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diff --git a/doc/compute_centro_atom.html b/doc/compute_centro_atom.html
index 597c924e0..c00718f23 100644
--- a/doc/compute_centro_atom.html
+++ b/doc/compute_centro_atom.html
@@ -1,72 +1,72 @@
<HTML>
<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
</CENTER>
<HR>
<H3>compute centro/atom command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID centro/atom
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>centro/atom = style name of this compute command
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute 1 all centro/atom
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the centro-symmetry parameter for
each atom in a group. In solid-state systems the centro-symmetry
parameter is a useful measure of the local lattice disorder around an
atom and can be used to characterize whether the atom is part of a
perfect lattice, a local defect (e.g. a dislocation or stacking
fault), or at a surface.
</P>
<P>The value of the centro-symmetry parameter will be 0.0 for atoms not
in the specified compute group.
</P>
<P>This parameter is computed using the following formula from
<A HREF = "#Kelchner">(Kelchner)</A>
</P>
<CENTER><IMG SRC = "Eqs/centro_symmetry.jpg">
</CENTER>
-<P>where the 12 nearest neighbors are found and Ri and Ri+6 are the
-vectors from the central atom to the opposite pair of nearest
-neighbors. Atoms not in the group are included in the 12 neighbors
-used in this calculation.
+<P>where the 12 nearest neighbors are found (for fcc lattices) and Ri and
+Ri+6 are the vectors from the central atom to the opposite pair of
+nearest neighbors. Atoms not in the group are included in the 12
+neighbors used in this calculation.
</P>
<P>The neighbor list needed to compute this quantity is constructed each
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 or to have multiple compute/dump commands, each of a
<I>centro/atom</I> style.
</P>
<P><B>Output info:</B>
</P>
<P>This compute calculates a scalar quantity for each atom, which can be
accessed by any command that uses per-atom computes as input. See
<A HREF = "Section_howto.html#4_15">this section</A> for an overview of LAMMPS
output options.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B> none
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Kelchner"></A>
<P><B>(Kelchner)</B> Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998).
</P>
</HTML>
diff --git a/doc/compute_centro_atom.txt b/doc/compute_centro_atom.txt
index a892f8c44..fc7f36f2e 100644
--- a/doc/compute_centro_atom.txt
+++ b/doc/compute_centro_atom.txt
@@ -1,66 +1,66 @@
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
compute centro/atom command :h3
[Syntax:]
compute ID group-ID centro/atom :pre
ID, group-ID are documented in "compute"_compute.html command
centro/atom = style name of this compute command :ul
[Examples:]
compute 1 all centro/atom :pre
[Description:]
Define a computation that calculates the centro-symmetry parameter for
each atom in a group. In solid-state systems the centro-symmetry
parameter is a useful measure of the local lattice disorder around an
atom and can be used to characterize whether the atom is part of a
perfect lattice, a local defect (e.g. a dislocation or stacking
fault), or at a surface.
The value of the centro-symmetry parameter will be 0.0 for atoms not
in the specified compute group.
This parameter is computed using the following formula from
"(Kelchner)"_#Kelchner
:c,image(Eqs/centro_symmetry.jpg)
-where the 12 nearest neighbors are found and Ri and Ri+6 are the
-vectors from the central atom to the opposite pair of nearest
-neighbors. Atoms not in the group are included in the 12 neighbors
-used in this calculation.
+where the 12 nearest neighbors are found (for fcc lattices) and Ri and
+Ri+6 are the vectors from the central atom to the opposite pair of
+nearest neighbors. Atoms not in the group are included in the 12
+neighbors used in this calculation.
The neighbor list needed to compute this quantity is constructed each
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 or to have multiple compute/dump commands, each of a
{centro/atom} style.
[Output info:]
This compute calculates a scalar quantity for each atom, which can be
accessed by any command that uses per-atom computes as input. See
"this section"_Section_howto.html#4_15 for an overview of LAMMPS
output options.
[Restrictions:] none
[Related commands:] none
[Default:] none
:line
:link(Kelchner)
[(Kelchner)] Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998).
diff --git a/doc/compute_temp_asphere.html b/doc/compute_temp_asphere.html
index e0441ac3f..181d8439f 100644
--- a/doc/compute_temp_asphere.html
+++ b/doc/compute_temp_asphere.html
@@ -1,108 +1,112 @@
<HTML>
<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
</CENTER>
<HR>
<H3>compute temp/asphere command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID temp/asphere bias-ID
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>temp/asphere = style name of this compute command
<LI>bias-ID = ID of a temperature compute that removes a velocity bias (optional)
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute 1 all temp/asphere
compute myTemp mobile temp/asphere tempCOM
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the temperature of a group of
aspherical particles, including a contribution from both their
translational and rotational kinetic energy. This differs from the
usual <A HREF = "compute_temp.html">compute temp</A> command, which assumes point
particles with only translational kinetic energy.
</P>
<P>For 3d aspherical particles, each has 3, 5, or 6 degrees of freedom (3
translational, remainder rotational), depending on whether the
particle is spherical, uniaxial, or biaxial. This is determined by
the <A HREF = "shape.html">shape</A> command. Uniaxial means two of its three shape
parameters are equal. Biaxial means all 3 shape parameters are
different.
</P>
<P>For 2d aspherical particles, each has 3 or 4 degrees of freedom (3
translational, remainder rotational), depending on whether the
particle is spherical, or biaxial. Biaxial means the x,y shape
parameters are unequal.
</P>
<P>IMPORTANT NOTE: These degrees of freedom assume that the interaction
potential between degenerate aspherical particles does not impart
rotational motion to the extra degrees of freedom. E.g. the <A HREF = "pair_gayberne.html">GayBerne
pair potential</A> does not impart torque to spherical
particles, so they do not rotate.
</P>
<P>The rotational kinetic energy is computed as 1/2 I w^2, where I is the
inertia tensor for the aspherical particle and w is its angular
velocity, which is computed from its angular momentum.
</P>
<P>IMPORTANT NOTE: For <A HREF = "dimension.html">2d models</A>, particles are treated
as ellipsoids, not ellipses, meaning their moments of inertia will be
the same as in 3d.
</P>
<P>A 6-component kinetic energy tensor is also calculated by this
compute. The formula for the components of the tensor is the same as
the above formula, except that v^2 and w^2 are replaced by vx*vy and
wx*wy for the xy component, and the appropriate elements of the
inertia tensor are used.
</P>
<P>The number of atoms contributing to the temperature is assumed to be
constant for the duration of the run; use the <I>dynamic</I> option of the
<A HREF = "compute_modify.html">compute_modify</A> command if this is not the case.
</P>
<P>If a <I>bias-ID</I> is specified it must be the ID of a temperature compute
that removes a "bias" velocity from each atom. This allows compute
temp/sphere to compute its thermal temperature after the translational
kinetic energy components have been altered in a prescribed way,
e.g. to remove a velocity profile. Thermostats that use this compute
will work with this bias term. See the doc pages for individual
computes that calculate a temperature and the doc pages for fixes that
perform thermostatting for more details.
</P>
<P>This compute subtracts out translational degrees-of-freedom due to
fixes that constrain molecular motion, such as <A HREF = "fix_shake.html">fix
shake</A> and <A HREF = "fix_rigid.html">fix rigid</A>. This means the
temperature of groups of atoms that include these constraints will be
computed correctly. If needed, the subtracted degrees-of-freedom can
be altered using the <I>extra</I> option of the
<A HREF = "compute_modify.html">compute_modify</A> command.
</P>
+<P>See <A HREF = "Section_howto.html#4_16">this howto section</A> of the manual for a
+discussion of different ways to compute temperature and perform
+thermostatting.
+</P>
<P><B>Output info:</B>
</P>
<P>The scalar value calculated by this compute is "intensive", meaning it
is independent of the number of atoms in the simulation. The vector
values are "extensive", meaning they scale with the number of atoms in
the simulation.
</P>
<P><B>Restrictions:</B>
</P>
<P>This compute requires that particles be represented as extended
ellipsoids and not point particles. This means they will have an
angular momentum and a shape which is determined by the
<A HREF = "shape.html">shape</A> command.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute_temp.html">compute temp</A>
</P>
<P><B>Default:</B> none
</P>
</HTML>
diff --git a/doc/compute_temp_asphere.txt b/doc/compute_temp_asphere.txt
index 9c8684bb6..9e3dbdc20 100755
--- a/doc/compute_temp_asphere.txt
+++ b/doc/compute_temp_asphere.txt
@@ -1,103 +1,107 @@
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
compute temp/asphere command :h3
[Syntax:]
compute ID group-ID temp/asphere bias-ID :pre
ID, group-ID are documented in "compute"_compute.html command
temp/asphere = style name of this compute command
bias-ID = ID of a temperature compute that removes a velocity bias (optional) :ul
[Examples:]
compute 1 all temp/asphere
compute myTemp mobile temp/asphere tempCOM :pre
[Description:]
Define a computation that calculates the temperature of a group of
aspherical particles, including a contribution from both their
translational and rotational kinetic energy. This differs from the
usual "compute temp"_compute_temp.html command, which assumes point
particles with only translational kinetic energy.
For 3d aspherical particles, each has 3, 5, or 6 degrees of freedom (3
translational, remainder rotational), depending on whether the
particle is spherical, uniaxial, or biaxial. This is determined by
the "shape"_shape.html command. Uniaxial means two of its three shape
parameters are equal. Biaxial means all 3 shape parameters are
different.
For 2d aspherical particles, each has 3 or 4 degrees of freedom (3
translational, remainder rotational), depending on whether the
particle is spherical, or biaxial. Biaxial means the x,y shape
parameters are unequal.
IMPORTANT NOTE: These degrees of freedom assume that the interaction
potential between degenerate aspherical particles does not impart
rotational motion to the extra degrees of freedom. E.g. the "GayBerne
pair potential"_pair_gayberne.html does not impart torque to spherical
particles, so they do not rotate.
The rotational kinetic energy is computed as 1/2 I w^2, where I is the
inertia tensor for the aspherical particle and w is its angular
velocity, which is computed from its angular momentum.
IMPORTANT NOTE: For "2d models"_dimension.html, particles are treated
as ellipsoids, not ellipses, meaning their moments of inertia will be
the same as in 3d.
A 6-component kinetic energy tensor is also calculated by this
compute. The formula for the components of the tensor is the same as
the above formula, except that v^2 and w^2 are replaced by vx*vy and
wx*wy for the xy component, and the appropriate elements of the
inertia tensor are used.
The number of atoms contributing to the temperature is assumed to be
constant for the duration of the run; use the {dynamic} option of the
"compute_modify"_compute_modify.html command if this is not the case.
If a {bias-ID} is specified it must be the ID of a temperature compute
that removes a "bias" velocity from each atom. This allows compute
temp/sphere to compute its thermal temperature after the translational
kinetic energy components have been altered in a prescribed way,
e.g. to remove a velocity profile. Thermostats that use this compute
will work with this bias term. See the doc pages for individual
computes that calculate a temperature and the doc pages for fixes that
perform thermostatting for more details.
This compute subtracts out translational degrees-of-freedom due to
fixes that constrain molecular motion, such as "fix
shake"_fix_shake.html and "fix rigid"_fix_rigid.html. This means the
temperature of groups of atoms that include these constraints will be
computed correctly. If needed, the subtracted degrees-of-freedom can
be altered using the {extra} option of the
"compute_modify"_compute_modify.html command.
+See "this howto section"_Section_howto.html#4_16 of the manual for a
+discussion of different ways to compute temperature and perform
+thermostatting.
+
[Output info:]
The scalar value calculated by this compute is "intensive", meaning it
is independent of the number of atoms in the simulation. The vector
values are "extensive", meaning they scale with the number of atoms in
the simulation.
[Restrictions:]
This compute requires that particles be represented as extended
ellipsoids and not point particles. This means they will have an
angular momentum and a shape which is determined by the
"shape"_shape.html command.
[Related commands:]
"compute temp"_compute_temp.html
[Default:] none

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