git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@12840 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/compute_gyration.html

@@ -28,19 +28,22 @@
 group of atoms, including all effects due to atoms passing thru
 periodic boundaries.
 </P>
-<P>Rg is a measure of the size of the group of atoms, and is computed by
+<P>Rg is a measure of the size of the group of atoms, and is computed as
-this formula
+the square root of the Rg^2 value in this formula
 </P>
 <CENTER><IMG SRC = "Eqs/compute_gyration.jpg">
 </CENTER>
 <P>where M is the total mass of the group, Rcm is the center-of-mass
 position of the group, and the sum is over all atoms in the group.
 </P>
-<P>A Rg tensor, stored as a 6-element vector, is also calculated by this
+<P>A Rg^2 tensor, stored as a 6-element vector, is also calculated by
-compute.  The formula for the components of the tensor is the same as
+this compute.  The formula for the components of the tensor is the
-the above formula, except that (Ri - Rcm)^2 is replaced by (Rix -
+same as the above formula, except that (Ri - Rcm)^2 is replaced by
-Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6 components of
+(Rix - Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6
-the vector are ordered xx, yy, zz, xy, xz, yz.
+components of the vector are ordered xx, yy, zz, xy, xz, yz.  Note
+that unlike the scalar Rg, each of the 6 values of the tensor is
+effectively a "squared" value, since the cross-terms may be negative
+and taking a sqrt() would be invalid.
 </P>
 <P>IMPORTANT NOTE: The coordinates of an atom contribute to Rg in
 "unwrapped" form, by using the image flags associated with each atom.
@@ -54,16 +57,15 @@ image</A> command.
 <P><B>Output info:</B>
 </P>
 <P>This compute calculates a global scalar (Rg) and a global vector of
-length 6 (Rg tensor), which can be accessed by indices 1-6.  These
+length 6 (Rg^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 <A HREF = "Section_howto.html#howto_15">Section_howto
 15</A> for an overview of LAMMPS output
 options.
 </P>
 <P>The scalar and vector values calculated by this compute are
-"intensive".  The scalar and vector values will be in distance
+"intensive".  The scalar and vector values will be in distance and
-<A HREF = "units.html">units</A>, since they are the square root of values
+distance^2 <A HREF = "units.html">units</A> respectively.
-represented by the formula above.
 </P>
 <P><B>Restrictions:</B> none
 </P>

doc/compute_gyration.txt

@@ -25,19 +25,22 @@ Define a computation that calculates the radius of gyration Rg of the
 group of atoms, including all effects due to atoms passing thru
 periodic boundaries.
 
-Rg is a measure of the size of the group of atoms, and is computed by
+Rg is a measure of the size of the group of atoms, and is computed as
-this formula
+the square root of the Rg^2 value in this formula
 
 :c,image(Eqs/compute_gyration.jpg)
 
 where M is the total mass of the group, Rcm is the center-of-mass
 position of the group, and the sum is over all atoms in the group.
 
-A Rg tensor, stored as a 6-element vector, is also calculated by this
+A Rg^2 tensor, stored as a 6-element vector, is also calculated by
-compute.  The formula for the components of the tensor is the same as
+this compute.  The formula for the components of the tensor is the
-the above formula, except that (Ri - Rcm)^2 is replaced by (Rix -
+same as the above formula, except that (Ri - Rcm)^2 is replaced by
-Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6 components of
+(Rix - Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6
-the vector are ordered xx, yy, zz, xy, xz, yz.
+components of the vector are ordered xx, yy, zz, xy, xz, yz.  Note
+that unlike the scalar Rg, each of the 6 values of the tensor is
+effectively a "squared" value, since the cross-terms may be negative
+and taking a sqrt() would be invalid.
 
 IMPORTANT NOTE: The coordinates of an atom contribute to Rg in
 "unwrapped" form, by using the image flags associated with each atom.
@@ -51,16 +54,15 @@ image"_set.html command.
 [Output info:]
 
 This compute calculates a global scalar (Rg) and a global vector of
-length 6 (Rg tensor), which can be accessed by indices 1-6.  These
+length 6 (Rg^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 "Section_howto
 15"_Section_howto.html#howto_15 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
+"intensive".  The scalar and vector values will be in distance and
-"units"_units.html, since they are the square root of values
+distance^2 "units"_units.html respectively.
-represented by the formula above.
 
 [Restrictions:] none
 

doc/compute_gyration_molecule.html

@@ -38,8 +38,8 @@ compute 2 molecule gyration/molecule tensor
 individual molecules.  The calculation includes all effects due to
 atoms passing thru periodic boundaries.
 </P>
-<P>Rg is a measure of the size of a molecule, and is computed by this
+<P>Rg is a measure of the size of a molecule, and is computed as the
-formula
+square root of the Rg^2 value in this formula
 </P>
 <CENTER><IMG SRC = "Eqs/compute_gyration.jpg">
 </CENTER>
@@ -48,11 +48,14 @@ position of the molecule, and the sum is over all atoms in the
 molecule and in the group.
 </P>
 <P>If the <I>tensor</I> keyword is specified, then the scalar Rg value is not
-calculated, but an Rg tensor is instead calculated for each molecule.
+calculated, but a 6-element Rg^2 tensor is instead calculated for each
-The formula for the components of the tensor is the same as the above
+molecule.  The formula for the components of the tensor is the same as
-formula, except that (Ri - Rcm)^2 is replaced by (Rix - Rcmx) * (Riy -
+the above formula, except that (Ri - Rcm)^2 is replaced by (Rix -
-Rcmy) for the xy component, etc.  The 6 components of the tensor are
+Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6 components of
-ordered xx, yy, zz, xy, xz, yz.
+the tensor are ordered xx, yy, zz, xy, xz, yz.  Note
+that unlike the scalar Rg, each of the 6 values of the tensor is
+effectively a "squared" value, since the cross-terms may be negative
+and taking a sqrt() would be invalid.
 </P>
 <P>Rg for a particular molecule is only computed if one or more of its
 atoms are in the specified group.  Normally all atoms in the molecule
@@ -87,9 +90,8 @@ section</A> for an overview of LAMMPS output
 options.
 </P>
 <P>All the vector or array values calculated by this compute are
-"intensive".  The vector or array values will be in distance
+"intensive".  The vector and aray values will be in distance and
-<A HREF = "units.html">units</A>, since they are the square root of values
+distance^2 <A HREF = "units.html">units</A> respectively.
-represented by the formula above.
 </P>
 <P><B>Restrictions:</B> none
 </P>

doc/compute_gyration_molecule.txt

@@ -30,8 +30,8 @@ Define a computation that calculates the radius of gyration Rg of
 individual molecules.  The calculation includes all effects due to
 atoms passing thru periodic boundaries.
 
-Rg is a measure of the size of a molecule, and is computed by this
+Rg is a measure of the size of a molecule, and is computed as the
-formula
+square root of the Rg^2 value in this formula
 
 :c,image(Eqs/compute_gyration.jpg)
 
@@ -40,11 +40,14 @@ position of the molecule, and the sum is over all atoms in the
 molecule and in the group.
 
 If the {tensor} keyword is specified, then the scalar Rg value is not
-calculated, but an Rg tensor is instead calculated for each molecule.
+calculated, but a 6-element Rg^2 tensor is instead calculated for each
-The formula for the components of the tensor is the same as the above
+molecule.  The formula for the components of the tensor is the same as
-formula, except that (Ri - Rcm)^2 is replaced by (Rix - Rcmx) * (Riy -
+the above formula, except that (Ri - Rcm)^2 is replaced by (Rix -
-Rcmy) for the xy component, etc.  The 6 components of the tensor are
+Rcmx) * (Riy - Rcmy) for the xy component, etc.  The 6 components of
-ordered xx, yy, zz, xy, xz, yz.
+the tensor are ordered xx, yy, zz, xy, xz, yz.  Note
+that unlike the scalar Rg, each of the 6 values of the tensor is
+effectively a "squared" value, since the cross-terms may be negative
+and taking a sqrt() would be invalid.
 
 Rg for a particular molecule is only computed if one or more of its
 atoms are in the specified group.  Normally all atoms in the molecule
@@ -79,9 +82,8 @@ section"_Section_howto.html#howto_15 for an overview of LAMMPS output
 options.
 
 All the vector or array values calculated by this compute are
-"intensive".  The vector or array values will be in distance
+"intensive".  The vector and aray values will be in distance and
-"units"_units.html, since they are the square root of values
+distance^2 "units"_units.html respectively.
-represented by the formula above.
 
 [Restrictions:] none
 

doc/fix_nvt_sllod.html

@@ -56,9 +56,13 @@ periodic boundaries since that is consistent with maintaining the
 velocity profile created by fix nvt/sllod.  LAMMPS will give an
 error if this setting is not consistent.
 </P>
-<P>The SLLOD equations of motion coupled to a Nose/Hoover thermostat are
+<P>The SLLOD equations of motion, originally proposed by Hoover and Ladd
-discussed in <A HREF = "#Tuckerman">(Tuckerman)</A> (eqs 4 and 5), which is what is
+(see <A HREF = "#Evans">(Evans and Morriss)</A>), were proven to be identical to
-implemented in LAMMPS in a velocity Verlet formulation.
+Newton's equations of motion for all forms of homogeneous flow by
+<A HREF = "#Daivis">(Daivis and Todd)</A>.  As implemented in LAMMPS, they are
+coupled to a Nose/Hoover chain thermostat in a velocity Verlet
+formulation, closely following the implementation used for the <A HREF = "fix_nh.html">fix
+nvt</A> command.
 </P>
 <P>Additional parameters affecting the thermostat are specified by
 keywords and values documented with the <A HREF = "fix_nh.html">fix nvt</A>
@@ -170,9 +174,12 @@ temp/deform</A>
 </P>
 <HR>
 
-<A NAME = "Tuckerman"></A>
+<A NAME = "Evans"></A>
 
-<P><B>(Tuckerman)</B> Tuckerman, Mundy, Balasubramanian, Klein, J Chem Phys,
+<P><B>(Evans and Morriss)</B> Evans and Morriss, Phys Rev A, 30, 1528 (1984).
-106, 5615 (1997).
+</P>
+<A NAME = "Daivis"></A>
+
+<P><B>(Daivis and Todd)</B> Daivis and Todd, J Chem Phys, 124, 194103 (2006).
 </P>
 </HTML>