file.
The rerun script can use a :doc:`special_bonds <special_bonds>` command
that includes all pairs in the neighbor list.
interactions between atoms in the same bond, angle, or dihedral. This is
the default setting for the :doc:`special_bonds <special_bonds>` command,
and means those pairwise interactions do not appear in the neighbor list.
Because this compute uses a neighbor list, it also means those pairs will
not be included in the group/group interaction. This does not apply when
using long-range Coulomb interactions
(\ *coul/long*, *coul/msm*, *coul/wolf* or similar). One way to get
around this would be to set *special_bond* scaling factors to very tiny
numbers that are not exactly zero (e.g., :math:`1.0 \times 10^{-50}`).
Another workaround would be to write a dump file and use the
:doc:`rerun <rerun>` command to compute the group/group interactions for
snapshots in the dump file. The rerun script can use a
:doc:`special_bonds <special_bonds>` command that includes all pairs in the
neighbor list.
If you desire a breakdown of the interactions into a pairwise and
Kspace component, simply invoke the compute twice with the appropriate
@ -132,20 +133,21 @@ Output info
"""""""""""
This compute calculates a global scalar (the energy) and a global
vector of length 3 (force), which can be accessed by indices 1-3.
vector of length 3 (force), which can be accessed by indices 1--3.
These values can be used by any command that uses global scalar or
vector values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
vector values from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
Both the scalar and vector values calculated by this compute are
"extensive". The scalar value will be in energy :doc:`units <units>`.
"extensive." The scalar value will be in energy :doc:`units <units>`.
The vector values will be in force :doc:`units <units>`.
Restrictions
""""""""""""
Not all pair styles can be evaluated in a pairwise mode as required by
this compute. For example, 3-body and other many-body potentials,
this compute. For example, three-body and other many-body potentials,
such as :doc:`Tersoff <pair_tersoff>` and
:doc:`Stillinger-Weber <pair_sw>` cannot be used. :doc:`EAM <pair_eam>`
potentials will re-use previously computed embedding term contributions,

37
doc/src/compute_gyration.rst
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@ -6,7 +6,7 @@ compute gyration command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID gyration
@ -23,51 +23,54 @@ Examples
Description
"""""""""""
Define a computation that calculates the radius of gyration Rg of the
Define a computation that calculates the radius of gyration :math:`R_g` of the
group of atoms, including all effects due to atoms passing through
periodic boundaries.
Rg is a measure of the size of the group of atoms, and is computed as
the square root of the Rg\^2 value in this formula
:math:`R_g` is a measure of the size of the group of atoms, and is computed as
the square root of the :math:`R_g^2` value in this formula
.. math::
{R_g}^2 = \frac{1}{M} \sum_i m_i (r_i - r_{cm})^2
R_g^2 = \frac{1}{M} \sum_i m_i (r_i - r_{\text{cm}})^2
where :math:`M` is the total mass of the group, :math:`r_{cm}` is the
where :math:`M` is the total mass of the group, :math:`r_{\text{cm}}` is the
center-of-mass position of the group, and the sum is over all atoms in
the group.
A :math:`{R_g}^2` tensor, stored as a 6-element vector, is also calculated
A :math:`R_g^2` tensor, stored as a 6-element vector, is also calculated
by this compute. The formula for the components of the tensor is the
same as the above formula, except that :math:`(r_i - r_{cm})^2` is replaced
by :math:`(r_{i,x} - r_{cm,x}) \cdot (r_{i,y} - r_{cm,y})` for the xy component,
and so on. The 6 components of the vector are ordered xx, yy, zz, xy, xz, yz.
Note that unlike the scalar :math:`R_g`, each of the 6 values of the tensor
same as the above formula, except that :math:`(r_i - r_{\text{cm}})^2` is
replaced by
:math:`(r_{i,x} - r_{\text{cm},x}) \cdot (r_{i,y} - r_{\text{cm},y})` for the
:math:`xy` component, and so on. The six components of the vector are ordered
:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
Note that unlike the scalar :math:`R_g`, each of the six values of the tensor
is effectively a "squared" value, since the cross-terms may be negative
and taking a sqrt() would be invalid.
and taking a square root would be invalid.
.. note::
The coordinates of an atom contribute to :math:`R_g` in "unwrapped" form,
by using the image flags associated with each atom. See the :doc:`dump custom <dump>` command for a discussion of "unwrapped" coordinates.
by using the image flags associated with each atom. See the
:doc:`dump custom <dump>` command for a discussion of "unwrapped" coordinates.
See the Atoms section of the :doc:`read_data <read_data>` command for a
discussion of image flags and how they are set for each atom. You can
reset the image flags (e.g. to 0) before invoking this compute by
reset the image flags (e.g., to 0) before invoking this compute by
using the :doc:`set image <set>` command.
Output info
"""""""""""
This compute calculates a global scalar (:math:`R_g`) and a global vector of
length 6 (:math:`{R_g}^2` tensor), which can be accessed by indices 1-6. These
length 6 (:math:`R_g^2` tensor), which can be accessed by indices 1--6. These
values can be used by any command that uses a global scalar value or
vector values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The scalar and vector values calculated by this compute are
"intensive". The scalar and vector values will be in distance and
distance\^2 :doc:`units <units>` respectively.
"intensive." The scalar and vector values will be in distance and
distance\ :math:`^2` :doc:`units <units>`, respectively.
Restrictions
""""""""""""

38
doc/src/compute_gyration_chunk.rst
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@ -6,7 +6,7 @@ compute gyration/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID gyration/chunk chunkID keyword value ...
@ -31,28 +31,31 @@ Examples
Description
"""""""""""
Define a computation that calculates the radius of gyration Rg for
Define a computation that calculates the radius of gyration :math:`R_g` for
multiple chunks of atoms.
In LAMMPS, chunks are collections of atoms defined by a :doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk). The ID for this command is specified
as chunkID. For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>` and :doc:`Howto chunk <Howto_chunk>`
molecule or atoms in a spatial bin.
See the :doc:`compute chunk/atom <compute_chunk_atom>` and
:doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.
This compute calculates the radius of gyration Rg for each chunk,
This compute calculates the radius of gyration :math:`R_g` for each chunk,
which includes all effects due to atoms passing through periodic
boundaries.
Rg is a measure of the size of a chunk, and is computed by this
:math:`R_g` is a measure of the size of a chunk, and is computed by the
formula
.. math::
{R_g}^2 = \frac{1}{M} \sum_i m_i (r_i - r_{cm})^2
R_g^2 = \frac{1}{M} \sum_i m_i (r_i - r_{\text{cm}})^2
where :math:`M` is the total mass of the chunk, :math:`r_{cm}` is
where :math:`M` is the total mass of the chunk, :math:`r_{\text{cm}}` is
the center-of-mass position of the chunk, and the sum is over all atoms in the
chunk.
@ -64,13 +67,13 @@ thus also not contribute to this calculation. You can specify the
"all" group for this command if you simply want to include atoms with
non-zero chunk IDs.
If the *tensor* keyword is specified, then the scalar Rg value is not
calculated, but an Rg tensor is instead calculated for each chunk.
If the *tensor* keyword is specified, then the scalar :math:`R_g` value is not
calculated, but an :math:`R_g` tensor is instead calculated for each chunk.
The formula for the components of the tensor is the same as the above
formula, except that :math:`(r_i - r_{cm})^2` is replaced by
:math:`(r_{i,x} - r_{cm,x}) \cdot (r_{i,y} - r_{cm,y})` for the xy
component, and so on. The 6 components of the tensor are
ordered xx, yy, zz, xy, xz, yz.
formula, except that :math:`(r_i - r_{\text{cm}})^2` is replaced by
:math:`(r_{i,x} - r_{\text{cm},x}) \cdot (r_{i,y} - r_{\text{cm},y})` for the
:math:`xy` component, and so on. The six components of the tensor are
ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
.. note::
@ -79,7 +82,7 @@ ordered xx, yy, zz, xy, xz, yz.
command for a discussion of "unwrapped" coordinates.
See the Atoms section of the :doc:`read_data <read_data>` command for a
discussion of image flags and how they are set for each atom. You can
reset the image flags (e.g. to 0) before invoking this compute by
reset the image flags (e.g., to 0) before invoking this compute by
using the :doc:`set image <set>` command.
The simplest way to output the results of the compute gyration/chunk
@ -98,8 +101,9 @@ Output info
This compute calculates a global vector if the *tensor* keyword is not
specified and a global array if it is. The length of the vector or
number of rows in the array = the number of chunks *Nchunk* as
calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>` command. If the *tensor* keyword
is specified, the global array has 6 columns. The vector or array can
calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>`
command. If the *tensor* keyword is specified, the global array has six
columns. The vector or array can
be accessed by any command that uses global values from a compute as
input. See the :doc:`Howto output <Howto_output>` page for an
overview of LAMMPS output options.

58
doc/src/compute_gyration_shape.rst
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@ -6,7 +6,7 @@ compute gyration/shape command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID gyration/shape compute-ID
@ -28,30 +28,33 @@ Define a computation that calculates the eigenvalues of the gyration tensor of a
group of atoms and three shape parameters. The computation includes all effects
due to atoms passing through periodic boundaries.
The three computed shape parameters are the asphericity, b, the acylindricity, c,
and the relative shape anisotropy, k:
The three computed shape parameters are the asphericity, :math:`b`,
the acylindricity, :math:`c`, and the relative shape anisotropy, :math:`k`,
viz.,
.. math::
c = & l_z - 0.5(l_y+l_x) \\
b = & l_y - l_x \\
k = & \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
b &= l_z - \frac12(l_y+l_x) \\
c &= l_y - l_x \\
k &= \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
where :math:`l_x` <= :math:`l_y` <= :math:`l_z` are the three eigenvalues of the gyration tensor. A general description
of these parameters is provided in :ref:`(Mattice) <Mattice1>` while an application to polymer systems
where :math:`l_x \le l_y \le l_z` are the three eigenvalues of the gyration
tensor. A general description of these parameters is provided in
:ref:`(Mattice) <Mattice1>` while an application to polymer systems
can be found in :ref:`(Theodorou) <Theodorou1>`.
The asphericity is always non-negative and zero only when the three principal
moments are equal. This zero condition is met when the distribution of particles
is spherically symmetric (hence the name asphericity) but also whenever the particle
distribution is symmetric with respect to the three coordinate axes, e.g.,
when the particles are distributed uniformly on a cube, tetrahedron or other Platonic
solid. The acylindricity is always non-negative and zero only when the two principal
moments are equal. This zero condition is met when the distribution of particles is
cylindrically symmetric (hence the name, acylindricity), but also whenever the particle
distribution is symmetric with respect to the two coordinate axes, e.g., when the
particles are distributed uniformly on a regular prism. the relative shape anisotropy
is bounded between zero (if all points are spherically symmetric) and one
(if all points lie on a line).
moments are equal. This zero condition is met when the distribution of
particles is spherically symmetric (hence the name asphericity) but also
whenever the particle distribution is symmetric with respect to the three
coordinate axes (e.g., when the particles are distributed uniformly on a cube,
tetrahedron or other Platonic solid). The acylindricity is always non-negative
and zero only when the two principal moments are equal. This zero condition is
met when the distribution of particles is cylindrically symmetric (hence the
name, acylindricity), but also whenever the particle distribution is symmetric
with respect to the two coordinate axes (e.g., when the
particles are distributed uniformly on a regular prism).
The relative shape anisotropy is bounded between zero (if all points are
spherically symmetric) and one (if all points lie on a line).
.. note::
@ -60,22 +63,23 @@ is bounded between zero (if all points are spherically symmetric) and one
See the :doc:`dump custom <dump>` command for a discussion of "unwrapped"
coordinates. See the Atoms section of the :doc:`read_data <read_data>`
command for a discussion of image flags and how they are set for each
atom. You can reset the image flags (e.g. to 0) before invoking this
atom. You can reset the image flags (e.g., to 0) before invoking this
compute by using the :doc:`set image <set>` command.
Output info
"""""""""""
This compute calculates a global vector of
length 6, which can be accessed by indices 1-6. The first three values are the
eigenvalues of the gyration tensor followed by the asphericity, the acylindricity
and the relative shape anisotropy. The computed values can be used by any command
that uses global vector values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
This compute calculates a global vector of length 6, which can be accessed by
indices 1--6. The first three values are the eigenvalues of the gyration tensor
followed by the asphericity, the acylindricity and the relative shape
anisotropy. The computed values can be used by any command that uses global
vector values from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The vector values calculated by this compute are
"intensive". The first five vector values will be in
distance\^2 :doc:`units <units>` while the sixth one is dimensionless.
"intensive." The first five vector values will be in
distance\ :math:`2` :doc:`units <units>` while the sixth one is dimensionless.
Restrictions
""""""""""""

59
doc/src/compute_gyration_shape_chunk.rst
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@ -6,7 +6,7 @@ compute gyration/shape/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID gyration/shape/chunk compute-ID
@ -28,28 +28,32 @@ Define a computation that calculates the eigenvalues of the gyration tensor and
three shape parameters of multiple chunks of atoms. The computation includes
all effects due to atoms passing through periodic boundaries.
The three computed shape parameters are the asphericity, b, the acylindricity, c,
and the relative shape anisotropy, k:
The three computed shape parameters are the asphericity, :math:`b`,
the acylindricity, :math:`c`, and the relative shape anisotropy, :math:`k`,
viz.,
.. math::
c = & l_z - 0.5(l_y+l_x) \\
b = & l_y - l_x \\
k = & \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
b &= l_z - \frac12(l_y+l_x) \\
c &= l_y - l_x \\
k &= \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
where :math:`l_x` <= :math:`l_y` <= :math:`l_z` are the three eigenvalues of the gyration tensor. A general description
of these parameters is provided in :ref:`(Mattice) <Mattice2>` while an application to polymer systems
can be found in :ref:`(Theodorou) <Theodorou2>`. The asphericity is always non-negative and zero
only when the three principal moments are equal. This zero condition is met when the distribution
of particles is spherically symmetric (hence the name asphericity) but also whenever the particle
distribution is symmetric with respect to the three coordinate axes, e.g.,
when the particles are distributed uniformly on a cube, tetrahedron or other Platonic
solid. The acylindricity is always non-negative and zero only when the two principal
moments are equal. This zero condition is met when the distribution of particles is
cylindrically symmetric (hence the name, acylindricity), but also whenever the particle
distribution is symmetric with respect to the two coordinate axes, e.g., when the
particles are distributed uniformly on a regular prism. the relative shape anisotropy
is bounded between zero (if all points are spherically symmetric) and one
where :math:`l_x \le l_y \le l_z` are the three eigenvalues of the gyration
tensor. A general description of these parameters is provided in
:ref:`(Mattice) <Mattice2>` while an application to polymer systems
can be found in :ref:`(Theodorou) <Theodorou2>`. The asphericity is always
non-negative and zero only when the three principal moments are equal.
This zero condition is met when the distribution of particles is spherically
symmetric (hence the name asphericity) but also whenever the particle
distribution is symmetric with respect to the three coordinate axes (e.g.,
when the particles are distributed uniformly on a cube, tetrahedron, or other
Platonic solid). The acylindricity is always non-negative and zero only when
the two principal moments are equal. This zero condition is met when the
distribution of particles is cylindrically symmetric (hence the name,
acylindricity), but also whenever the particle distribution is symmetric with
respect to the two coordinate axes (e.g., when the particles are distributed
uniformly on a regular prism). The relative shape anisotropy
is bounded between 0 (if all points are spherically symmetric) and 1
(if all points lie on a line).
The tensor keyword must be specified in the compute gyration/chunk command.
@ -61,22 +65,23 @@ The tensor keyword must be specified in the compute gyration/chunk command.
See the :doc:`dump custom <dump>` command for a discussion of "unwrapped"
coordinates. See the Atoms section of the :doc:`read_data <read_data>`
command for a discussion of image flags and how they are set for each
atom. You can reset the image flags (e.g. to 0) before invoking this
atom. You can reset the image flags (e.g., to 0) before invoking this
compute by using the :doc:`set image <set>` command.
Output info
"""""""""""
This compute calculates a global array with six columns,
which can be accessed by indices 1-6. The first three columns are the
eigenvalues of the gyration tensor followed by the asphericity, the acylindricity
and the relative shape anisotropy. The computed values can be used by any command
that uses global array values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
which can be accessed by indices 1--6. The first three columns are the
eigenvalues of the gyration tensor followed by the asphericity, the
acylindricity and the relative shape anisotropy. The computed values can be
used by any command that uses global array values from a compute as input.
See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
output options.
The array calculated by this compute is
"intensive". The first five columns will be in
distance\^2 :doc:`units <units>` while the sixth one is dimensionless.
"intensive." The first five columns will be in
distance\ :math:`^2` :doc:`units <units>` while the sixth one is dimensionless.
Restrictions
""""""""""""

58
doc/src/compute_heat_flux.rst
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@ -6,7 +6,7 @@ compute heat/flux command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID heat/flux ke-ID pe-ID stress-ID
@ -28,13 +28,13 @@ Description
Define a computation that calculates the heat flux vector based on
contributions from atoms in the specified group. This can be used by
itself to measure the heat flux through a set of atoms (e.g. a region
itself to measure the heat flux through a set of atoms (e.g., a region
between two thermostatted reservoirs held at different temperatures),
or to calculate a thermal conductivity using the equilibrium
Green-Kubo formalism.
For other non-equilibrium ways to compute a thermal conductivity, see
the :doc:`Howto kappa <Howto_kappa>` doc page.. These include use of
the :doc:`Howto kappa <Howto_kappa>` doc page. These include use of
the :doc:`fix thermal/conductivity <fix_thermal_conductivity>` command
for the Muller-Plathe method. Or the :doc:`fix heat <fix_heat>` command
which can add or subtract heat from groups of atoms.
@ -52,12 +52,12 @@ third calculates per-atom stress (\ *stress-ID*\ ).
(or any group whose atoms are superset of the atoms in this compute's
group). LAMMPS does not check for this.
In case of two-body interactions, the heat flux is defined as:
In case of two-body interactions, the heat flux :math:`\mathbf{J}` is defined as
.. math::
\mathbf{J} &= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\
&= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \sum_{i<j} \left( \mathbf{F}_{ij} \cdot \mathbf{v}_j \right) \mathbf{r}_{ij} \right] \\
&= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_{i<j} \left( \mathbf{F}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right) \right) \mathbf{r}_{ij} \right]
&= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_{i<j} \bigl( \mathbf{F}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right) \bigr) \mathbf{r}_{ij} \right]
:math:`e_i` in the first term of the equation
is the per-atom energy (potential and kinetic).
@ -68,12 +68,12 @@ See :doc:`compute stress/atom <compute_stress_atom>`
and :doc:`compute centroid/stress/atom <compute_stress_atom>`
for possible definitions of atomic stress :math:`\mathbf{S}_i`
in the case of bonded and many-body interactions.
The tensor multiplies :math:`\mathbf{v}_i` as a 3x3 matrix-vector multiply
The tensor multiplies :math:`\mathbf{v}_i` by a :math:`3\times3` matrix
to yield a vector.
Note that as discussed below, the 1/:math:`{V}` scaling factor in the
equation for :math:`\mathbf{J}` is NOT included in the calculation performed by
these computes; you need to add it for a volume appropriate to the atoms
included in the calculation.
Note that as discussed below, the :math:`1/V` scaling factor in the
equation for :math:`\mathbf{J}` is **not** included in the calculation
performed by these computes; you need to add it for a volume appropriate to the
atoms included in the calculation.
.. note::
@ -103,7 +103,7 @@ included in the calculation.
contribution when computed via :doc:`compute stress/atom <compute_stress_atom>`
are highly unphysical and should not be used.
The Green-Kubo formulas relate the ensemble average of the
The Green--Kubo formulas relate the ensemble average of the
auto-correlation of the heat flux :math:`\mathbf{J}`
to the thermal conductivity :math:`\kappa`:
@ -112,17 +112,18 @@ to the thermal conductivity :math:`\kappa`:
----------
The heat flux can be output every so many timesteps (e.g. via the
The heat flux can be output every so many timesteps (e.g., via the
:doc:`thermo_style custom <thermo_style>` command). Then as a
post-processing operation, an auto-correlation can be performed, its
integral estimated, and the Green-Kubo formula above evaluated.
integral estimated, and the Green--Kubo formula above evaluated.
The :doc:`fix ave/correlate <fix_ave_correlate>` command can calculate
the auto-correlation. The trap() function in the
:doc:`variable <variable>` command can calculate the integral.
An example LAMMPS input script for solid Ar is appended below. The
result should be: average conductivity ~0.29 in W/mK.
An example LAMMPS input script for solid argon is appended below. The
result should be an average conductivity
:math:`\approx 0.29~\mathrm{W/m \cdot K}`.
----------
@ -130,22 +131,22 @@ Output info
"""""""""""
This compute calculates a global vector of length 6.
The first 3 components are the :math:`x`, :math:`y`, :math:`z`
components of the full heat flux vector,
i.e. (:math:`J_x`, :math:`J_y`, :math:`J_z`).
The next 3 components are the :math:`x`, :math:`y`, :math:`z` components
of just the convective portion of the flux, i.e. the
first term in the equation for :math:`\mathbf{J}`.
Each component can be
accessed by indices 1-6. These values can be used by any command that
uses global vector values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The first three components are the :math:`x`, :math:`y`, and :math:`z`
components of the full heat flux vector
(i.e., :math:`J_x`, :math:`J_y`, and :math:`J_z`).
The next three components are the :math:`x`, :math:`y`, and :math:`z`
components of just the convective portion of the flux (i.e., the
first term in the equation for :math:`\mathbf{J}`).
Each component can be accessed by indices 1--6. These values can be used by any
command that uses global vector values from a compute as input.
See the :doc:`Howto output <Howto_output>` documentation for an overview of
LAMMPS output options.
The vector values calculated by this compute are "extensive", meaning
The vector values calculated by this compute are "extensive," meaning
they scale with the number of atoms in the simulation. They can be
divided by the appropriate volume to get a flux, which would then be
an "intensive" value, meaning independent of the number of atoms in
the simulation. Note that if the compute is "all", then the
the simulation. Note that if the compute is "all," then the
appropriate volume to divide by is the simulation box volume.
However, if a sub-group is used, it should be the volume containing
those atoms.
@ -172,6 +173,9 @@ none
----------
Example Input File
------------------
.. code-block:: LAMMPS
# Sample LAMMPS input script for thermal conductivity of solid Ar

4
doc/src/compute_hexorder_atom.rst
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@ -6,7 +6,7 @@ compute hexorder/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID hexorder/atom keyword values ...
@ -102,7 +102,7 @@ Output info
This compute calculates a per-atom array with 2 columns, giving the
real and imaginary parts :math:`q_n`, a complex number restricted to the
unit disk of the complex plane i.e. :math:`Re(q_n)^2 + Im(q_n)^2 <= 1`.
unit disk of the complex plane (i.e., :math:`\Re(q_n)^2 + \Im(q_n)^2 \le 1`).
These values can be accessed by any command that uses per-atom values
from a compute as input. See the :doc:`Howto output <Howto_output>` doc

69
doc/src/compute_hma.rst
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@ -6,20 +6,23 @@ compute hma command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID hma temp-ID keyword ...
* ID, group-ID are documented in :doc:`compute <compute>` command
* hma = style name of this compute command
* temp-ID = ID of fix that specifies the set temperature during canonical simulation
* keyword = *anharmonic* *u* *p Pharm* *cv*
* one or more keywords or keyword/argument pairs must be appended
* keyword = *anharmonic* or *u* or *p* or *cv*
.. parsed-literal::
*anharmonic* = compute will return anharmonic property values
*u* = compute will return potential energy
*p* = compute will return pressure. the following keyword must be the difference between the harmonic pressure and lattice pressure as described below
*p* value = Pharm = compute will return pressure
Pharm = difference between the harmonic pressure and lattice pressure
as described below
*cv* = compute will return the heat capacity
Examples
@ -74,44 +77,48 @@ A detailed description of this method can be found in (:ref:`Moustafa <hma-Moust
.. math::
\left< U\right>_{HMA} = \frac{d}{2} (N-1) k_B T + \left< U + \frac{1}{2} F\bullet\Delta r \right>
\left< U\right>_\text{HMA} = \frac{d}{2} (N-1) k_B T + \left< U + \frac{1}{2} \vec F\cdot\Delta \vec r \right>
where :math:`N` is the number of atoms in the system, :math:`k_B` is Boltzmann's
constant, :math:`T` is the temperature, :math:`d` is the
dimensionality of the system (2 or 3 for 2d/3d), :math:`F\bullet\Delta r` is the sum of dot products of the
atomic force vectors and displacement (from lattice sites) vectors, and :math:`U` is the sum of
pair, bond, angle, dihedral, improper, kspace (long-range), and fix energies.
constant, :math:`T` is the temperature, :math:`d` is the dimensionality of the
system (2 or 3 for 2d/3d), :math:`\vec F\cdot\Delta\vec r` is the sum of dot
products of the atomic force vectors and displacement (from lattice sites)
vectors, and :math:`U` is the sum of pair, bond, angle, dihedral, improper,
kspace (long-range), and fix energies.
The pressure is computed by the formula:
.. math::
\left< P\right>_{HMA} = \Delta \hat P + \left< P_{vir} + \frac{\beta \Delta \hat P - \rho}{d(N-1)} F\bullet\Delta r \right>
\left< P\right>_{HMA} = \Delta \hat P + \left< P_\text{vir}
+ \frac{\beta \Delta \hat P - \rho}{d(N-1)} \vec F\cdot\Delta \vec r \right>
where :math:`\rho` is the number density of the system, :math:`\Delta \hat P` is the
difference between the harmonic and lattice pressure, :math:`P_{vir}` is
the virial pressure computed as the sum of pair, bond, angle, dihedral,
improper, kspace (long-range), and fix contributions to the force on each
atom, and :math:`k_B=1/k_B T`. Although the method will work for any value of :math:`\Delta \hat P`
where :math:`\rho` is the number density of the system, :math:`\Delta \hat P`
is the difference between the harmonic and lattice pressure,
:math:`P_\text{vir}` is the virial pressure computed as the sum of pair, bond,
angle, dihedral, improper, kspace (long-range), and fix contributions to the
force on each atom, and :math:`k_B=1/k_B T`. Although the method will work for
any value of :math:`\Delta \hat P`
specified (use pressure :doc:`units <units>`), the precision of the resultant
pressure is sensitive to :math:`\Delta \hat P`; the precision tends to be
best when :math:`\Delta \hat P` is the actual the difference between the lattice
pressure and harmonic pressure.
best when :math:`\Delta \hat P` is the actual the difference between the
lattice pressure and harmonic pressure.
.. math::
\left<C_V \right>_{HMA} = \frac{d}{2} (N-1) k_B + \frac{1}{k_B T^2} \left( \left<
U_{HMA}^2 \right> - \left<U_{HMA}\right>^2 \right) + \frac{1}{4 T}
\left< F\bullet\Delta r + \Delta r \bullet \Phi \bullet \Delta r \right>
\left<C_V \right>_\text{HMA} = \frac{d}{2} (N-1) k_B
+ \frac{1}{k_B T^2} \left( \left<U_\text{HMA}^2 \right>
- \left<U_\text{HMA}\right>^2 \right) + \frac{1}{4 T}
\left<\vec F\cdot\Delta\vec r + \Delta r \cdot\Phi\cdot \Delta\vec r\right>
where :math:`\Phi` is the Hessian matrix. The compute hma command
computes the full expression for :math:`C_V` except for the
:math:`\left<U_{HMA}^2\right>^2` in the variance term, which can be obtained by
passing the *u* keyword; you must add this extra contribution to the :math:`C_V`
value reported by this compute. The variance term can cause significant
round-off error when computing :math:`C_V`. To address this, the *anharmonic*
keyword can be passed and/or the output format can be specified with more
digits.
:math:`\left<U_\text{HMA}\right>^2` in the variance term, which can be obtained
by passing the *u* keyword; you must add this extra contribution to the
:math:`C_V` value reported by this compute. The variance term can cause
significant round-off error when computing :math:`C_V`. To address this, the
*anharmonic* keyword can be passed and/or the output format can be specified
with more digits.
.. code-block:: LAMMPS
@ -124,8 +131,10 @@ When using this keyword, the compute must be first active (it must be included
via a :doc:`thermo_style custom <thermo_style>` command) while the atoms are
still at their lattice sites (before equilibration).
The temp-ID specified with compute hma command should be same as the fix-ID of Nose-Hoover (:doc:`fix nvt <fix_nh>`) or
Berendsen (:doc:`fix temp/berendsen <fix_temp_berendsen>`) thermostat used for the simulation. While using this command, Langevin thermostat
The temp-ID specified with compute hma command should be same as the fix-ID of
the Nose--Hoover (:doc:`fix nvt <fix_nh>`) or
Berendsen (:doc:`fix temp/berendsen <fix_temp_berendsen>`) thermostat used for
the simulation. While using this command, the Langevin thermostat
(:doc:`fix langevin <fix_langevin>`)
should be avoided as its extra forces interfere with the HMA implementation.
@ -160,10 +169,10 @@ Output info
This compute calculates a global vector that includes the n properties
requested as arguments to the command (the potential energy, pressure and/or heat
capacity). The elements of the vector can be accessed by indices 1-n by any
capacity). The elements of the vector can be accessed by indices 1--n by any
command that uses global vector values as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output options.
The vector values calculated by this compute are "extensive". The
The vector values calculated by this compute are "extensive." The
scalar value will be in energy :doc:`units <units>`.
Restrictions
@ -180,7 +189,7 @@ Related commands
:doc:`compute pe <compute_pe>`, :doc:`compute pressure <compute_pressure>`
:doc:`dynamical matrix <dynamical_matrix>` provides a finite difference
formulation of the hessian provided by Pair's single_hessian, which is used by
formulation of the Hessian provided by Pair's single_hessian, which is used by
this compute.
Default

14
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@ -6,7 +6,7 @@ compute improper command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID improper
@ -34,11 +34,13 @@ total energy contributed by one or more of the hybrid sub-styles.
Output info
"""""""""""
This compute calculates a global vector of length N where N is the
number of sub_styles defined by the :doc:`improper_style hybrid <improper_style>` command. which can be accessed by indices
1-N. These values can be used by any command that uses global scalar
or vector values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
This compute calculates a global vector of length :math:`N`, where :math:`N` is
the number of sub_styles defined by the
:doc:`improper_style hybrid <improper_style>` command.
These styles can be accessed by the indices 1 through :math:`N`.
These values can be used by any command that uses global scalar or vector
values from a compute as input. See the :doc:`Howto output <Howto_output>`
page for an overview of LAMMPS output options.
The vector values are "extensive" and will be in energy
:doc:`units <units>`.

7
doc/src/compute_improper_local.rst
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@ -6,7 +6,7 @@ compute improper/local command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID improper/local value1 value2 ...
@ -40,7 +40,7 @@ the individual improper styles listed on
The local data stored by this command is generated by looping over all
the atoms owned on a processor and their impropers. An improper will
only be included if all 4 atoms in the improper are in the specified
only be included if all four atoms in the improper are in the specified
compute group.
Note that as atoms migrate from processor to processor, there will be
@ -69,7 +69,8 @@ array is the number of impropers. If a single keyword is specified, a
local vector is produced. If two or more keywords are specified, a
local array is produced where the number of columns = the number of
keywords. The vector or array can be accessed by any command that
uses local values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
uses local values from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The output for *chi* will be in degrees.

33
doc/src/compute_inertia_chunk.rst
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@ -6,7 +6,7 @@ compute inertia/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID inertia/chunk chunkID
@ -27,16 +27,20 @@ Description
Define a computation that calculates the inertia tensor for multiple
chunks of atoms.
In LAMMPS, chunks are collections of atoms defined by a :doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk). The ID for this command is specified
as chunkID. For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>` and :doc:`Howto chunk <Howto_chunk>`
molecule or atoms in a spatial bin. See the
:doc:`compute chunk/atom <compute_chunk_atom>` and
:doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.
This compute calculates the 6 components of the symmetric inertia
tensor for each chunk, ordered Ixx,Iyy,Izz,Ixy,Iyz,Ixz. The
calculation includes all effects due to atoms passing through periodic
This compute calculates the six components of the symmetric inertia
tensor for each chunk, ordered
:math:`I_{xx},I_{yy},I_{zz},I_{xy},I_{yz},I_{xz}`.
The calculation includes all effects due to atoms passing through periodic
boundaries.
Note that only atoms in the specified group contribute to the
@ -55,7 +59,8 @@ non-zero chunk IDs.
of "unwrapped" coordinates. See the Atoms section of the
:doc:`read_data <read_data>` command for a discussion of image flags and
how they are set for each atom. You can reset the image flags
(e.g. to 0) before invoking this compute by using the :doc:`set image <set>` command.
(e.g., to 0) before invoking this compute by using the
:doc:`set image <set>` command.
The simplest way to output the results of the compute inertia/chunk
calculation to a file is to use the :doc:`fix ave/time <fix_ave_time>`
@ -71,14 +76,16 @@ Output info
"""""""""""
This compute calculates a global array where the number of rows = the
number of chunks *Nchunk* as calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>` command. The number of columns =
6 for the 6 components of the inertia tensor for each chunk, ordered
as listed above. These values can be accessed by any command that
uses global array values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
number of chunks *Nchunk* as calculated by the specified
:doc:`compute chunk/atom <compute_chunk_atom>` command.
The number of columns is 6, one for each of the 6 components of the inertia
tensor for each chunk, ordered as listed above. These values can be accessed
by any command that uses global array values from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The array values are "intensive". The array values will be in
mass\*distance\^2 :doc:`units <units>`.
The array values are "intensive." The array values will be in
mass\*distance\ :math:`^2` :doc:`units <units>`.
Restrictions
""""""""""""

15
doc/src/compute_ke.rst
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@ -6,7 +6,7 @@ compute ke command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ke
@ -27,7 +27,8 @@ Define a computation that calculates the translational kinetic energy
of a group of particles.
The kinetic energy of each particle is computed as :math:`\frac{1}{2} m
v^2`, where *m* and *v* are the mass and velocity of the particle.
v^2`, where *m* and *v* are the mass and velocity of the particle,
respectively.
There is a subtle difference between the quantity calculated by this
compute and the kinetic energy calculated by the *ke* or *etotal*
@ -38,10 +39,10 @@ formula above. For thermodynamic output, the *ke* keyword infers
kinetic energy from the temperature of the system with
:math:`\frac{1}{2} k_B T` of energy for each degree of freedom. For the
default temperature computation via the :doc:`compute temp
<compute_temp>` command, these are the same. But different computes
that calculate temperature can subtract out different non-thermal
components of velocity and/or include different degrees of freedom
(translational, rotational, etc).
<compute_temp>` command, these are the same.
However, different computes that calculate temperature can subtract out
different non-thermal components of velocity and/or include different degrees
of freedom (translational, rotational, etc.).
Output info
"""""""""""
@ -51,7 +52,7 @@ can be used by any command that uses a global scalar value from a
compute as input. See the :doc:`Howto output <Howto_output>` doc page
for an overview of LAMMPS output options.
The scalar value calculated by this compute is "extensive". The
The scalar value calculated by this compute is "extensive." The
scalar value will be in energy :doc:`units <units>`.
Restrictions

6
doc/src/compute_ke_atom.rst
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@ -6,7 +6,7 @@ compute ke/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ke/atom
@ -26,8 +26,8 @@ Description
Define a computation that calculates the per-atom translational
kinetic energy for each atom in a group.
The kinetic energy is simply 1/2 m v\^2, where m is the mass and v is
the velocity of each atom.
The kinetic energy is simply :math:`\frac12 m v^2`, where :math:`m` is the mass
and :math:`v` is the velocity of each atom.
The value of the kinetic energy will be 0.0 for atoms not in the
specified compute group.

2
doc/src/compute_ke_atom_eff.rst
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@ -6,7 +6,7 @@ compute ke/atom/eff command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ke/atom/eff

8
doc/src/compute_ke_eff.rst
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@ -6,7 +6,7 @@ compute ke/eff command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ke/eff
@ -29,9 +29,9 @@ group of eFF particles (nuclei and electrons), as modeled with the
The kinetic energy for each nucleus is computed as :math:`\frac{1}{2} m
v^2` and the kinetic energy for each electron is computed as
:math:`\frac{1}{2}(m_e v^2 + \frac{3}{4} m_e s^2)`, where *m*
corresponds to the nuclear mass, :math:`m_e` to the electron mass, *v*
to the translational velocity of each particle, and *s* to the radial
:math:`\frac{1}{2}(m_e v^2 + \frac{3}{4} m_e s^2)`, where :math:`m`
corresponds to the nuclear mass, :math:`m_e` to the electron mass, :math:`v`
to the translational velocity of each particle, and :math:`s` to the radial
velocity of the electron, respectively.
There is a subtle difference between the quantity calculated by this

17
doc/src/compute_ke_rigid.rst
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@ -6,7 +6,7 @@ compute ke/rigid command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ke/rigid fix-ID
@ -25,11 +25,13 @@ Description
"""""""""""
Define a computation that calculates the translational kinetic energy
of a collection of rigid bodies, as defined by one of the :doc:`fix rigid <fix_rigid>` command variants.
of a collection of rigid bodies, as defined by one of the
:doc:`fix rigid <fix_rigid>` command variants.
The kinetic energy of each rigid body is computed as 1/2 M Vcm\^2,
where M is the total mass of the rigid body, and Vcm is its
center-of-mass velocity.
The kinetic energy of each rigid body is computed as
:math:`\frac12 M V_\text{cm}^2`,
where :math:`M` is the total mass of the rigid body, and :math:`V_\text{cm}`
is its center-of-mass velocity.
The *fix-ID* should be the ID of one of the :doc:`fix rigid <fix_rigid>`
commands which defines the rigid bodies. The group specified in the
@ -42,10 +44,11 @@ Output info
This compute calculates a global scalar (the summed KE of all the
rigid bodies). This value can be used by any command that uses a
global scalar value from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
global scalar value from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The scalar value calculated by this compute is "extensive". The
The scalar value calculated by this compute is "extensive." The
scalar value will be in energy :doc:`units <units>`.
Restrictions

17
doc/src/compute_mesont.rst
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@ -6,30 +6,29 @@ compute mesont command
Syntax
""""""
.. code-block:: LAMMPS
.. parsed-literal::
compute ID group-ID mesont mode
compute ID group-ID mesont style
* ID, group-ID are documented in :doc:`compute <compute>` command
* mesont = style name of the compute command
* mode = one of estretch, ebend, etube (see details below)
* style = *estretch* or *ebend* or *etube*
Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute 1 all mesont estretch
Description
"""""""""""
These computes define computations for the stretching (estretch), bending
(ebend), and intertube (etube) per-node (atom) and total energies. The
evaluated value is selected by a parameter passed to the compute: estretch,
ebend, etube.
These computes define computations for the stretching (*estretch*), bending
(*ebend*), and intertube (*etube*) per-node (atom) and total energies. The
evaluated value is selected by the style parameter passed to the compute
(*estretch*, *ebend*,or *etube*).
Output info
"""""""""""

39
doc/src/compute_mliap.rst
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@ -36,10 +36,10 @@ Description
"""""""""""
Compute style *mliap* provides a general interface to the gradient
of machine-learning interatomic potentials w.r.t. model parameters.
of machine-learning interatomic potentials with respect to model parameters.
It is used primarily for calculating the gradient of energy, force, and
stress components w.r.t. model parameters, which is useful when training
:doc:`mliap pair_style <pair_mliap>` models to match target data.
stress components with respect to model parameters, which is useful when
training :doc:`mliap pair_style <pair_mliap>` models to match target data.
It provides separate
definitions of the interatomic potential functional form (*model*)
and the geometric quantities that characterize the atomic positions
@ -58,8 +58,8 @@ The compute *mliap* command must be followed by two keywords
The *model* keyword is followed by the model style (*linear*,
*quadratic* or *mliappy*). The *mliappy* model is only available if
LAMMPS is built with the *mliappy* python module. There are
:ref:`specific installation instructions <mliap>` for that.
LAMMPS is built with the *mliappy* Python module. There are
:ref:`specific installation instructions <mliap>` for that module.
The *descriptor* keyword is followed by a descriptor style, and
additional arguments. The compute currently supports two descriptor
@ -79,13 +79,13 @@ described in detail there.
must match the value of *nelems* in the descriptor file.
Compute *mliap* calculates a global array containing gradient information.
The number of columns in the array is :math:`nelems \times nparams + 1`.
The first row of the array contain the derivative of potential energy w.r.t. to
each parameter and each element. The last six rows
The number of columns in the array is *nelems* :math:`\times` *nparams* + 1.
The first row of the array contain the derivative of potential energy with
respect to. to each parameter and each element. The last six rows
of the array contain the corresponding derivatives of the
virial stress tensor, listed in Voigt notation: *pxx*, *pyy*, *pzz*,
*pyz*, *pxz*, *pxy*. In between the energy and stress rows are
the 3\*\ *N* rows containing the derivatives of the force components.
*pyz*, *pxz*, and *pxy*. In between the energy and stress rows are
the :math:`3N` rows containing the derivatives of the force components.
See section below on output for a detailed description of how
rows and columns are ordered.
@ -107,19 +107,19 @@ layout in the global array.
The optional keyword *gradgradflag* controls how the force
gradient is calculated. A value of 1 requires that the model provide
the matrix of double gradients of energy w.r.t. both parameters
the matrix of double gradients of energy with respect to both parameters
and descriptors. For the linear and quadratic models this matrix is
sparse and so is easily calculated and stored. For other models, this
matrix may be prohibitively expensive to calculate and store.
A value of 0 requires that the descriptor provide the derivative
of the descriptors w.r.t. the position of every neighbor atom.
of the descriptors with respect to the position of every neighbor atom.
This is not optimal for linear and quadratic models, but may be
a better choice for more complex models.
Atoms not in the group do not contribute to this compute.
Neighbor atoms not in the group do not contribute to this compute.
The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (i.e. each time a snapshot of atoms
time the calculation is performed (i.e., each time a snapshot of atoms
is dumped). Thus it can be inefficient to compute/dump this quantity
too frequently.
@ -144,17 +144,20 @@ too frequently.
Output info
"""""""""""
Compute *mliap* evaluates a global array.
The columns are arranged into
Compute *mliap* evaluates a global array. The columns are arranged into
*nelems* blocks, listed in order of element *I*\ . Each block
contains one column for each of the *nparams* model parameters.
A final column contains the corresponding energy, force component
on an atom, or virial stress component. The rows of the array appear
in the following order:
* 1 row: Derivatives of potential energy w.r.t. each parameter of each element.
* 3\*\ *N* rows: Derivatives of force components. x, y, and z components of force on atom *i* appearing in consecutive rows. The atoms are sorted based on atom ID.
* 6 rows: Derivatives of virial stress tensor w.r.t. each parameter of each element. The ordering of the rows follows Voigt notation: *pxx*, *pyy*, *pzz*, *pyz*, *pxz*, *pxy*.
* 1 row: Derivatives of potential energy with respect to each parameter of each element.
* :math:`3N` rows: Derivatives of force components; the *x*, *y*, and *z*
components of the force on atom *i* appear in consecutive rows. The atoms are
sorted based on atom ID.
* 6 rows: Derivatives of the virial stress tensor with respect to each
parameter of each element. The ordering of the rows follows Voigt notation:
*pxx*, *pyy*, *pzz*, *pyz*, *pxz*, *pxy*.
These values can be accessed by any command that uses a global array
from a compute as input. See the :doc:`Howto output <Howto_output>` doc

7
doc/src/compute_momentum.rst
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@ -6,7 +6,7 @@ compute momentum command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID momentum
@ -24,7 +24,8 @@ Description
"""""""""""
Define a computation that calculates the translational momentum *p*
of a group of particles. It is computed as the sum :math:`\vec{p} = \sum_i m_i \cdot \vec{v}_i`
of a group of particles. It is computed as the sum
:math:`\vec{p} = \sum_i m_i \cdot \vec{v}_i`
over all particles in the compute group, where *m* and *v* are
the mass and velocity vector of the particle, respectively.
@ -36,7 +37,7 @@ length 3. This value can be used by any command that uses a global
vector value from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The vector value calculated by this compute is "extensive". The vector
The vector value calculated by this compute is "extensive." The vector
value will be in mass\*velocity :doc:`units <units>`.
Restrictions

19
doc/src/compute_msd.rst
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@ -6,7 +6,7 @@ compute msd command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID msd keyword values ...
@ -34,12 +34,13 @@ Description
Define a computation that calculates the mean-squared displacement
(MSD) of the group of atoms, including all effects due to atoms
passing through periodic boundaries. For computation of the non-Gaussian
parameter of mean-squared displacement, see the :doc:`compute msd/nongauss <compute_msd_nongauss>` command.
parameter of mean-squared displacement, see the
:doc:`compute msd/nongauss <compute_msd_nongauss>` command.
A vector of four quantities is calculated by this compute. The first 3
elements of the vector are the squared dx,dy,dz displacements, summed
and averaged over atoms in the group. The fourth element is the total
squared displacement, i.e. (dx\*dx + dy\*dy + dz\*dz), summed and
A vector of four quantities is calculated by this compute. The first three
elements of the vector are the squared *dx*, *dy*, and *dz* displacements,
summed and averaged over atoms in the group. The fourth element is the total
squared displacement (i.e., :math:`dx^2 + dy^2 + dz^2`), summed and
averaged over atoms in the group.
The slope of the mean-squared displacement (MSD) versus time is
@ -100,12 +101,12 @@ Output info
"""""""""""
This compute calculates a global vector of length 4, which can be
accessed by indices 1-4 by any command that uses global vector values
accessed by indices 1--4 by any command that uses global vector values
from a compute as input. See the :doc:`Howto output <Howto_output>` doc
page for an overview of LAMMPS output options.
The vector values are "intensive". The vector values will be in
distance\^2 :doc:`units <units>`.
The vector values are "intensive." The vector values will be in
distance\ :math:`^2` :doc:`units <units>`.
Restrictions
""""""""""""

44
doc/src/compute_msd_chunk.rst
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@ -6,7 +6,7 @@ compute msd/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID msd/chunk chunkID
@ -27,19 +27,21 @@ Description
Define a computation that calculates the mean-squared displacement
(MSD) for multiple chunks of atoms.
In LAMMPS, chunks are collections of atoms defined by a :doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk). The ID for this command is specified
as chunkID. For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>` and :doc:`Howto chunk <Howto_chunk>`
molecule or atoms in a spatial bin. See the
:doc:`compute chunk/atom <compute_chunk_atom>` and
:doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.
Four quantities are calculated by this compute for each chunk. The
first 3 quantities are the squared dx,dy,dz displacements of the
center-of-mass. The fourth component is the total squared displacement,
i.e. (dx\*dx + dy\*dy + dz\*dz) of the center-of-mass. These
calculations include all effects due to atoms passing through periodic
boundaries.
first 3 quantities are the squared *dx*, *dy*, and *dz* displacements of the
center-of-mass. The fourth component is the total squared displacement
(i.e., :math:`dx^2 + dy^2 + dz^2`) of the center-of-mass. These calculations
include all effects due to atoms passing through periodic boundaries.
Note that only atoms in the specified group contribute to the
calculation. The :doc:`compute chunk/atom <compute_chunk_atom>` command
@ -58,12 +60,14 @@ compute command was first invoked.
.. note::
The number of chunks *Nchunk* calculated by the :doc:`compute chunk/atom <compute_chunk_atom>` command must remain constant each
time this compute is invoked, so that the displacement for each chunk
The number of chunks *Nchunk* calculated by the
:doc:`compute chunk/atom <compute_chunk_atom>` command must remain constant
each time this compute is invoked, so that the displacement for each chunk
from its original position can be computed consistently. If *Nchunk*
does not remain constant, an error will be generated. If needed, you
can enforce a constant *Nchunk* by using the *nchunk once* or *ids
once* options when specifying the :doc:`compute chunk/atom <compute_chunk_atom>` command.
can enforce a constant *Nchunk* by using the *nchunk once* or *ids once*
options when specifying the :doc:`compute chunk/atom <compute_chunk_atom>`
command.
.. note::
@ -84,7 +88,8 @@ compute command was first invoked.
"unwrapped" coordinates. See the Atoms section of the
:doc:`read_data <read_data>` command for a discussion of image flags and
how they are set for each atom. You can reset the image flags
(e.g. to 0) before invoking this compute by using the :doc:`set image <set>` command.
(e.g., to 0) before invoking this compute by using the
:doc:`set image <set>` command.
.. note::
@ -109,14 +114,15 @@ Output info
"""""""""""
This compute calculates a global array where the number of rows = the
number of chunks *Nchunk* as calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>` command. The number of columns =
4 for dx,dy,dz and the total displacement. These values can be
accessed by any command that uses global array values from a compute
as input. See the :doc:`Howto output <Howto_output>` page for an
number of chunks *Nchunk* as calculated by the specified
:doc:`compute chunk/atom <compute_chunk_atom>` command.
The number of columns = 4 for *dx*, *dy*, *dz*, and the total displacement.
These values can be accessed by any command that uses global array values from
a compute as input. See the :doc:`Howto output <Howto_output>` page for an
overview of LAMMPS output options.
The array values are "intensive". The array values will be in
distance\^2 :doc:`units <units>`.
The array values are "intensive." The array values will be in
distance\ :math:`^2` :doc:`units <units>`.
Restrictions
""""""""""""

30
doc/src/compute_msd_nongauss.rst
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@ -6,7 +6,7 @@ compute msd/nongauss command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID msd/nongauss keyword values ...
@ -35,21 +35,21 @@ Define a computation that calculates the mean-squared displacement
including all effects due to atoms passing through periodic boundaries.
A vector of three quantities is calculated by this compute. The first
element of the vector is the total squared dx,dy,dz displacements
drsquared = (dx\*dx + dy\*dy + dz\*dz) of atoms, and the second is the
fourth power of these displacements drfourth = (dx\*dx + dy\*dy +
dz\*dz)\*(dx\*dx + dy\*dy + dz\*dz), summed and averaged over atoms in the
group. The third component is the nonGaussian diffusion parameter NGP =
3\*drfourth/(5\*drsquared\*drsquared), i.e.
element of the vector is the total squared displacement,
:math:`dr^2 = dx^2 + dy^2 + dz^2`, of the atoms, and the second is the
fourth power of these displacements, :math:`dr^4 = (dx^2 + dy^2 + dz^2)^2`,
summed and averaged over atoms in the group. The third component is the
non-Gaussian diffusion parameter NGP,
.. math::
NGP(t) = 3<(r(t)-r(0))^4>/(5<(r(t)-r(0))^2>^2) - 1
\text{NGP}(t) = \frac{3\left\langle(r(t)-r(0))^4\right\rangle}
{5\left\langle(r(t)-r(0))^2\right\rangle^2} - 1.
The NGP is a commonly used quantity in studies of dynamical
heterogeneity. Its minimum theoretical value (-0.4) occurs when all
atoms have the same displacement magnitude. NGP=0 for Brownian
diffusion, while NGP > 0 when some mobile atoms move faster than
heterogeneity. Its minimum theoretical value :math:`(-0.4)` occurs when all
atoms have the same displacement magnitude. :math:`\text{NGP}=0` for Brownian
diffusion, while :math:`\text{NGP} > 0` when some mobile atoms move faster than
others.
If the *com* option is set to *yes* then the effect of any drift in
@ -63,13 +63,13 @@ Output info
"""""""""""
This compute calculates a global vector of length 3, which can be
accessed by indices 1-3 by any command that uses global vector values
accessed by indices 1--3 by any command that uses global vector values
from a compute as input. See the :doc:`Howto output <Howto_output>` doc
page for an overview of LAMMPS output options.
The vector values are "intensive". The first vector value will be in
distance\^2 :doc:`units <units>`, the second is in distance\^4 units, and
the third is dimensionless.
The vector values are "intensive." The first vector value will be in
distance\ :math:`^2` :doc:`units <units>`, the second is in
distance\ :math:`^4` units, and the third is dimensionless.
Restrictions
""""""""""""

2
doc/src/compute_nbond_atom.rst
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@ -6,7 +6,7 @@ compute nbond/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID nbond/atom

36
doc/src/compute_omega_chunk.rst
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@ -6,7 +6,7 @@ compute omega/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID omega/chunk chunkID
@ -27,18 +27,23 @@ Description
Define a computation that calculates the angular velocity (omega) of
multiple chunks of atoms.
In LAMMPS, chunks are collections of atoms defined by a :doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk). The ID for this command is specified
as chunkID. For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>` and :doc:`Howto chunk <Howto_chunk>`
molecule or atoms in a spatial bin. See the
:doc:`compute chunk/atom <compute_chunk_atom>` and
:doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.
This compute calculates the 3 components of the angular velocity
vector for each chunk, via the formula L = Iw where L is the angular
momentum vector of the chunk, I is its moment of inertia tensor, and w
is omega = angular velocity of the chunk. The calculation includes
all effects due to atoms passing through periodic boundaries.
This compute calculates the three components of the angular velocity
vector for each chunk via the formula
:math:`\vec L = \mathrm{I}\cdot \vec\omega`, where :math:`\vec L` is the
angular momentum vector of the chunk, :math:`\mathrm{I}` is its moment of
inertia tensor, and :math:`\omega` is the angular velocity of the chunk.
The calculation includes all effects due to atoms passing through periodic
boundaries.
Note that only atoms in the specified group contribute to the
calculation. The :doc:`compute chunk/atom <compute_chunk_atom>` command
@ -56,7 +61,8 @@ non-zero chunk IDs.
of "unwrapped" coordinates. See the Atoms section of the
:doc:`read_data <read_data>` command for a discussion of image flags and
how they are set for each atom. You can reset the image flags
(e.g. to 0) before invoking this compute by using the :doc:`set image <set>` command.
(e.g., to 0) before invoking this compute by using the
:doc:`set image <set>` command.
The simplest way to output the results of the compute omega/chunk
calculation to a file is to use the :doc:`fix ave/time <fix_ave_time>`
@ -71,14 +77,14 @@ command, for example:
Output info
"""""""""""
This compute calculates a global array where the number of rows = the
number of chunks *Nchunk* as calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>` command. The number of columns =
3 for the 3 xyz components of the angular velocity for each chunk.
This compute calculates a global array where the number of rows is the
number of chunks *Nchunk* as calculated by the specified :doc:`compute chunk/atom <compute_chunk_atom>` command. The number of columns is 3 for the three
(*x*, *y*, *z*) components of the angular velocity for each chunk.
These values can be accessed by any command that uses global array
values from a compute as input. See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
values from a compute as input. See the :doc:`Howto output <Howto_output>`
page for an overview of LAMMPS output options.
The array values are "intensive". The array values will be in
The array values are "intensive." The array values will be in
velocity/distance :doc:`units <units>`.
Restrictions

95
doc/src/compute_orientorder_atom.rst
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@ -9,7 +9,7 @@ Accelerator Variants: *orientorder/atom/kk*
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID orientorder/atom keyword values ...
@ -42,30 +42,30 @@ Description
"""""""""""
Define a computation that calculates a set of bond-orientational
order parameters :math:`Q_l` for each atom in a group. These order parameters
order parameters :math:`Q_\ell` for each atom in a group. These order parameters
were introduced by :ref:`Steinhardt et al. <Steinhardt>` as a way to
characterize the local orientational order in atomic structures.
For each atom, :math:`Q_l` is a real number defined as follows:
For each atom, :math:`Q_\ell` is a real number defined as follows:
.. math::
\bar{Y}_{lm} = & \frac{1}{nnn}\sum_{j = 1}^{nnn} Y_{lm}( \theta( {\bf r}_{ij} ), \phi( {\bf r}_{ij} ) ) \\
Q_l = & \sqrt{\frac{4 \pi}{2 l + 1} \sum_{m = -l}^{m = l} \bar{Y}_{lm} \bar{Y}^*_{lm}}
\bar{Y}_{\ell m} = & \frac{1}{nnn}\sum_{j = 1}^{nnn} Y_{\ell m}\bigl( \theta( {\bf r}_{ij} ), \phi( {\bf r}_{ij} ) \bigr) \\
Q_\ell = & \sqrt{\frac{4 \pi}{2 \ell + 1} \sum_{m = -\ell }^{m = \ell } \bar{Y}_{\ell m} \bar{Y}^*_{\ell m}}
The first equation defines the local order parameters as averages
of the spherical harmonics :math:`Y_{lm}` for each neighbor.
of the spherical harmonics :math:`Y_{\ell m}` for each neighbor.
These are complex number components of the 3D analog of the 2D order
parameter :math:`q_n`, which is implemented as LAMMPS compute
:doc:`hexorder/atom <compute_hexorder_atom>`.
The summation is over the *nnn* nearest
neighbors of the central atom.
The angles :math:`theta` and :math:`phi` are the standard spherical polar angles
neighbors of the central atom. The angles :math:`\theta` and :math:`\phi` are
the standard spherical polar angles
defining the direction of the bond vector :math:`r_{ij}`.
The phase and sign of :math:`Y_{lm}` follow the standard conventions,
so that :math:`{\rm sign}(Y_{ll}(0,0)) = (-1)^l`.
The second equation defines :math:`Q_l`, which is a
The phase and sign of :math:`Y_{\ell m}` follow the standard conventions,
so that :math:`\mathrm{sign}(Y_{\ell\ell}(0,0)) = (-1)^\ell`.
The second equation defines :math:`Q_\ell`, which is a
rotationally invariant non-negative amplitude obtained by summing
over all the components of degree *l*\ .
over all the components of degree :math:`\ell`.
The optional keyword *cutoff* defines the distance cutoff
used when searching for neighbors. The default value, also
@ -73,7 +73,7 @@ the maximum allowable value, is the cutoff specified
by the pair style.
The optional keyword *nnn* defines the number of nearest
neighbors used to calculate :math:`Q_l`. The default value is 12.
neighbors used to calculate :math:`Q_\ell`. The default value is 12.
If the value is NULL, then all neighbors up to the
specified distance cutoff are used.
@ -84,32 +84,45 @@ degree of each order parameter. Because :math:`Q_2` and all odd-degree order
parameters are zero for atoms in cubic crystals (see
:ref:`Steinhardt <Steinhardt>`), the default order parameters are :math:`Q_4`,
:math:`Q_6`, :math:`Q_8`, :math:`Q_{10}`, and :math:`Q_{12}`. For the FCC
crystal with *nnn* =12, :math:`Q_4 = \sqrt{\frac{7}{192}} = 0.19094...`.
crystal with *nnn* =12,
.. math::
Q_4 = \sqrt{\frac{7}{192}} \approx 0.19094
The numerical values of all order
parameters up to :math:`Q_12` for a range of commonly encountered
parameters up to :math:`Q_{12}` for a range of commonly encountered
high-symmetry structures are given in Table I of :ref:`Mickel et al. <Mickel>`,
and these can be reproduced with this compute.
The optional keyword *wl* will output the third-order invariants :math:`W_l`
The optional keyword *wl* will output the third-order invariants :math:`W_\ell`
(see Eq. 1.4 in :ref:`Steinhardt <Steinhardt>`) for the same degrees as
for the :math:`Q_l` parameters. For the FCC crystal with *nnn* =12,
:math:`W_4` = -sqrt(14/143).(49/4096)/Pi\^1.5 = -0.0006722136...
for the :math:`Q_\ell` parameters. For the FCC crystal with *nnn* = 12,
.. math::
W_4 = -\sqrt{\frac{14}{143}} \left(\frac{49}{4096}\right) \pi^{-3/2} \approx -0.0006722136
The optional keyword *wl/hat* will output the normalized third-order
invariants :math:`\hat{W}_l` (see Eq. 2.2 in :ref:`Steinhardt <Steinhardt>`)
for the same degrees as for the :math:`Q_l` parameters. For the FCC crystal
with *nnn* =12, :math:`\hat{W}_4 = -\frac{7}{3} \sqrt{\frac{2}{429}} = -0.159317...`
The numerical
values of :math:`\hat{W}_l` for a range of commonly encountered high-symmetry
structures are given in Table I of :ref:`Steinhardt <Steinhardt>`, and these
can be reproduced with this keyword.
invariants :math:`\hat{W}_\ell` (see Eq. 2.2 in :ref:`Steinhardt <Steinhardt>`)
for the same degrees as for the :math:`Q_\ell` parameters. For the FCC crystal
with *nnn* =12,
.. math::
\hat{W}_4 = -\frac{7}{3} \sqrt{\frac{2}{429}} \approx -0.159317
The numerical values of :math:`\hat{W}_\ell` for a range of commonly
encountered high-symmetry structures are given in Table I of
:ref:`Steinhardt <Steinhardt>`, and these can be reproduced with this keyword.
The optional keyword *components* will output the components of the
*normalized* complex vector :math:`\hat{Y}_{lm} = \bar{Y}_{lm}/|\bar{Y}_{lm}|` of degree *ldegree*\,
which must be included in the list of order parameters to be computed. This option can be used
in conjunction with :doc:`compute coord_atom <compute_coord_atom>` to
calculate the ten Wolde's criterion to identify crystal-like
particles, as discussed in :ref:`ten Wolde <tenWolde2>`.
*normalized* complex vector
:math:`\hat{Y}_{\ell m} = \bar{Y}_{\ell m}/|\bar{Y}_{\ell m}|`
of degree *ldegree*\, which must be included in the list of order parameters to
be computed. This option can be used in conjunction with
:doc:`compute coord_atom <compute_coord_atom>` to calculate the ten Wolde's
criterion to identify crystal-like particles, as discussed in
:ref:`ten Wolde <tenWolde2>`.
The optional keyword *chunksize* is only applicable when using the
the KOKKOS package and is ignored otherwise. This keyword controls
@ -119,12 +132,12 @@ if there are 32768 atoms in the simulation and the *chunksize*
is set to 16384, the parameter calculation will be broken up
into two passes.
The value of :math:`Q_l` is set to zero for atoms not in the
The value of :math:`Q_\ell` is set to zero for atoms not in the
specified compute group, as well as for atoms that have less than
*nnn* neighbors within the distance cutoff, unless *nnn* is NULL.
The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (i.e. each time a snapshot of atoms
time the calculation is performed (i.e., each time a snapshot of atoms
is dumped). Thus it can be inefficient to compute/dump this quantity
too frequently.
@ -155,19 +168,21 @@ Output info
"""""""""""
This compute calculates a per-atom array with *nlvalues* columns,
giving the :math:`Q_l` values for each atom, which are real numbers on the
range :math:`0 <= Q_l <= 1`.
giving the :math:`Q_\ell` values for each atom, which are real numbers in the
range :math:`0 \le Q_\ell \le 1`.
If the keyword *wl* is set to yes, then the :math:`W_l` values for each
If the keyword *wl* is set to yes, then the :math:`W_\ell` values for each
atom will be added to the output array, which are real numbers.
If the keyword *wl/hat* is set to yes, then the :math:`\hat{W}_l`
If the keyword *wl/hat* is set to yes, then the :math:`\hat{W}_\ell`
values for each atom will be added to the output array, which are real numbers.
If the keyword *components* is set, then the real and imaginary parts
of each component of *normalized* :math:`\hat{Y}_{lm}` will be added to the
output array in the following order: :math:`{\rm Re}(\hat{Y}_{-m}), {\rm Im}(\hat{Y}_{-m}),
{\rm Re}(\hat{Y}_{-m+1}), {\rm Im}(\hat{Y}_{-m+1}), \dots , {\rm Re}(\hat{Y}_m), {\rm Im}(\hat{Y}_m)`.
of each component of *normalized* :math:`\hat{Y}_{\ell m}` will be added to the
output array in the following order:
:math:`\Re(\hat{Y}_{-m}),` :math:`\Im(\hat{Y}_{-m}),`
:math:`\Re(\hat{Y}_{-m+1}),` :math:`\Im(\hat{Y}_{-m+1}), \dotsc,`
:math:`\Re(\hat{Y}_m),` :math:`\Im(\hat{Y}_m).`
In summary, the per-atom array will contain *nlvalues* columns, followed by
an additional *nlvalues* columns if *wl* is set to yes, followed by
@ -193,7 +208,7 @@ Default
"""""""
The option defaults are *cutoff* = pair style cutoff, *nnn* = 12,
*degrees* = 5 4 6 8 10 12 i.e. :math:`Q_4`, :math:`Q_6`, :math:`Q_8`, :math:`Q_{10}`, and :math:`Q_{12}`,
*degrees* = 5 4 6 8 10 12 (i.e., :math:`Q_4`, :math:`Q_6`, :math:`Q_8`, :math:`Q_{10}`, and :math:`Q_{12}`),
*wl* = no, *wl/hat* = no, *components* off, and *chunksize* = 16384
----------

4
doc/src/compute_pair.rst
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@ -6,7 +6,7 @@ compute pair command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pair pstyle [nstyle] [evalue]
@ -74,7 +74,7 @@ Output info
This compute calculates a global scalar which is *epair* or *evdwl* or
*ecoul*\ . If the pair style supports it, it also calculates a global
vector of length >= 1, as determined by the pair style. These values
vector of length :math:`\ge` 1, as determined by the pair style. These values
can be used by any command that uses global scalar or vector values
from a compute as input. See the :doc:`Howto output <Howto_output>` doc
page for an overview of LAMMPS output options.

27
doc/src/compute_pair_local.rst
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@ -6,7 +6,7 @@ compute pair/local command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pair/local value1 value2 ... keyword args ...
@ -57,7 +57,7 @@ force cutoff distance for that interaction, as defined by the
commands.
The value *dist* is the distance between the pair of atoms.
The values *dx*, *dy*, and *dz* are the xyz components of the
The values *dx*, *dy*, and *dz* are the :math:`(x,y,z)` components of the
*distance* between the pair of atoms. This value is always the
distance from the atom of lower to the one with the higher id.
@ -65,21 +65,21 @@ The value *eng* is the interaction energy for the pair of atoms.
The value *force* is the force acting between the pair of atoms, which
is positive for a repulsive force and negative for an attractive
force. The values *fx*, *fy*, and *fz* are the xyz components of
force. The values *fx*, *fy*, and *fz* are the :math:`(x,y,z)` components of
*force* on atom I.
A pair style may define additional pairwise quantities which can be
accessed as *p1* to *pN*, where N is defined by the pair style. Most
pair styles do not define any additional quantities, so N = 0. An
accessed as *p1* to *pN*, where :math:`N` is defined by the pair style. Most
pair styles do not define any additional quantities, so :math:`N = 0`. An
example of ones that do are the :doc:`granular pair styles <pair_gran>`
which calculate the tangential force between two particles and return
its components and magnitude acting on atom I for N = 1,2,3,4. See
individual pair styles for details.
its components and magnitude acting on atom :math:`I` for
:math:`N \in \{1,2,3,4\}`. See individual pair styles for details.
When using *pN* with pair style *hybrid*, the output will be the Nth
quantity from the sub-style that computes the pairwise interaction
(based on atom types). If that sub-style does not define a *pN*,
the output will be 0.0. The maximum allowed N is the maximum number
the output will be 0.0. The maximum allowed :math:`N` is the maximum number
of quantities provided by any sub-style.
When using *pN* with pair style *hybrid/overlay* the quantities
@ -104,7 +104,9 @@ the pairwise cutoff defined by the :doc:`pair_style <pair_style>`
command for the types of the two atoms is used. For the *radius*
setting, the sum of the radii of the two particles is used as a
cutoff. For example, this is appropriate for granular particles which
only interact when they are overlapping, as computed by :doc:`granular pair styles <pair_gran>`. Note that if a granular model defines atom
only interact when they are overlapping, as computed by
:doc:`granular pair styles <pair_gran>`.
Note that if a granular model defines atom
types such that all particles of a specific type are monodisperse
(same diameter), then the two settings are effectively identical.
@ -113,7 +115,8 @@ no consistent ordering of the entries within the local vector or array
from one timestep to the next. The only consistency that is
guaranteed is that the ordering on a particular timestep will be the
same for local vectors or arrays generated by other compute commands.
For example, pair output from the :doc:`compute property/local <compute_property_local>` command can be combined
For example, pair output from the
:doc:`compute property/local <compute_property_local>` command can be combined
with data from this command and output by the :doc:`dump local <dump>`
command in a consistent way.
@ -127,13 +130,13 @@ Here is an example of how to do this:
.. note::
For pairs, if two atoms I,J are involved in 1-2, 1-3, 1-4
For pairs, if two atoms I,J are involved in 1--2, 1--3, and 1--4
interactions within the molecular topology, their pairwise interaction
may be turned off, and thus they may not appear in the neighbor list,
and will not be part of the local data created by this command. More
specifically, this will be true of I,J pairs with a weighting factor
of 0.0; pairs with a non-zero weighting factor are included. The
weighting factors for 1-2, 1-3, and 1-4 pairwise interactions are set
weighting factors for 1--2, 1--3, and 1--4 pairwise interactions are set
by the :doc:`special_bonds <special_bonds>` command. An exception is if
long-range Coulombics are being computed via the
:doc:`kspace_style <kspace_style>` command, then atom pairs with

14
doc/src/compute_pe.rst
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@ -6,7 +6,7 @@ compute pe command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pe keyword ...
@ -27,19 +27,19 @@ Description
"""""""""""
Define a computation that calculates the potential energy of the
entire system of atoms. The specified group must be "all". See the
entire system of atoms. The specified group must be "all." See the
:doc:`compute pe/atom <compute_pe_atom>` command if you want per-atom
energies. These per-atom values could be summed for a group of atoms
via the :doc:`compute reduce <compute_reduce>` command.
The energy is calculated by the various pair, bond, etc potentials
The energy is calculated by the various pair, bond, etc. potentials
defined for the simulation. If no extra keywords are listed, then the
potential energy is the sum of pair, bond, angle, dihedral, improper,
kspace (long-range), and fix energy. I.e. it is as if all the
keywords were listed. If any extra keywords are listed, then only
:math:`k`-space (long-range), and fix energy (i.e., it is as though all the
keywords were listed). If any extra keywords are listed, then only
those components are summed to compute the potential energy.
The Kspace contribution requires 1 extra FFT each timestep the energy
The :math:`k`-space contribution requires 1 extra FFT each timestep the energy
is calculated, if using the PPPM solver via the :doc:`kspace_style pppm <kspace_style>` command. Thus it can increase the cost of the
PPPM calculation if it is needed on a large fraction of the simulation
timesteps.
@ -73,7 +73,7 @@ value can be used by any command that uses a global scalar value from
a compute as input. See the :doc:`Howto output <Howto_output>` doc page
for an overview of LAMMPS output options.
The scalar value calculated by this compute is "extensive". The
The scalar value calculated by this compute is "extensive." The
scalar value will be in energy :doc:`units <units>`.
Restrictions

19
doc/src/compute_pe_atom.rst
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@ -6,7 +6,7 @@ compute pe/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pe/atom keyword ...
@ -34,20 +34,20 @@ you want the potential energy of the entire system.
The per-atom energy is calculated by the various pair, bond, etc
potentials defined for the simulation. If no extra keywords are
listed, then the potential energy is the sum of pair, bond, angle,
dihedral,improper, kspace (long-range), and fix energy. I.e. it is as
if all the keywords were listed. If any extra keywords are listed,
dihedral, improper, :math:`k`-space (long-range), and fix energy (i.e., it is as
though all the keywords were listed). If any extra keywords are listed,
then only those components are summed to compute the potential energy.
Note that the energy of each atom is due to its interaction with all
other atoms in the simulation, not just with other atoms in the group.
For an energy contribution produced by a small set of atoms (e.g. 4
For an energy contribution produced by a small set of atoms (e.g., 4
atoms in a dihedral or 3 atoms in a Tersoff 3-body interaction), that
energy is assigned in equal portions to each atom in the set.
E.g. 1/4 of the dihedral energy to each of the 4 atoms.
energy is assigned in equal portions to each atom in the set (e.g., 1/4 of the
dihedral energy to each of the four atoms).
The :doc:`dihedral_style charmm <dihedral_charmm>` style calculates
pairwise interactions between 1-4 atoms. The energy contribution of
pairwise interactions between 1--4 atoms. The energy contribution of
these terms is included in the pair energy, not the dihedral energy.
The KSpace contribution is calculated using the method in
@ -81,8 +81,9 @@ in the last 2 columns of thermo output:
.. note::
The per-atom energy does not include any Lennard-Jones tail
corrections to the energy added by the :doc:`pair_modify tail yes <pair_modify>` command, since those are contributions to the
global system energy.
corrections to the energy added by the
:doc:`pair_modify tail yes <pair_modify>` command, since those are
contributions to the global system energy.
Output info
"""""""""""

17
doc/src/compute_plasticity_atom.rst
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@ -6,7 +6,7 @@ compute plasticity/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID plasticity/atom
@ -24,16 +24,19 @@ Description
"""""""""""
Define a computation that calculates the per-atom plasticity for each
atom in a group. This is a quantity relevant for :doc:`Peridynamics models <pair_peri>`. See `this document <PDF/PDLammps_overview.pdf>`_
atom in a group. This is a quantity relevant for
:doc:`Peridynamics models <pair_peri>`.
See `this document <PDF/PDLammps_overview.pdf>`_
for an overview of LAMMPS commands for Peridynamics modeling.
The plasticity for a Peridynamic particle is the so-called consistency
parameter (lambda). For elastic deformation lambda = 0, otherwise
lambda > 0 for plastic deformation. For details, see
parameter (:math:`\lambda`). For elastic deformation, :math:`\lambda = 0`,
otherwise :math:`\lambda > 0` for plastic deformation. For details, see
:ref:`(Mitchell) <Mitchell>` and the PDF doc included in the LAMMPS
distribution in `doc/PDF/PDLammps_EPS.pdf <PDF/PDLammps_EPS.pdf>`_.
This command can be invoked for one of the Peridynamic :doc:`pair styles <pair_peri>`: peri/eps.
This command can be invoked for one of the Peridynamic
:doc:`pair styles <pair_peri>`: peri/eps.
The plasticity value will be 0.0 for atoms not in the specified
compute group.
@ -46,7 +49,7 @@ any command that uses per-atom values from a compute as input. See
the :doc:`Howto output <Howto_output>` page for an overview of
LAMMPS output options.
The per-atom vector values are unitless numbers (lambda) >= 0.0.
The per-atom vector values are unitless numbers :math:`\lambda \ge 0.0`.
Restrictions
""""""""""""
@ -70,5 +73,5 @@ none
.. _Mitchell:
**(Mitchell)** Mitchell, "A non-local, ordinary-state-based
viscoelasticity model for peridynamics", Sandia National Lab Report,
viscoelasticity model for peridynamics," Sandia National Lab Report,
8064:1-28 (2011).

72
doc/src/compute_pressure.rst
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@ -6,7 +6,7 @@ compute pressure command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pressure temp-ID keyword ...
@ -29,7 +29,8 @@ Description
"""""""""""
Define a computation that calculates the pressure of the entire system
of atoms. The specified group must be "all". See the :doc:`compute stress/atom <compute_stress_atom>` command if you want per-atom
of atoms. The specified group must be "all." See the
:doc:`compute stress/atom <compute_stress_atom>` command if you want per-atom
pressure (stress). These per-atom values could be summed for a group
of atoms via the :doc:`compute reduce <compute_reduce>` command.
@ -37,35 +38,36 @@ The pressure is computed by the formula
.. math::
P = \frac{N k_B T}{V} + \frac{\sum_{i}^{N'} r_i \bullet f_i}{dV}
P = \frac{N k_B T}{V} + \frac{1}{V d}\sum_{i=1}^{N'} \vec r_i \cdot \vec f_i
where *N* is the number of atoms in the system (see discussion of DOF
below), :math:`k_B` is the Boltzmann constant, *T* is the temperature, d
is the dimensionality of the system (2 or 3 for 2d/3d), and *V* is the
below), :math:`k_B` is the Boltzmann constant, *T* is the temperature, *d*
is the dimensionality of the system (2 for 2d, 3 for 3d), and *V* is the
system volume (or area in 2d). The second term is the virial, equal to
-dU/dV, computed for all pairwise as well as 2-body, 3-body, 4-body,
many-body, and long-range interactions, where :math:`r_i` and
:math:`f_i` are the position and force vector of atom *i*, and the black
dot indicates a dot product. This is computed in parallel for each
sub-domain and then summed over all parallel processes. Thus N'
necessarily includes atoms from neighboring sub-domains (so-called ghost
atoms) and the position and force vectors of ghost atoms are thus
:math:`-dU/dV`, computed for all pairwise as well as 2-body, 3-body, 4-body,
many-body, and long-range interactions, where :math:`\vec r_i` and
:math:`\vec f_i` are the position and force vector of atom *i*, and the
dot indicates the dot product (scalar product). This is computed in parallel
for each sub-domain and then summed over all parallel processes. Thus
:math:`N'` necessarily includes atoms from neighboring sub-domains (so-called
ghost atoms) and the position and force vectors of ghost atoms are thus
included in the summation. Only when running in serial and without
periodic boundary conditions is N' = N = the number of atoms in the
system. :doc:`Fixes <fix>` that impose constraints (e.g. the :doc:`fix
periodic boundary conditions is :math:`N' = N` the number of atoms in the
system. :doc:`Fixes <fix>` that impose constraints (e.g., the :doc:`fix
shake <fix_shake>` command) may also contribute to the virial term.
A symmetric pressure tensor, stored as a 6-element vector, is also
calculated by this compute. The 6 components of the vector are
ordered xx, yy, zz, xy, xz, yz. The equation for the I,J components
(where I and J = x,y,z) is similar to the above formula, except that
the first term uses components of the kinetic energy tensor and the
calculated by this compute. The six components of the vector are
ordered :math:`xx,` :math:`yy,` :math:`zz,` :math:`xy,` :math:`xz,` :math:`yz.`
The equation for the :math:`(I,J)` components (where :math:`I` and :math:`J`
are :math:`x`, :math:`y`, or :math:`z`) is similar to the above formula,
except that the first term uses components of the kinetic energy tensor and the
second term uses components of the virial tensor:
.. math::
P_{IJ} = \frac{\sum_{k}^{N} m_k v_{k_I} v_{k_J}}{V} +
\frac{\sum_{k}^{N'} r_{k_I} f_{k_J}}{V}
P_{IJ} = \frac{1}{V}\sum_{k=1}^{N} m_k v_{k_I} v_{k_J} +
\frac{1}{V}\sum_{k=1}^{N'} r_{k_I} f_{k_J}.
If no extra keywords are listed, the entire equations above are
calculated. This includes a kinetic energy (temperature) term and the
@ -89,27 +91,30 @@ command. If the kinetic energy is not included in the pressure, than
the temperature compute is not used and can be specified as NULL.
Normally the temperature compute used by compute pressure should
calculate the temperature of all atoms for consistency with the virial
term, but any compute style that calculates temperature can be used,
e.g. one that excludes frozen atoms or other degrees of freedom.
term, but any compute style that calculates temperature can be used
(e.g., one that excludes frozen atoms or other degrees of freedom).
Note that if desired the specified temperature compute can be one that
subtracts off a bias to calculate a temperature using only the thermal
velocity of the atoms, e.g. by subtracting a background streaming
velocity. See the doc pages for individual :doc:`compute commands <compute>` to determine which ones include a bias.
velocity of the atoms (e.g., by subtracting a background streaming
velocity).
See the doc pages for individual :doc:`compute commands <compute>` to determine
which ones include a bias.
Also note that the N in the first formula above is really
degrees-of-freedom divided by d = dimensionality, where the DOF value
is calculated by the temperature compute. See the various :doc:`compute temperature <compute>` styles for details.
Also note that the :math:`N` in the first formula above is really
degrees-of-freedom divided by :math:`d` = dimensionality, where the DOF value
is calculated by the temperature compute.
See the various :doc:`compute temperature <compute>` styles for details.
A compute of this style with the ID of "thermo_press" is created when
A compute of this style with the ID of thermo_press is created when
LAMMPS starts up, as if this command were in the input script:
.. code-block:: LAMMPS
compute thermo_press all pressure thermo_temp
where "thermo_temp" is the ID of a similarly defined compute of style
"temp". See the "thermo_style" command for more details.
where thermo_temp is the ID of a similarly defined compute of style
"temp." See the :doc:`thermo_style <thermo_style>` command for more details.
----------
@ -122,15 +127,16 @@ Output info
This compute calculates a global scalar (the pressure) and a global
vector of length 6 (pressure tensor), which can be accessed by indices
1-6. These values can be used by any command that uses global scalar
1--6. These values can be used by any command that uses global scalar
or vector values from a compute as input. See the :doc:`Howto output
<Howto_output>` page for an overview of LAMMPS output options.
The ordering of values in the symmetric pressure tensor is as follows:
pxx, pyy, pzz, pxy, pxz, pyz.
:math:`p_{xx},` :math:`p_{yy},` :math:`p_{zz},` :math:`p_{xy},`
:math:`p_{xz},` :math:`p_{yz}.`
The scalar and vector values calculated by this compute are
"intensive". The scalar and vector values will be in pressure
"intensive." The scalar and vector values will be in pressure
:doc:`units <units>`.
Restrictions

8
doc/src/compute_pressure_uef.rst
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@ -6,7 +6,7 @@ compute pressure/uef command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID pressure/uef temp-ID keyword ...
@ -42,14 +42,14 @@ Restrictions
""""""""""""
This fix is part of the UEF package. It is only enabled if LAMMPS
was built with that package. See the :doc:`Build package <Build_package>` page for more info.
was built with that package. See the :doc:`Build package <Build_package>` page
for more info.
This command can only be used when :doc:`fix nvt/uef <fix_nh_uef>`
or :doc:`fix npt/uef <fix_nh_uef>` is active.
The kinetic contribution to the pressure tensor
will be accurate only when
the compute specified by *temp-ID* is a
will be accurate only when the compute specified by *temp-ID* is a
:doc:`compute temp/uef <compute_temp_uef>`.
Related commands

36
doc/src/compute_property_atom.rst
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@ -6,7 +6,7 @@ compute property/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID property/atom input1 input2 ...
@ -127,7 +127,7 @@ LAMMPS.
The values are stored in a per-atom vector or array as discussed
below. Zeroes are stored for atoms not in the specified group or for
quantities that are not defined for a particular particle in the group
(e.g. *shapex* if the particle is not an ellipsoid).
(e.g., *shapex* if the particle is not an ellipsoid).
Attributes *i_name*, *d_name*, *i2_name*, *d2_name* refer to custom
per-atom integer and floating-point vectors or arrays that have been
@ -135,7 +135,7 @@ added via the :doc:`fix property/atom <fix_property_atom>` command.
When that command is used specific names are given to each attribute
which are the "name" portion of these attributes. For arrays *i2_name*
and *d2_name*, the column of the array must also be included following
the name in brackets: e.g. d2_xyz[2], i2_mySpin[3].
the name in brackets (e.g., d2_xyz[2] or i2_mySpin[3]).
The additional quantities only accessible via this command, and not
directly via the :doc:`dump custom <dump>` command, are as follows.
@ -144,21 +144,21 @@ directly via the :doc:`dump custom <dump>` command, are as follows.
number of explicit bonds assigned to an atom. Note that if the
:doc:`newton bond <newton>` command is set to *on*\ , which is the
default, then every bond in the system is assigned to only one of the
two atoms in the bond. Thus a bond between atoms I,J may be tallied
for either atom I or atom J. If :doc:`newton bond off <newton>` is
set, it will be tallied with both atom I and atom J.
two atoms in the bond. Thus a bond between atoms :math:`I` and :math:`J` may
be tallied for either atom :math:`I` or atom :math:`J`.
If :doc:`newton bond off <newton>` is set, it will be tallied with both atom
:math:`I` and atom :math:`J`.
*Shapex*, *shapey*, and *shapez* are defined for ellipsoidal particles
and define the 3d shape of each particle.
The quantities *shapex*, *shapey*, and *shapez* are defined for ellipsoidal
particles and define the 3d shape of each particle.
*Quatw*, *quati*, *quatj*, and *quatk* are defined for ellipsoidal
particles and body particles and store the 4-vector quaternion
The quantities *quatw*, *quati*, *quatj*, and *quatk* are defined for
ellipsoidal particles and body particles and store the 4-vector quaternion
representing the orientation of each particle. See the :doc:`set <set>`
command for an explanation of the quaternion vector.
*End1x*, *end1y*, *end1z*, *end2x*, *end2y*, *end2z*, are
defined for line segment particles and define the end points of each
line segment.
*End1x*, *end1y*, *end1z*, *end2x*, *end2y*, *end2z*, are defined for line
segment particles and define the end points of each line segment.
*Corner1x*, *corner1y*, *corner1z*, *corner2x*, *corner2y*,
*corner2z*, *corner3x*, *corner3y*, *corner3z*, are defined for
@ -179,12 +179,12 @@ per-atom values from a compute as input. See the :doc:`Howto output
<Howto_output>` page for an overview of LAMMPS output options.
The vector or array values will be in whatever :doc:`units <units>` the
corresponding attribute is in, e.g. velocity units for vx, charge
units for q, etc.
corresponding attribute is in (e.g., velocity units for *vx*, charge
units for *q*).
For the spin quantities, sp is in the units of the Bohr magneton, spx,
spy, and spz are unitless quantities, and fmx, fmy and fmz are given
in rad/THz.
For the spin quantities, *sp* is in the units of the Bohr magneton;
*spx*, *spy*, and *spz* are unitless quantities; and *fmx*, *fmy*, and *fmz*
are given in rad/THz.
Restrictions
""""""""""""

29
doc/src/compute_property_chunk.rst
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@ -6,7 +6,7 @@ compute property/chunk command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID property/chunk chunkID input1 input2 ...
@ -35,19 +35,24 @@ Description
Define a computation that stores the specified attributes of chunks of
atoms.
In LAMMPS, chunks are collections of atoms defined by a :doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
In LAMMPS, chunks are collections of atoms defined by a
:doc:`compute chunk/atom <compute_chunk_atom>` command, which assigns each atom
to a single chunk (or no chunk). The ID for this command is specified
as chunkID. For example, a single chunk could be the atoms in a
molecule or atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>` and :doc:`Howto chunk <Howto_chunk>`
doc pages for details of how chunks can be defined and examples of how
they can be used to measure properties of a system.
as chunkID. For example, a single chunk could be the atoms in a molecule or
atoms in a spatial bin. See the :doc:`compute chunk/atom <compute_chunk_atom>`
and :doc:`Howto chunk <Howto_chunk>` doc pages for details of how chunks can be
defined and examples of how they can be used to measure properties of a system.
This compute calculates and stores the specified attributes of chunks
as global data so they can be accessed by other :doc:`output commands <Howto_output>` and used in conjunction with other
commands that generate per-chunk data, such as :doc:`compute com/chunk <compute_com_chunk>` or :doc:`compute msd/chunk <compute_msd_chunk>`.
as global data so they can be accessed by other
:doc:`output commands <Howto_output>` and used in conjunction with other
commands that generate per-chunk data, such as
:doc:`compute com/chunk <compute_com_chunk>` or
:doc:`compute msd/chunk <compute_msd_chunk>`.
Note that only atoms in the specified group contribute to the
calculation of the *count* attribute. The :doc:`compute chunk/atom <compute_chunk_atom>` command defines its own group;
calculation of the *count* attribute. The
:doc:`compute chunk/atom <compute_chunk_atom>` command defines its own group;
atoms will have a chunk ID = 0 if they are not in that group,
signifying they are not assigned to a chunk, and will thus also not
contribute to this calculation. You can specify the "all" group for
@ -59,7 +64,7 @@ The *count* attribute is the number of atoms in the chunk.
The *id* attribute stores the original chunk ID for each chunk. It
can only be used if the *compress* keyword was set to *yes* for the
:doc:`compute chunk/atom <compute_chunk_atom>` command referenced by
chunkID. This means that the original chunk IDs (e.g. molecule IDs)
chunkID. This means that the original chunk IDs (e.g., molecule IDs)
will have been compressed to remove chunk IDs with no atoms assigned
to them. Thus a compressed chunk ID of 3 may correspond to an original
chunk ID (molecule ID in this case) of 415. The *id* attribute will
@ -75,7 +80,7 @@ is the center point of the bin in the corresponding dimension. Style
Note that if the value of the *units* keyword used in the :doc:`compute chunk/atom command <compute_chunk_atom>` is *box* or *lattice*, the
*coordN* attributes will be in distance :doc:`units <units>`. If the
value of the *units* keyword is *reduced*, the *coordN* attributes
will be in unitless reduced units (0-1).
will be in unitless reduced units (0--1).
The simplest way to output the results of the compute property/chunk
calculation to a file is to use the :doc:`fix ave/time <fix_ave_time>`
@ -105,7 +110,7 @@ accessed by any command that uses global values from a compute as
input. See the :doc:`Howto output <Howto_output>` page for an
overview of LAMMPS output options.
The vector or array values are "intensive". The values will be
The vector or array values are "intensive." The values will be
unitless or in the units discussed above.
Restrictions

85
doc/src/compute_property_local.rst
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@ -6,37 +6,65 @@ compute property/local command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID property/local attribute1 attribute2 ... keyword args ...
* ID, group-ID are documented in :doc:`compute <compute>` command
* property/local = style name of this compute command
* one or more attributes may be appended
* one or more attributes of the same type (neighbor, pair, bond, angle,
dihedral, or improper) may be appended
.. parsed-literal::
possible attributes = natom1 natom2 ntype1 ntype2
patom1 patom2 ptype1 ptype2
batom1 batom2 btype
aatom1 aatom2 aatom3 atype
datom1 datom2 datom3 datom4 dtype
iatom1 iatom2 iatom3 iatom4 itype
possible attributes = natom1, natom2, ntype1, ntype2,
patom1, patom2, ptype1, ptype2,
batom1, batom2, btype,
aatom1, aatom2, aatom3, atype,
datom1, datom2, datom3, datom4, dtype,
iatom1, iatom2, iatom3, iatom4, itype
* Neighbor attributes
.. parsed-literal::
natom1, natom2 = IDs of 2 atoms in each pair (within neighbor cutoff)
ntype1, ntype2 = type of 2 atoms in each pair (within neighbor cutoff)
patom1, patom2 = IDs of 2 atoms in each pair (within force cutoff)
ptype1, ptype2 = type of 2 atoms in each pair (within force cutoff)
batom1, batom2 = IDs of 2 atoms in each bond
btype = bond type of each bond
aatom1, aatom2, aatom3 = IDs of 3 atoms in each angle
atype = angle type of each angle
datom1, datom2, datom3, datom4 = IDs of 4 atoms in each dihedral
dtype = dihedral type of each dihedral
iatom1, iatom2, iatom3, iatom4 = IDs of 4 atoms in each improper
itype = improper type of each improper
natom1, natom2 = store IDs of 2 atoms in each pair (within neighbor cutoff)
ntype1, ntype2 = store types of 2 atoms in each pair (within neighbor cutoff)
* Pair attributes
.. parsed-literal::
patom1, patom2 = store IDs of 2 atoms in each pair (within force cutoff)
ptype1, ptype2 = store types of 2 atoms in each pair (within force cutoff)
* Bond attributes
.. parsed-literal::
batom1, batom2 = store IDs of 2 atoms in each bond
btype = store bond type of each bond
* Angle attributes
.. parsed-literal::
aatom1, aatom2, aatom3 = store IDs of 3 atoms in each angle
atype = store angle type of each angle
* Dihedral attributes
.. parsed-literal::
datom1, datom2, datom3, datom4 = store IDs of 4 atoms in each dihedral
dtype = store dihedral type of each dihedral
* Improper attributes
.. parsed-literal::
iatom1, iatom2, iatom3, iatom4 = store IDs of 4 atoms in each improper
itype = store improper type of each improper
* zero or more keyword/arg pairs may be appended
* keyword = *cutoff*
@ -113,21 +141,21 @@ same for local vectors or arrays generated by other compute commands.
For example, output from the :doc:`compute bond/local <compute_bond_local>` command can be combined with bond
atom indices from this command and output by the :doc:`dump local <dump>` command in a consistent way.
The *natom1* and *natom2*, or *patom1* and *patom2* attributes refer
The *natom1* and *natom2* or *patom1* and *patom2* attributes refer
to the atom IDs of the 2 atoms in each pairwise interaction computed
by the :doc:`pair_style <pair_style>` command. The *ntype1* and
*ntype2*, or *ptype1* and *ptype2* attributes refer to the atom types
*ntype2* or *ptype1* and *ptype2* attributes refer to the atom types
of the 2 atoms in each pairwise interaction.
.. note::
For pairs, if two atoms I,J are involved in 1-2, 1-3, 1-4
For pairs, if two atoms :math:`I,J` are involved in 1--2, 1--3, 1--4
interactions within the molecular topology, their pairwise interaction
may be turned off, and thus they may not appear in the neighbor list,
and will not be part of the local data created by this command. More
specifically, this may be true of I,J pairs with a weighting factor of
0.0; pairs with a non-zero weighting factor are included. The
weighting factors for 1-2, 1-3, and 1-4 pairwise interactions are set
specifically, this may be true of :math:`I,J` pairs with a weighting factor
of 0.0; pairs with a non-zero weighting factor are included. The
weighting factors for 1--2, 1--3, and 1--4 pairwise interactions are set
by the :doc:`special_bonds <special_bonds>` command.
The *batom1* and *batom2* attributes refer to the atom IDs of the 2
@ -136,7 +164,7 @@ the type of the bond, from 1 to Nbtypes = # of bond types. The number
of bond types is defined in the data file read by the
:doc:`read_data <read_data>` command.
The attributes that start with "a", "d", "i", refer to similar values
The attributes that start with "a," "d," and "i" refer to similar values
for :doc:`angles <angle_style>`, :doc:`dihedrals <dihedral_style>`, and
:doc:`impropers <improper_style>`.
@ -149,7 +177,8 @@ the array is the number of bonds, angles, etc. 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 :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
that uses local values from a compute as input. See the
:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
options.
The vector or array values will be integers that correspond to the

44
doc/src/compute_ptm_atom.rst
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@ -6,13 +6,13 @@ compute ptm/atom command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID ptm/atom structures threshold group2-ID
* ID, group-ID are documented in :doc:`compute <compute>` command
* ptm/atom = style name of this compute command
* structures = structure types to search for
* structures = *default* or *all* or any hyphen-separated combination of *fcc*, *hcp*, *bcc*, *ico*, *sc*, *dcub*, *dhex*, or *graphene* = structure types to search for
* threshold = lattice distortion threshold (RMSD)
* group2-ID determines which group is used for neighbor selection (optional, default "all")
@ -43,9 +43,10 @@ Currently, there are seven lattice structures PTM recognizes:
* dhex (diamond hexagonal) = 7
* graphene = 8
The value of the PTM structure will be 0 for unknown types and -1 for atoms not in the specified
compute group. The choice of structures to search for can be specified using the "structures"
argument, which is a hyphen-separated list of structure keywords.
The value of the PTM structure will be 0 for unknown types and :math:`-1` for
atoms not in the specified compute group. The choice of structures to search
for can be specified using the "structures" argument, which is a
hyphen-separated list of structure keywords.
Two convenient pre-set options are provided:
* default: fcc-hcp-bcc-ico
@ -63,21 +64,25 @@ The deviation is calculated as:
.. math::
\text{RMSD}(\mathbf{u}, \mathbf{v}) = \min_{s, \mathbf{Q}} \sqrt{\frac{1}{N} \sum\limits_{i=1}^{N}
{\left|\left| s[\vec{u_i} - \overline{\mathbf{u}}] - \mathbf{Q} \vec{v_i} \right|\right|}^2}
\text{RMSD}(\mathbf{u}, \mathbf{v})
= \min_{s, \mathbf{Q}} \sqrt{\frac{1}{N} \sum\limits_{i=1}^{N}
{\left\lVert s[\vec{u_i} - \mathbf{\bar{u}}]
- \mathbf{Q} \cdot \vec{v_i} \right\rVert}^2}
Here, u and v contain the coordinates of the local and ideal structures respectively,
s is a scale factor, and Q is a rotation. The best match is identified by the
lowest RMSD value, using the optimal scaling, rotation, and correspondence between the
Here, :math:`\vec u` and :math:`\vec v` contain the coordinates of the local
and ideal structures respectively, :math:`s` is a scale factor, and
:math:`\mathbf Q` is a rotation. The best match is identified by the lowest
RMSD value, using the optimal scaling, rotation, and correspondence between the
points.
The 'threshold' keyword sets an upper limit on the maximum permitted deviation before
a local structure is identified as disordered. Typical values are in the range 0.1-0.15,
but larger values may be desirable at higher temperatures.
A value of 0 is equivalent to infinity and can be used if no threshold is desired.
The *threshold* keyword sets an upper limit on the maximum permitted deviation
before a local structure is identified as disordered. Typical values are in
the range 0.1--0.15, but larger values may be desirable at higher temperatures.
A value of 0 is equivalent to infinity and can be used if no threshold is
desired.
The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (e.g. each time a snapshot of atoms
time the calculation is performed (e.g., each time a snapshot of atoms
is dumped). Thus it can be inefficient to compute/dump this quantity
too frequently or to have multiple compute/dump commands, each with a
*ptm/atom* style. By default the compute processes **all** neighbors
@ -102,11 +107,12 @@ Results are stored in the per-atom array in the following order:
* qy
* qz
The type is a number from -1 to 8. The rmsd is a positive real number.
The type is a number from :math:`-1` to 8. The rmsd is a positive real number.
The interatomic distance is computed from the scale factor in the RMSD equation.
The (qw,qx,qy,qz) parameters represent the orientation of the local structure
in quaternion form. The reference coordinates for each template (from which the
orientation is determined) can be found in the *ptm_constants.h* file in the PTM source directory.
The :math:`(qw,qx,qy,qz)` parameters represent the orientation of the local
structure in quaternion form. The reference coordinates for each template
(from which the orientation is determined) can be found in the
*ptm_constants.h* file in the PTM source directory.
For atoms that are not within the compute group-ID, all values are set to zero.
Restrictions

94
doc/src/compute_rdf.rst
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@ -6,7 +6,7 @@ compute rdf command
Syntax
""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute ID group-ID rdf Nbin itype1 jtype1 itype2 jtype2 ... keyword/value ...
@ -38,7 +38,7 @@ Description
"""""""""""
Define a computation that calculates the radial distribution function
(RDF), also called g(r), and the coordination number for a group of
(RDF), also called :math:`g(r)`, and the coordination number for a group of
particles. Both are calculated in histogram form by binning pairwise
distances into *Nbin* bins from 0.0 to the maximum force cutoff
defined by the :doc:`pair_style <pair_style>` command or the cutoff
@ -58,27 +58,27 @@ shell of distances in 3d and a thin ring of distances in 2d.
using long-range coulomb interactions (\ *coul/long*, *coul/msm*,
*coul/wolf* or similar. One way to get around this would be to set
special_bond scaling factors to very tiny numbers that are not exactly
zero (e.g. 1.0e-50). Another workaround is to write a dump file, and
use the :doc:`rerun <rerun>` command to compute the RDF for snapshots in
the dump file. The rerun script can use a
zero (e.g., :math:`1.0 \times 10^{-50}`). Another workaround is to write a
dump file, and use the :doc:`rerun <rerun>` command to compute the RDF for
snapshots in the dump file. The rerun script can use a
:doc:`special_bonds <special_bonds>` command that includes all pairs in
the neighbor list.
By default the RDF is computed out to the maximum force cutoff defined
by the :doc:`pair_style <pair_style>` command. If the *cutoff* keyword
is used, then the RDF is computed accurately out to the *Rcut* > 0.0
is used, then the RDF is computed accurately out to the *Rcut* :math:`> 0.0`
distance specified.
.. note::
Normally, you should only use the *cutoff* keyword if no pair
style is defined, e.g. the :doc:`rerun <rerun>` command is being used to
post-process a dump file of snapshots. Or if you really want the RDF
style is defined (e.g., the :doc:`rerun <rerun>` command is being used to
post-process a dump file of snapshots) or if you really want the RDF
for distances beyond the pair_style force cutoff and cannot easily
post-process a dump file to calculate it. This is because using the
*cutoff* keyword incurs extra computation and possibly communication,
which may slow down your simulation. If you specify a *Rcut* <= force
cutoff, you will force an additional neighbor list to be built at
which may slow down your simulation. If you specify *Rcut* :math:`\le`
force cutoff, you will force an additional neighbor list to be built at
every timestep this command is invoked (or every reneighboring
timestep, whichever is less frequent), which is inefficient. LAMMPS
will warn you if this is the case. If you specify a *Rcut* > force
@ -92,56 +92,56 @@ distance specified.
The *itypeN* and *jtypeN* arguments are optional. These arguments
must come in pairs. If no pairs are listed, then a single histogram
is computed for g(r) between all atom types. If one or more pairs are
is computed for :math:`g(r)` between all atom types. If one or more pairs are
listed, then a separate histogram is generated for each
*itype*,\ *jtype* pair.
The *itypeN* and *jtypeN* settings can be specified in one of two
ways. An explicit numeric value can be used, as in the fourth example
above. Or a wild-card asterisk can be used to specify a range of atom
types. This takes the form "\*" or "\*n" or "n\*" or "m\*n". If N = the
number of atom types, then an asterisk with no numeric values means
all types from 1 to N. A leading asterisk means all types from 1 to n
(inclusive). A trailing asterisk means all types from n to N
(inclusive). A middle asterisk means all types from m to n
(inclusive).
types. This takes the form "\*" or "\*n" or "m\*" or "m\*n". If
:math:`N` is the number of atom types, then an asterisk with no numeric values
means all types from 1 to :math:`N`. A leading asterisk means all types from 1
to n (inclusive). A trailing asterisk means all types from m to :math:`N`
(inclusive). A middle asterisk means all types from m to n (inclusive).
If both *itypeN* and *jtypeN* are single values, as in the fourth example
above, this means that a g(r) is computed where atoms of type *itypeN*
above, this means that a :math:`g(r)` is computed where atoms of type *itypeN*
are the central atom, and atoms of type *jtypeN* are the distribution
atom. If either *itypeN* and *jtypeN* represent a range of values via
the wild-card asterisk, as in the fifth example above, this means that a
g(r) is computed where atoms of any of the range of types represented
:math:`g(r)` is computed where atoms of any of the range of types represented
by *itypeN* are the central atom, and atoms of any of the range of
types represented by *jtypeN* are the distribution atom.
Pairwise distances are generated by looping over a pairwise neighbor
list, just as they would be in a :doc:`pair_style <pair_style>`
computation. The distance between two atoms I and J is included in a
specific histogram if the following criteria are met:
computation. The distance between two atoms :math:`I` and :math:`J` is
included in a specific histogram if the following criteria are met:
* atoms I,J are both in the specified compute group
* the distance between atoms I,J is less than the maximum force cutoff
* the type of the I atom matches itypeN (one or a range of types)
* the type of the J atom matches jtypeN (one or a range of types)
* atoms :math:`I` and :math:`J` are both in the specified compute group
* the distance between atoms :math:`I` and :math:`J` is less than the maximum
force cutoff
* the type of the :math:`I` atom matches *itypeN* (one or a range of types)
* the type of the :math:`J` atom matches *jtypeN* (one or a range of types)
It is OK if a particular pairwise distance is included in more than
one individual histogram, due to the way the *itypeN* and *jtypeN*
arguments are specified.
The g(r) value for a bin is calculated from the histogram count by
The :math:`g(r)` value for a bin is calculated from the histogram count by
scaling it by the idealized number of how many counts there would be
if atoms of type *jtypeN* were uniformly distributed. Thus it
involves the count of *itypeN* atoms, the count of *jtypeN* atoms, the
volume of the entire simulation box, and the volume of the bin's thin
shell in 3d (or the area of the bin's thin ring in 2d).
A coordination number coord(r) is also calculated, which is the number
of atoms of type *jtypeN* within the current bin or closer, averaged
A coordination number :math:`\mathrm{coord}(r)` is also calculated, which is
the number of atoms of type *jtypeN* within the current bin or closer, averaged
over atoms of type *itypeN*\ . This is calculated as the area- or
volume-weighted sum of g(r) values over all bins up to and including
volume-weighted sum of :math:`g(r)` values over all bins up to and including
the current bin, multiplied by the global average volume density of
atoms of type jtypeN.
atoms of type *jtypeN*.
The simplest way to output the results of the compute rdf calculation
to a file is to use the :doc:`fix ave/time <fix_ave_time>` command, for
@ -155,41 +155,43 @@ example:
Output info
"""""""""""
This compute calculates a global array with the number of rows =
*Nbins*, and the number of columns = 1 + 2\*Npairs, where Npairs is the
number of I,J pairings specified. The first column has the bin
coordinate (center of the bin), Each successive set of 2 columns has
the g(r) and coord(r) values for a specific set of *itypeN* versus
*jtypeN* interactions, as described above. These values can be used
This compute calculates a global array in which the number of rows is
*Nbins* and the number of columns is :math:`1 + 2N_\text{pairs}`, where
:math:`N_\text{pairs}` is the number of :math:`I,J` pairings specified.
The first column has the bin coordinate (center of the bin), and each
successive set of two columns has the :math:`g(r)` and :math:`\text{coord}(r)`
values for a specific set of *itypeN* versus *jtypeN* interactions,
as described above. These values can be used
by any command that uses a global values from a compute as input. See
the :doc:`Howto output <Howto_output>` page for an overview of
LAMMPS output options.
The array values calculated by this compute are all "intensive".
The array values calculated by this compute are all "intensive."
The first column of array values will be in distance
:doc:`units <units>`. The g(r) columns of array values are normalized
numbers >= 0.0. The coordination number columns of array values are
also numbers >= 0.0.
:doc:`units <units>`. The :math:`g(r)` columns of array values are normalized
numbers :math:`\ge 0.0`. The coordination number columns of array values are
also numbers :math:`\ge 0.0`.
Restrictions
""""""""""""
The RDF is not computed for distances longer than the force cutoff,
since processors (in parallel) don't know about atom coordinates for
since processors (in parallel) do not know about atom coordinates for
atoms further away than that distance. If you want an RDF for larger
distances, you can use the :doc:`rerun <rerun>` command to post-process
a dump file and set the cutoff for the potential to be longer in the
rerun script. Note that in the rerun context, the force cutoff is
arbitrary, since you are not running dynamics and thus are not changing
your model. The definition of g(r) used by LAMMPS is only appropriate
your model. The definition of :math:`g(r)` used by LAMMPS is only appropriate
for characterizing atoms that are uniformly distributed throughout the
simulation cell. In such cases, the coordination number is still
correct and meaningful. As an example, if a large simulation cell
contains only one atom of type *itypeN* and one of *jtypeN*, then g(r)
contains only one atom of type *itypeN* and one of *jtypeN*, then :math:`g(r)`
will register an arbitrarily large spike at whatever distance they
happen to be at, and zero everywhere else. Coord(r) will show a step
change from zero to one at the location of the spike in g(r).
happen to be at, and zero everywhere else.
The function :math:`\text{coord}(r)` will show a step
change from zero to one at the location of the spike in :math:`g(r)`.
.. note::
@ -198,7 +200,7 @@ change from zero to one at the location of the spike in g(r).
parameters need to be re-computed in every step and include collective
communication operations. This will reduce performance and limit
parallel efficiency and scaling. For systems, where only the type
of atoms changes (e.g. when using :doc:`fix atom/swap <fix_atom_swap>`),
of atoms changes (e.g., when using :doc:`fix atom/swap <fix_atom_swap>`),
you need to explicitly request the dynamic normalization updates
via :doc:`compute_modify dynamic yes <compute_modify>`

4
doc/src/set.rst
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@ -14,8 +14,8 @@ Syntax
* ID = atom ID range or type range or mol ID range or group ID or region ID
* one or more keyword/value pairs may be appended
* keyword = *type* or *type/fraction* or *type/ratio* or *type/subset*
or *mol* or *x* or *y* or *z* or *charge* or *dipole* or
*dipole/random* or *quat* or *spin* or *spin/random* or
or *mol* or *x* or *y* or *z* or *vx* or *vy* or *vz* or *charge* or
*dipole* or *dipole/random* or *quat* or *spin* or *spin/random* or
*quat* or *quat/random* or *diameter* or *shape* or
*length* or *tri* or *theta* or *theta/random* or *angmom* or
*omega* or *mass* or *density* or *density/disc* or