Commit2 JT 040519

- added angle in doc
- improved doc neb/spin

doc/src/Eqs/neb_spin_angle.tex

@@ -0,0 +1,15 @@
+\documentclass[preview]{standalone}
+\usepackage{varwidth}
+\usepackage[utf8x]{inputenc}
+\usepackage{amsmath, amssymb, graphics, setspace}
+
+\begin{document}
+\begin{varwidth}{50in}
+  \begin{equation}
+    \omega_i^{\nu} = 
+    (\nu - 1) \Delta \omega_i
+    {\rm ~~and~~} \Delta \omega_i = \frac{\omega_i}{Q-1}
+  , \nonumber
+  \end{equation}
+\end{varwidth}
+\end{document}

doc/src/neb_spin.txt

@@ -103,8 +103,6 @@ from such an initial path.  In this case, you will want to generate
 initial states for the intermediate replicas that are geometrically
 closer to the MEP and read them in.
 
-###################################################################
-
 :line
 
 For a {file-style} setting of {final}, a filename is specified which
@@ -115,7 +113,7 @@ assigned to that atom in the final replica.  Each intermediate replica
 also assigns a new spin to that atom in an interpolated manner.  
 This is done by using the current direction of the spin at the starting 
 point and the read-in direction as the final point.  
-The angular distance between them is calculated, and the new direction 
+The "angular distance" between them is calculated, and the new direction 
 is assigned to be a fraction of the angular distance.
 
 NOTE: The "angular distance" between the starting and final point is 
@@ -126,47 +124,31 @@ is achieved using Rodrigues formula:
 
 :c,image(Eqs/neb_spin_rodrigues_formula.jpg)
 
-with m_i^I is the initial spin configuration for the spin i,  
-where the rotation and k_i is defined as:
+where m_i^I is the initial spin configuration for the spin i,
+omega_i^nu is a rotation angle defined as:
+
+:c,image(Eqs/neb_spin_angle.jpg)
+
+with nu the image number, Q the total number of images, and 
+omega_i the total rotation between the initial and final spins.
+k_i defines a rotation axis such as:
 
 :c,image(Eqs/neb_spin_k.jpg)
 
-The distance between them is calculated, and the new position
-is assigned to be a fraction of the distance.  E.g. if there are 10
-replicas, the 2nd replica will assign a position that is 10% of the
-distance along a line between the starting and final point, and the
-9th replica will assign a position that is 90% of the distance along
-the line.  Note that for this procedure to produce consistent
-coordinates across all the replicas, the current coordinates need to
-be the same in all replicas.  LAMMPS does not check for this, but
-invalid initial configurations will likely result if it is not the
-case.
-
-NOTE: The "distance" between the starting and final point is
-calculated in a minimum-image sense for a periodic simulation box.
-This means that if the two positions are on opposite sides of a box
-(periodic in that dimension), the distance between them will be small,
-because the periodic image of one of the atoms is close to the other.
-Similarly, even if the assigned position resulting from the
-interpolation is outside the periodic box, the atom will be wrapped
-back into the box when the NEB calculation begins.
+if the initial and final spins are not aligned.
+If the initial and final spins are aligned, then their cross
+product is null, and the expression above does not apply.
+If they point toward the same direction, the intermediate images 
+conserve the same orientation.
+If the initial and final spins are aligned, but point toward
+opposite directions, an arbitrary rotation vector belonging to
+the plane perpandicular to initial and final spins is chosen. 
+In this case, a warning message is displayed.
 
 For a {file-style} setting of {each}, a filename is specified which is
-assumed to be unique to each replica.  This can be done by using a
-variable in the filename, e.g.
-
-variable i equal part
-neb 0.0 0.001 1000 500 50 each coords.initial.$i :pre
-
-which in this case will substitute the partition ID (0 to N-1) for the
-variable I, which is also effectively the replica ID.  See the
-"variable"_variable.html command for other options, such as using
-world-, universe-, or uloop-style variables.
-
-Each replica (except the first replica) will read its file, formatted
-as described below, and for any atom that appears in the file, assign
-the specified coordinates to its atom.  The various files do not need
-to contain the same set of atoms.
+assumed to be unique to each replica. 
+See the "neb"_neb.html documentation page for more information about this 
+option.
 
 For a {file-style} setting of {none}, no filename is specified.  Each
 replica is assumed to already be in its initial configuration at the
@@ -188,23 +170,25 @@ command is issued.
 
 A NEB calculation proceeds in two stages, each of which is a
 minimization procedure, performed via damped dynamics.  To enable
-this, you must first define a damped dynamics
-"min_style"_min_style.html, such as {quickmin} or {fire}.  The {cg},
-{sd}, and {hftn} styles cannot be used, since they perform iterative
-line searches in their inner loop, which cannot be easily synchronized
-across multiple replicas.
+this, you must first define a damped spin dynamics
+"min_style"_min_style.html, using the {spin} style (see
+"min_spin"_min_spin.html for more information).  
+The other styles cannot be used, since they relax the lattice
+degrees of freedom instead of the spins.
 
 The minimizer tolerances for energy and force are set by {etol} and
 {ftol}, the same as for the "minimize"_minimize.html command.
 
-A non-zero {etol} means that the NEB calculation will terminate if the
+A non-zero {etol} means that the GNEB calculation will terminate if the
 energy criterion is met by every replica.  The energies being compared
 to {etol} do not include any contribution from the inter-replica
 nudging forces, since these are non-conservative.  A non-zero {ftol}
-means that the NEB calculation will terminate if the force criterion
-is met by every replica.  The forces being compared to {ftol} include
+means that the GNEB calculation will terminate if the torque criterion
+is met by every replica.  The torques being compared to {ftol} include
 the inter-replica nudging forces.
 
+###################################################################
+
 The maximum number of iterations in each stage is set by {N1} and
 {N2}.  These are effectively timestep counts since each iteration of
 damped dynamics is like a single timestep in a dynamics