[cig-commits] commit: Finished cohesive cell figure. Added nondiemsionalization paragraph to manuscript.

Mercurial hg at geodynamics.org
Wed Mar 28 09:37:49 PDT 2012


changeset:   89:12e125af3774
tag:         tip
user:        Brad Aagaard <baagaard at usgs.gov>
date:        Wed Mar 28 09:37:40 2012 -0700
files:       faultRup.tex figs/cohesivecell.tex figs/generatefigs.sh
description:
Finished cohesive cell figure. Added nondiemsionalization paragraph to manuscript.


diff -r 78a253a2443f -r 12e125af3774 faultRup.tex
--- a/faultRup.tex	Tue Mar 27 21:11:40 2012 -0700
+++ b/faultRup.tex	Wed Mar 28 09:37:40 2012 -0700
@@ -357,8 +357,6 @@ construct a system with the form $\mathb
 \mathbf{b}(t+\Delta t) - \mathbf{A} \cdot \mathbf{u}(t)$, where
 $\mathbf{u}(t+\Delta t) = \mathbf{u}(t) + \mathbf{du}$.
 
-\brad{Add description of nondimensionalization?}
-
 % ------------------------------------------------------------------
 \subsection{Quasi-static Simulations}
 
@@ -523,7 +521,6 @@ so that the upper portion of the Jacobia
     \frac{1}{\Delta t^2} \int_{V} \rho \mathbf{N}_m^T\ \cdot \mathbf{N}_n \, dV.
 \end{equation}
 
-
 % ------------------------------------------------------------------
 % Taking advantage of the commonality
 
@@ -541,6 +538,24 @@ significantly reduces development time a
 significantly reduces development time and simplifies maintenance
 compared to maintaining different codes for quasi-static and dynamic
 simulations.
+
+
+% ------------------------------------------------------------------
+\subsection{Nondimensionalization}
+
+The domain decomposition approach for implementing fault slip with
+Lagrange multipliers requires solving for both the displacement field
+and the Lagrange multipliers, which correspond to fault tractions. We
+expect the displacements to be generally on the order of mm to m
+whereas the fault tractions will be on the order of 10$^6$ Pa. Thus,
+if we use dimensioned quantities in SI units, then we would expec the
+solution to include terms that differ by up to nine orders of
+magnitude. This results in a rather ill-conditioned system. We avoid
+this ill-conditioning by nondimensionalizing all of the quantities
+involved in the problem based upon user-specified scales
+\citep{PyLith:manual:1.6.2}, facilitating forming well-conditioned
+systems of equations for problems across a wide range of spatial and
+temporal scales.
 
 
 % ------------------------------------------------------------------
@@ -1111,8 +1126,9 @@ avoid performing a line search in comput
 
 % ------------------------------------------------------------------
 \section{Performance Benchmark}
+
 \begin{itemize}
-\item \brad{Solver test or quasi-static strike-slip benchmark?}
+\item \brad{Solver test}
 \item Comparison of preconditioner performance
 \item Weak scaling performance for field split with custom preconditioner
 \end{itemize}
@@ -1122,7 +1138,7 @@ avoid performing a line search in comput
 \begin{itemize}
 \item Savage and Prescott
   \begin{itemize}
-  \item Compare performance of hex8 and tet4
+  \item Compare hex8 and tet4 against analytic solution
   \end{itemize}
 \item Spontaneous rupture benchmark: TPV12, TPV13
   \begin{itemize}
@@ -1205,20 +1221,25 @@ MGK acknowledges partial support from NS
   \label{fig:domain:decomposition}
 \end{figure}
 
-\begin{figure}
-  \brad{TODO: ADD DIAGRAM}
-  %\noindent\includegraphics{figs/cohesive_cell}
-  \caption{Construction of cohesive cells for a fault. (a) For each
+\begin{figure*}
+  \noindent\includegraphics{figs/cohesivecell}
+  \caption{Construction of cohesive cells for a fault. (a) Original
+    mesh with fault normal and fault vertices identified. (b) For each
     vertex on the fault, introduce a vertex on the positive side of
     the fault $S_{f^+}$ and a vertex corresponding to the Lagrange
     multiplier constraint between the pair of vertices on the positive
-    and negative sides of the fault. (b) Replace the vertices in the
-    cell attached to the positive side of the fault with the newly
-    created vertices. (b) Construct cohesive cells with
-    zero volume from the vertices on the positive side of the fault,
-    negative side of the fault, and Lagrange multiplier constraints.}
+    and negative sides of the fault. (c) Identify cells with faces on
+    the fault. Use the orientation of each face to identify cells on
+    the positive and negative sides of the fault. Replace vertices in
+    cells on the positive side of the fault with the newly created
+    vertices. (d) Classify remaining cells with vertices on the fault
+    using breadth-first search, and replace original vertices in cells
+    on positive side of the fault with newly created
+    vertices. Construct cohesive cells with zero volume from the
+    vertices on the positive side of the fault, negative side of the
+    fault, and Lagrange multiplier constraints.}
   \label{fig:cohesive:cell}
-\end{figure}
+\end{figure*}
 
 
 % ------------------------------------------------------------------
diff -r 78a253a2443f -r 12e125af3774 figs/cohesivecell.tex
--- a/figs/cohesivecell.tex	Tue Mar 27 21:11:40 2012 -0700
+++ b/figs/cohesivecell.tex	Wed Mar 28 09:37:40 2012 -0700
@@ -1,4 +1,5 @@
 \documentclass{article}
+\usepackage[none]{hyphenat}
 \usepackage{helvet}
 \renewcommand{\familydefault}{phv}
 
@@ -17,30 +18,26 @@
 \pgfsetlayers{background,main}
 
 
-\begin{tikzpicture}
+\begin{tikzpicture}[>=latex,line width=0.75pt]
 
-\usetikzlibrary{shapes,fit,calc}%
+\usetikzlibrary{shapes,calc}%
 
 \colorlet{colpositive}{red}
 \colorlet{colnegative}{blue}
 \colorlet{collagrange}{orange}
-\colorlet{colother}{mdslate}
+\colorlet{colother}{dkslate}
 
 \tikzstyle{title}=[text width=37mm,font=\bfseries\large]
 
-\tikzstyle{vertex}=[circle,color=colother,fill=mdslate,inner sep=1.5pt]
-
-\tikzstyle{vertexf}=[circle,color=colpositive,fill=red,inner sep=1.5pt]
-\tikzstyle{vertexp}=[circle,color=colpositive,fill=red,inner sep=1.5pt]
-\tikzstyle{vertexn}=[circle,color=colnegative,fill=blue,inner sep=1.5pt]
+\tikzstyle{vertex}=[circle,color=colother,fill=colother,inner sep=1.5pt]
+\tikzstyle{vertexp}=[circle,color=colpositive,fill=colpositive,inner sep=1.5pt]
+\tikzstyle{vertexn}=[circle,color=colnegative,fill=colnegative,inner sep=1.5pt]
 \tikzstyle{vertexl}=[circle,color=collagrange,fill=collagrange,inner sep=1.5pt]
 
-\tikzstyle{fsurfp}=[color=colpositive,very thick]
-\tikzstyle{fsurfn}=[color=colnegative,very thick]
+\tikzstyle{fsurfp}=[color=colpositive,line width=1.5pt]
+\tikzstyle{fsurfn}=[color=colnegative,line width=1.5pt]
 
-
-\tikzstyle{cell}=[color=black]
-
+\tikzstyle{cell}=[color=black,line width=0.5pt]
 \tikzstyle{cellp}=[fill=colpositive!30]
 \tikzstyle{celln}=[fill=colnegative!30]
 
@@ -56,12 +53,12 @@
 % ----------------------------------------------------------------------
 % Original mesh
 
-\node[title] at ($ (o1)+(0,35mm) $) {a) Original mesh};
+\node[title] at ($ (o1)+(0,35mm) $) {(a) Original mesh};
 
 % Vertices
-\node[vertexf] (v1) at ($ (o1)+(0mm,+15mm) $) {};
-\node[vertexf] (v2) at (o1) {};
-\node[vertexf] (v3) at ($ (o1)+(0mm,-15mm) $) {};
+\node[vertexn] (v1) at ($ (o1)+(0mm,+15mm) $) {};
+\node[vertexn] (v2) at (o1) {};
+\node[vertexn] (v3) at ($ (o1)+(0mm,-15mm) $) {};
 
 \node[vertex] (v4) at ($ (o1)+(-11.25mm,+7.5mm) $) {};
 \node[vertex] (v5) at ($ (o1)+(-11.25mm,-7.5mm) $) {};
@@ -75,29 +72,32 @@
 \node[vertex] (v11) at ($ (o1)+(+7.5mm,-26.25mm) $) {};
 
 % Cells
-\draw [cell] (v1) -- (v4) -- (v2) -- (v1);
-\draw [cell]  (v2) -- (v5) -- (v3) -- (v2);
-\draw [cell]  (v1) -- (v2) -- (v6) -- (v1);
-\draw [cell]  (v2) -- (v3) -- (v7) -- (v2);
+\draw[cell] (v1) -- (v4) -- (v2) -- (v1);
+\draw[cell]  (v2) -- (v5) -- (v3) -- (v2);
+\draw[cell]  (v1) -- (v2) -- (v6) -- (v1);
+\draw[cell]  (v2) -- (v3) -- (v7) -- (v2);
 
-\draw [cell]  (v1) -- (v9) -- (v8) -- (v1);
-\draw [cell]  (v1) -- (v8) -- (v4) -- (v1);
-\draw [cell]  (v2) -- (v4) -- (v5) -- (v2);
-\draw [cell]  (v3) -- (v5) -- (v10) -- (v3);
-\draw [cell]  (v3) -- (v10) -- (v11) -- (v3);
-\draw [cell]  (v3) -- (v11) -- (v7) -- (v3);
-\draw [cell]  (v2) -- (v7) -- (v6) -- (v2);
-\draw [cell]  (v1) -- (v6) -- (v9) -- (v1);
+\draw[cell]  (v1) -- (v9) -- (v8) -- (v1);
+\draw[cell]  (v1) -- (v8) -- (v4) -- (v1);
+\draw[cell]  (v2) -- (v4) -- (v5) -- (v2);
+\draw[cell]  (v3) -- (v5) -- (v10) -- (v3);
+\draw[cell]  (v3) -- (v10) -- (v11) -- (v3);
+\draw[cell]  (v3) -- (v11) -- (v7) -- (v3);
+\draw[cell]  (v2) -- (v7) -- (v6) -- (v2);
+\draw[cell]  (v1) -- (v6) -- (v9) -- (v1);
 
-\draw [fsurfp] (v1) -- (v2) -- (v3);
+\draw[fsurfn] (v1) -- (v2) -- (v3);
 
-\node(tlabel) [color=colpositive] at ($ (o1)+(-10mm,-35mm) $) {fault vertex};
-\path [color=colpositive,->] (tlabel) edge [bend right] (v3);
+\node(tlabel) [color=colnegative] at ($ (o1)+(-10mm,-35mm) $) {fault vertex};
+\path[color=colnegative,->] (tlabel) edge [bend right] (v3);
+
+\coordinate[color=black,label=right:{$\mathbf{n}$}] (nlabel) at ($ (o1)+(5mm,-7.5mm) $);
+\path[color=black,->] ($ (o1)+(0mm,-7.5mm) $) edge (nlabel);
 
 % ----------------------------------------------------------------------
 % Add vertices, create cohesive cell
 
-\node[title] at ($ (o2)+(0,35mm) $) {b) Add collocated vertices};
+\node[title] at ($ (o2)+(0,35mm) $) {(b) Add colocated vertices};
 
 % Vertices
 \node[vertexl] (v7) at ($ (o2)+(0mm,+15mm) $) {};
@@ -113,11 +113,11 @@
 \node[vertexp] (v3) at ($ (o2)+(0mm,-15mm)+(2mm,0mm) $) {};
 
 % surface and edges
-\draw [fsurfp] (v1) -- (v2) -- (v3);
-\draw [fsurfn] (v4) -- (v5) -- (v6);
-\draw [color=black] (v1) -- (v7) -- (v4);
-\draw [color=black] (v2) -- (v8) -- (v5);
-\draw [color=black] (v3) -- (v9) -- (v6);
+\draw[fsurfp] (v1) -- (v2) -- (v3);
+\draw[fsurfn] (v4) -- (v5) -- (v6);
+\draw[cell] (v1) -- (v7) -- (v4);
+\draw[cell] (v2) -- (v8) -- (v5);
+\draw[cell] (v3) -- (v9) -- (v6);
 
 % Fault surface labels
 \node(tlabel) [color=colnegative] at ($ (o2)+(-10mm,+20mm) $) {$S_{f-}$};
@@ -128,13 +128,13 @@
 
 
 % Fault vertex labels
-\node(tlabel) [text width=25mm,color=colnegative] at ($ (o2)+(-10mm,-25mm) $) {Vertex on negative side};
+\node(tlabel) [text width=25mm,align=right,color=colnegative] at ($ (o2)+(-17mm,-25mm) $) {Original fault vertex (negative side)};
 \path [color=colnegative,->] (tlabel.north east) edge [bend right] (v6);
 
-\node(tlabel) [text width=25mm,color=collagrange] at ($ (o2)+(-5mm,-35mm) $) {Lagrange multiplier vertex};
+\node(tlabel) [text width=25mm,align=right,color=collagrange] at ($ (o2)+(-12mm,-35mm) $) {Add Lagrange multiplier vertex};
 \path [color=collagrange,->] (tlabel.north east) edge [bend right] (v9);
 
-\node(tlabel) [text width=25mm,color=colpositive] at ($(o2)+(0mm,-45mm) $) {Original fault vertex (positive side)};
+\node(tlabel) [text width=25mm,align=right,color=colpositive] at ($(o2)+(-7mm,-45mm) $) {Add vertex on positive side};
 \path [color=colpositive,->] (tlabel.north east) edge [bend right] (v3);
 
 
@@ -142,7 +142,7 @@
 % ----------------------------------------------------------------------
 % Update cells with faces on fault
 
-\node[title] at ($ (o3)+(0,35mm) $) {c) Update cells with fault faces};
+\node[title] at ($ (o3)+(0,35mm) $) {(c) Update cells with fault faces};
 
 \coordinate (p1) at ($ (o3)+(0mm,+15mm)+(1mm,0mm) $);
 \coordinate (p2) at ($ (o3)+(1mm,0mm) $);
@@ -181,31 +181,31 @@
 \node[vertex] (v13) at (p13) {};
 
 % surface and edges
-\draw [color=colpositive,very thick] (v1) -- (v2) -- (v3);
-\draw [color=colnegative,very thick] (v4) -- (v5) -- (v6);
+\draw[fsurfp] (v1) -- (v2) -- (v3);
+\draw[fsurfn] (v4) -- (v5) -- (v6);
 % Don't draw edges of cohesive cell
-%\draw [color=black] (v1) -- (v7) -- (v4);
-%\draw [color=black] (v2) -- (v8) -- (v5);
-%\draw [color=black] (v3) -- (v9) -- (v6);
+%\draw[cell] (v1) -- (v7) -- (v4);
+%\draw[cell] (v2) -- (v8) -- (v5);
+%\draw[cell] (v3) -- (v9) -- (v6);
 
 
 \begin{pgfonlayer}{background}
 % cells
-\fill [celln] (p5) -- (p4) -- (p10) -- cycle;
-\fill [celln] (p6) -- (p5) -- (p11) -- cycle;
-\fill [cellp] (p1) -- (p2) -- (p12) -- cycle;
-\fill [cellp] (p2) -- (p3) -- (p13) -- cycle;
+\fill[celln] (p5) -- (p4) -- (p10) -- cycle;
+\fill[celln] (p6) -- (p5) -- (p11) -- cycle;
+\fill[cellp] (p1) -- (p2) -- (p12) -- cycle;
+\fill[cellp] (p2) -- (p3) -- (p13) -- cycle;
 
-\draw [cell] (p5) -- (p4) -- (p10) -- cycle;
-\draw [cell] (p6) -- (p5) -- (p11) -- cycle;
-\draw [cell] (p1) -- (p2) -- (p12) -- cycle;
-\draw [cell] (p2) -- (p3) -- (p13) -- cycle;
+\draw[cell] (p5) -- (p4) -- (p10) -- cycle;
+\draw[cell] (p6) -- (p5) -- (p11) -- cycle;
+\draw[cell] (p1) -- (p2) -- (p12) -- cycle;
+\draw[cell] (p2) -- (p3) -- (p13) -- cycle;
 \end{pgfonlayer}
 
-\node [classify] at ($ 1/3*(p5)+1/3*(p4)+1/3*(p10) $) {-};
-\node [classify] at ($ 1/3*(p6)+1/3*(p5)+1/3*(p11) $) {-};
-\node [classify] at ($ 1/3*(p1)+1/3*(p2)+1/3*(p12) $) {+};
-\node [classify] at ($ 1/3*(p2)+1/3*(p3)+1/3*(p13) $) {+};
+\node[classify] at ($ 1/3*(p5)+1/3*(p4)+1/3*(p10) $) {-};
+\node[classify] at ($ 1/3*(p6)+1/3*(p5)+1/3*(p11) $) {-};
+\node[classify] at ($ 1/3*(p1)+1/3*(p2)+1/3*(p12) $) {+};
+\node[classify] at ($ 1/3*(p2)+1/3*(p3)+1/3*(p13) $) {+};
 
 
 % Fault vertex labels
@@ -219,7 +219,7 @@
 % ----------------------------------------------------------------------
 % Classify cells and update other cells
 
-\node[title] at ($ (o4)+(0,35mm) $) {d) Classify cells and replace vertices};
+\node[title] at ($ (o4)+(0,35mm) $) {(d) Classify cells and update remaining cells};
 
 \coordinate (p1) at ($ (o4)+(0mm,+15mm)+(1mm,0mm) $);
 \coordinate (p2) at ($ (o4)+(1mm,0mm) $);
@@ -269,60 +269,60 @@
 \node[vertex] (v17) at (p17) {};
 
 % surface and edges
-\draw [color=colpositive,very thick] (v1) -- (v2) -- (v3);
-\draw [color=colnegative,very thick] (v4) -- (v5) -- (v6);
+\draw[fsurfp] (v1) -- (v2) -- (v3);
+\draw[fsurfn] (v4) -- (v5) -- (v6);
 % Don't draw edge of cohesive cells
-%\draw [color=black] (v1) -- (v7) -- (v4);
-%\draw [color=black] (v2) -- (v8) -- (v5);
-%\draw [color=black] (v3) -- (v9) -- (v6);
+%\draw[cell] (v1) -- (v7) -- (v4);
+%\draw[cell] (v2) -- (v8) -- (v5);
+%\draw[cell] (v3) -- (v9) -- (v6);
 
 \begin{pgfonlayer}{background}
 % cells
-\fill [celln] (p5) -- (p4) -- (p10) -- cycle;
-\fill [celln] (p6) -- (p5) -- (p11) -- cycle;
-\fill [cellp] (p1) -- (p2) -- (p12) -- cycle;
-\fill [cellp] (p2) -- (p3) -- (p13) -- cycle;
+\fill[celln] (p5) -- (p4) -- (p10) -- cycle;
+\fill[celln] (p6) -- (p5) -- (p11) -- cycle;
+\fill[cellp] (p1) -- (p2) -- (p12) -- cycle;
+\fill[cellp] (p2) -- (p3) -- (p13) -- cycle;
 
-\fill [celln] (p4) -- (p14) -- (p10) -- cycle;
-\fill [celln] (p5) -- (p10) -- (p11) -- cycle;
-\fill [celln] (p6) -- (p11) -- (p16) -- cycle;
-\fill [celln] (p6) -- (p16) -- (p17) -- cycle;
+\fill[celln] (p4) -- (p14) -- (p10) -- cycle;
+\fill[celln] (p5) -- (p10) -- (p11) -- cycle;
+\fill[celln] (p6) -- (p11) -- (p16) -- cycle;
+\fill[celln] (p6) -- (p16) -- (p17) -- cycle;
 
-\fill [cellp] (p3) -- (p17) -- (p13) -- cycle;
-\fill [cellp] (p2) -- (p13) -- (p12) -- cycle;
-\fill [cellp] (p1) -- (p12) -- (p15) -- cycle;
-\fill [cellp] (p1) -- (p15) -- (p14) -- cycle;
+\fill[cellp] (p3) -- (p17) -- (p13) -- cycle;
+\fill[cellp] (p2) -- (p13) -- (p12) -- cycle;
+\fill[cellp] (p1) -- (p12) -- (p15) -- cycle;
+\fill[cellp] (p1) -- (p15) -- (p14) -- cycle;
 
-\draw [cell] (p5) -- (p4) -- (p10) -- cycle;
-\draw [cell] (p6) -- (p5) -- (p11) -- cycle;
-\draw [cell] (p1) -- (p2) -- (p12) -- cycle;
-\draw [cell] (p2) -- (p3) -- (p13) -- cycle;
+\draw[cell] (p5) -- (p4) -- (p10) -- cycle;
+\draw[cell] (p6) -- (p5) -- (p11) -- cycle;
+\draw[cell] (p1) -- (p2) -- (p12) -- cycle;
+\draw[cell] (p2) -- (p3) -- (p13) -- cycle;
 
-\draw [cell] (p4) -- (p14) -- (p10) -- cycle;
-\draw [cell] (p5) -- (p10) -- (p11) -- cycle;
-\draw [cell] (p6) -- (p11) -- (p16) -- cycle;
-\draw [cell] (p6) -- (p16) -- (p17) -- cycle;
+\draw[cell] (p4) -- (p14) -- (p10) -- cycle;
+\draw[cell] (p5) -- (p10) -- (p11) -- cycle;
+\draw[cell] (p6) -- (p11) -- (p16) -- cycle;
+\draw[cell] (p6) -- (p16) -- (p17) -- cycle;
 
-\draw [cell] (p3) -- (p17) -- (p13) -- cycle;
-\draw [cell] (p2) -- (p13) -- (p12) -- cycle;
-\draw [cell] (p1) -- (p12) -- (p15) -- cycle;
-\draw [cell] (p1) -- (p15) -- (p14) -- cycle;
+\draw[cell] (p3) -- (p17) -- (p13) -- cycle;
+\draw[cell] (p2) -- (p13) -- (p12) -- cycle;
+\draw[cell] (p1) -- (p12) -- (p15) -- cycle;
+\draw[cell] (p1) -- (p15) -- (p14) -- cycle;
 \end{pgfonlayer}
 
-\node [classify] at ($ 1/3*(p5)+1/3*(p4)+1/3*(p10) $) {-};
-\node [classify] at ($ 1/3*(p6)+1/3*(p5)+1/3*(p11) $) {-};
-\node [classify] at ($ 1/3*(p1)+1/3*(p2)+1/3*(p12) $) {+};
-\node [classify] at ($ 1/3*(p2)+1/3*(p3)+1/3*(p13) $) {+};
+\node[classify] at ($ 1/3*(p5)+1/3*(p4)+1/3*(p10) $) {-};
+\node[classify] at ($ 1/3*(p6)+1/3*(p5)+1/3*(p11) $) {-};
+\node[classify] at ($ 1/3*(p1)+1/3*(p2)+1/3*(p12) $) {+};
+\node[classify] at ($ 1/3*(p2)+1/3*(p3)+1/3*(p13) $) {+};
 
-\node [classify] at ($ 1/3*(p4)+1/3*(p14)+1/3*(p10) $) {-};
-\node [classify] at ($ 1/3*(p5)+1/3*(p10)+1/3*(p11) $) {-};
-\node [classify] at ($ 1/3*(p6)+1/3*(p11)+1/3*(p16) $) {-};
-\node [classify] at ($ 1/3*(p6)+1/3*(p16)+1/3*(p17) $) {-};
+\node[classify] at ($ 1/3*(p4)+1/3*(p14)+1/3*(p10) $) {-};
+\node[classify] at ($ 1/3*(p5)+1/3*(p10)+1/3*(p11) $) {-};
+\node[classify] at ($ 1/3*(p6)+1/3*(p11)+1/3*(p16) $) {-};
+\node[classify] at ($ 1/3*(p6)+1/3*(p16)+1/3*(p17) $) {-};
 
-\node [classify] at ($ 1/3*(p3)+1/3*(p17)+1/3*(p13) $) {+};
-\node [classify] at ($ 1/3*(p2)+1/3*(p13)+1/3*(p12) $) {+};
-\node [classify] at ($ 1/3*(p1)+1/3*(p12)+1/3*(p15) $) {+};
-\node [classify] at ($ 1/3*(p1)+1/3*(p15)+1/3*(p14) $) {+};
+\node[classify] at ($ 1/3*(p3)+1/3*(p17)+1/3*(p13) $) {+};
+\node[classify] at ($ 1/3*(p2)+1/3*(p13)+1/3*(p12) $) {+};
+\node[classify] at ($ 1/3*(p1)+1/3*(p12)+1/3*(p15) $) {+};
+\node[classify] at ($ 1/3*(p1)+1/3*(p15)+1/3*(p14) $) {+};
 
 \end{tikzpicture}
 \end{document}
diff -r 78a253a2443f -r 12e125af3774 figs/generatefigs.sh
--- a/figs/generatefigs.sh	Tue Mar 27 21:11:40 2012 -0700
+++ b/figs/generatefigs.sh	Wed Mar 28 09:37:40 2012 -0700
@@ -11,10 +11,11 @@ s/%!PS-Adobe-2.0/%!PS-Adobe-2.0 EPSF-2.0
 /%%DocumentPaperSizes: Letter/d
 /%%Pages: 1/d
 /%%PageOrder: Ascend/d
+/%%BeginPaperSize:/{N;N;N;N;N;d}
 EOF
 
 f=cohesivecell
-sed -e "s/%%BoundingBox: 0 0 612 792/%%BoundingBox: 72 400 600 760/g" $f.ps | sed -f eps.sed > $f.tmp
+sed -e "s/%%BoundingBox: 0 0 612 792/%%BoundingBox: 148 412 595 670/g" $f.ps > $f.tmp
 
 for f in $pgffiles; do
   sed -f eps.sed $f.tmp > $f.eps



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