git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@3989 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/centro_symmetry.tex

@@ -3,7 +3,7 @@
 \begin{document}
 
 $$
-   P = \sum_{i = 1}^{6} | \vec{R}_i + \vec{R}_{i+6} |^2
+   CS = \sum_{i = 1}^{N/2} | \vec{R}_i + \vec{R}_{i+N/2} |^2
 $$
 
-\end{document}
+\end{document}

doc/Section_start.html

@@ -38,7 +38,7 @@ tar xvf lammps*.tar
 <P>This will create a LAMMPS directory containing two files and several
 sub-directories:
 </P>
-<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
+<DIV ALIGN=center><TABLE  BORDER=1 >
 <TR><TD >README</TD><TD > text file</TD></TR>
 <TR><TD >LICENSE</TD><TD > the GNU General Public License (GPL)</TD></TR>
 <TR><TD >bench</TD><TD > benchmark problems</TD></TR>
@@ -350,7 +350,7 @@ package".
 </P>
 <P>The current list of standard packages is as follows:
 </P>
-<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
+<DIV ALIGN=center><TABLE  BORDER=1 >
 <TR><TD >asphere </TD><TD > aspherical particles and force fields</TD></TR>
 <TR><TD >class2 </TD><TD > class 2 force fields</TD></TR>
 <TR><TD >colloid </TD><TD > colloidal particle force fields</TD></TR>
@@ -760,7 +760,7 @@ output is performed.
 <P>Specify a variable that will be defined for substitution purposes when
 the input script is read.  "Name" is the variable name which can be a
 single character (referenced as $x in the input script) or a full
-string (referenced as $\<I>abc\</I>).  The value can be any string.  Using
+string (referenced as ${abc}).  The value can be any string.  Using
 this command-line option is equivalent to putting the line "variable
 name index value" at the beginning of the input script.  Defining an
 index variable as a command-line argument overrides any setting for

doc/compute_centro_atom.html

@@ -13,14 +13,17 @@
 </H3>
 <P><B>Syntax:</B>
 </P>
-<PRE>compute ID group-ID centro/atom 
+<PRE>compute ID group-ID centro/atom lattice 
 </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 
+<LI>centro/atom = style name of this compute command
+<LI>lattice = <I>fcc</I> or <I>bcc</I> or N = # of neighbors per atom to include 
 </UL>
 <P><B>Examples:</B>
 </P>
-<PRE>compute 1 all centro/atom 
+<PRE>compute 1 all centro/atom fcc 
+</PRE>
+<PRE>compute 1 all centro/atom 8 
 </PRE>
 <P><B>Description:</B>
 </P>
@@ -39,10 +42,32 @@ in the specified compute group.
 </P>
 <CENTER><IMG SRC = "Eqs/centro_symmetry.jpg">
 </CENTER>
-<P>where the 12 nearest neighbors are found (for fcc lattices) and Ri and
+<P>where the <I>N</I> nearest neighbors or each atom are identified and Ri and
-Ri+6 are the vectors from the central atom to the opposite pair of
+Ri+N/2 are vectors from the central atom to a particular pair of
-nearest neighbors.  Atoms not in the group are included in the 12
+nearest neighbors.  There are N*(N-1)/2 possible neighbor pairs that
-neighbors used in this calculation.
+can contribute to this formula.  The quantity in the sum is computed
+for each, and the N/2 smallest are used.  This will typically be for
+pairs of atoms in symmetrically opposite positions with respect to the
+central atom; hence the i+N/2 notation.
+</P>
+<P><I>N</I> is an input parameter, which should be set to correspond to the
+number of nearest neighbors in the underlying lattice of atoms.  If
+the keyword <I>fcc</I> or <I>bcc</I> is used, <I>N</I> is set to 12 and 8
+respectively.  More generally, <I>N</I> can be set to a positive, even
+integer.
+</P>
+<P>For an atom on a lattice site, surrounded by atoms on a perfect
+lattice, the centro-symmetry parameter will be 0.  It will be near 0
+for small thermal perturbations of a perfect lattice.  If a point
+defect exists, the symmetry is broken, and the parameter will be a
+larger positive value.  An atom at a surface will have a large
+positive parameter.  If the atom does not have <I>N</I> neighbors (within
+the potential cutoff), then its centro-symmetry parameter is set to
+0.0.
+</P>
+<P>Only atoms within the cutoff of the pairwise neighbor list are
+considered as possible neighbors.  Atoms not in the compute group are
+included in the <I>N</I> neighbors used in this calculation.
 </P>
 <P>The neighbor list needed to compute this quantity is constructed each
 time the calculation is performed (e.g. each time a snapshot of atoms
@@ -57,6 +82,12 @@ any command that uses per-atom values from a compute as input.  See
 <A HREF = "Section_howto.html#4_15">this section</A> for an overview of LAMMPS
 output options.
 </P>
+<P>The per-atom vector values are unitless values >= 0.0.  Their
+magnitude depends on the lattice style due to the number of
+contibuting neighbor pairs in the summation in the formula above.  And
+it depends on the local defects surrounding the central atom, as
+described above.
+</P>
 <P><B>Restrictions:</B> none
 </P>
 <P><B>Related commands:</B>

doc/compute_centro_atom.txt

@@ -10,14 +10,16 @@ compute centro/atom command :h3
 
 [Syntax:]
 
-compute ID group-ID centro/atom :pre
+compute ID group-ID centro/atom lattice :pre
 
 ID, group-ID are documented in "compute"_compute.html command
-centro/atom = style name of this compute command :ul
+centro/atom = style name of this compute command
+lattice = {fcc} or {bcc} or N = # of neighbors per atom to include :ul
 
 [Examples:]
 
-compute 1 all centro/atom :pre
+compute 1 all centro/atom fcc :pre
+compute 1 all centro/atom 8 :pre
 
 [Description:]
 
@@ -36,10 +38,32 @@ This parameter is computed using the following formula from
 
 :c,image(Eqs/centro_symmetry.jpg)
 
-where the 12 nearest neighbors are found (for fcc lattices) and Ri and
+where the {N} nearest neighbors or each atom are identified and Ri and
-Ri+6 are the vectors from the central atom to the opposite pair of
+Ri+N/2 are vectors from the central atom to a particular pair of
-nearest neighbors.  Atoms not in the group are included in the 12
+nearest neighbors.  There are N*(N-1)/2 possible neighbor pairs that
-neighbors used in this calculation.
+can contribute to this formula.  The quantity in the sum is computed
+for each, and the N/2 smallest are used.  This will typically be for
+pairs of atoms in symmetrically opposite positions with respect to the
+central atom; hence the i+N/2 notation.
+
+{N} is an input parameter, which should be set to correspond to the
+number of nearest neighbors in the underlying lattice of atoms.  If
+the keyword {fcc} or {bcc} is used, {N} is set to 12 and 8
+respectively.  More generally, {N} can be set to a positive, even
+integer.
+
+For an atom on a lattice site, surrounded by atoms on a perfect
+lattice, the centro-symmetry parameter will be 0.  It will be near 0
+for small thermal perturbations of a perfect lattice.  If a point
+defect exists, the symmetry is broken, and the parameter will be a
+larger positive value.  An atom at a surface will have a large
+positive parameter.  If the atom does not have {N} neighbors (within
+the potential cutoff), then its centro-symmetry parameter is set to
+0.0.
+
+Only atoms within the cutoff of the pairwise neighbor list are
+considered as possible neighbors.  Atoms not in the compute group are
+included in the {N} neighbors used in this calculation.
 
 The neighbor list needed to compute this quantity is constructed each
 time the calculation is performed (e.g. each time a snapshot of atoms
@@ -54,6 +78,12 @@ any command that uses per-atom values from a compute as input.  See
 "this section"_Section_howto.html#4_15 for an overview of LAMMPS
 output options.
 
+The per-atom vector values are unitless values >= 0.0.  Their
+magnitude depends on the lattice style due to the number of
+contibuting neighbor pairs in the summation in the formula above.  And
+it depends on the local defects surrounding the central atom, as
+described above.
+
 [Restrictions:] none
 
 [Related commands:]