[cig-commits] commit: Add template.xml
Mercurial
hg at geodynamics.org
Thu Sep 29 12:49:14 PDT 2011
changeset: 371:864429d7016b
tag: tip
user: Walter Landry <wlandry at caltech.edu>
date: Thu Sep 29 12:47:17 2011 -0700
files: Q2Pm1_input/cookbook/template.xml UPGRADE doc/gale.lyx doc/images/tracers.eps doc/images/tracers.png doc/tracer.gp tools/generate_pvd.cxx
description:
Add template.xml
diff -r d2ffcc29d112 -r 864429d7016b Q2Pm1_input/cookbook/template.xml
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Q2Pm1_input/cookbook/template.xml Thu Sep 29 12:47:17 2011 -0700
@@ -0,0 +1,439 @@
+<?xml version="1.0"?>
+<StGermainData xmlns="http://www.vpac.org/StGermain/XML_IO_Handler/Jun2003">
+ <import>
+ <toolbox>Underworld</toolbox>
+ </import>
+ <plugins>
+ <struct>
+ <param name="Type">Underworld_EulerDeform</param>
+ <param name="Context">context</param>
+ </struct>
+ <struct>
+ <param name="Type">Underworld_VTKOutput</param>
+ <param name="Context">context</param>
+ </struct>
+ <struct>
+ <param name="Type">StgFEM_StandardConditionFunctions</param>
+ <param name="Context">context</param>
+ </struct>
+ </plugins>
+ <struct name="components">
+ <struct name="context">
+ <param name="Type">UnderworldContext</param>
+ </struct>
+ <struct name="mesh-Q2">
+ <param name="Type">FeMesh</param>
+ <param name="elementType">quadratic</param>
+ </struct>
+ <struct name="Q2Mesh-generator">
+ <param name="Type">C2Generator</param>
+ <param name="mesh">mesh-Q2</param>
+ <param name="dim">dim</param>
+ <param name="shadowDepth">shadowDepth</param>
+ <param name="regular">False</param>
+ <list name="size">
+ <param>elementResI</param>
+ <param>elementResJ</param>
+ <param>elementResK</param>
+ </list>
+ <list name="minCoord">
+ <param>minX</param>
+ <param>minY</param>
+ <param>minZ</param>
+ </list>
+ <list name="maxCoord">
+ <param>maxX</param>
+ <param>maxY</param>
+ <param>maxZ</param>
+ </list>
+ </struct>
+ <struct name="mesh-Pm1">
+ <param name="Type">FeMesh</param>
+ <param name="elementType">linear-inner</param>
+ </struct>
+ <struct name="Pm1Mesh-generator">
+ <param name="Type">Inner2DGenerator</param>
+ <param name="mesh">mesh-Pm1</param>
+ <param name="elementMesh">mesh-Q2</param>
+ <param name="dim">dim</param>
+ <param name="shadowDepth">shadowDepth</param>
+ <param name="regular">False</param>
+ <list name="size">
+ <param>elementResI</param>
+ <param>elementResJ</param>
+ <param>elementResK</param>
+ </list>
+ <list name="minCoord">
+ <param>minX</param>
+ <param>minY</param>
+ <param>minZ</param>
+ </list>
+ <list name="maxCoord">
+ <param>maxX</param>
+ <param>maxY</param>
+ <param>maxZ</param>
+ </list>
+ </struct>
+ <struct name="velocity">
+ <param name="Type">MeshVariable</param>
+ <param name="mesh">mesh-Q2</param>
+ <param name="Rank">Vector</param>
+ <param name="DataType">Double</param>
+ <param name="VectorComponentCount">dim</param>
+ <list name="names">
+ <param>vx</param>
+ <param>vy</param>
+ <param>vz</param>
+ </list>
+ </struct>
+ <struct name="velocityBCs">
+ <param name="Type">CompositeVC</param>
+ <param name="Data">mesh-Q2</param>
+ </struct>
+ <struct name="velocityICs">
+ <param name="Type">CompositeVC</param>
+ <param name="Data">mesh-Q2</param>
+ </struct>
+ <struct name="velocityDofLayout">
+ <param name="Type">DofLayout</param>
+ <param name="mesh">mesh-Q2</param>
+ <param name="BaseVariableCount">dim</param>
+ <list name="BaseVariables">
+ <param>vx</param>
+ <param>vy</param>
+ <param>vz</param>
+ </list>
+ </struct>
+ <struct name="VelocityField">
+ <param name="Type">FeVariable</param>
+ <param name="FEMesh">mesh-Q2</param>
+ <param name="DofLayout">velocityDofLayout</param>
+ <param name="BC">velocityBCs</param>
+ <param name="IC">velocityICs</param>
+ <param name="LinkedDofInfo">velocityLinkedDofs</param>
+ </struct>
+ <struct name="VelocityGradientsField">
+ <param name="Type">OperatorFeVariable</param>
+ <param name="Operator">Gradient</param>
+ <param name="FeVariable">VelocityField</param>
+ </struct>
+ <struct name="StrainRateField">
+ <param name="Type">OperatorFeVariable</param>
+ <param name="Operator">TensorSymmetricPart</param>
+ <param name="FeVariable">VelocityGradientsField</param>
+ </struct>
+ <struct name="StrainRateInvariantField">
+ <param name="Type">OperatorFeVariable</param>
+ <param name="Operator">SymmetricTensor_Invariant</param>
+ <param name="FeVariable">StrainRateField</param>
+ </struct>
+ <struct name="pressure">
+ <param name="Type">MeshVariable</param>
+ <param name="mesh">mesh-Pm1</param>
+ <param name="Rank">Scalar</param>
+ <param name="DataType">Double</param>
+ </struct>
+ <struct name="pressureDofLayout">
+ <param name="Type">DofLayout</param>
+ <param name="mesh">mesh-Pm1</param>
+ <list name="BaseVariables">
+ <param>pressure</param>
+ </list>
+ </struct>
+ <struct name="PressureField">
+ <param name="Type">FeVariable</param>
+ <param name="FEMesh">mesh-Pm1</param>
+ <param name="DofLayout">pressureDofLayout</param>
+ <param name="LinkedDofInfo">pressureLinkedDofs</param>
+ </struct>
+ <struct name="StressField">
+ <param name="Type">StressField</param>
+ <param name="StrainRateField">StrainRateField</param>
+ <param name="Context">context</param>
+ <param name="ConstitutiveMatrix">constitutiveMatrix</param>
+ <param name="Swarm">picIntegrationPoints</param>
+ <param name="Mesh">mesh-Q2</param>
+ <param name="IC">stressICs</param>
+ </struct>
+ <struct name="ViscosityField">
+ <param name="Type">ViscosityField</param>
+ <param name="Context">context</param>
+ <param name="Swarm">picIntegrationPoints</param>
+ <param name="Mesh">mesh-Q2</param>
+ <param name="ConstitutiveMatrix">constitutiveMatrix</param>
+ </struct>
+ <struct name="cellLayout">
+ <param name="Type">ElementCellLayout</param>
+ <param name="Mesh">mesh-Q2</param>
+ </struct>
+ <struct name="particleLayout">
+ <param name="Type">GaussParticleLayout</param>
+ <param name="gaussParticles">3</param>
+ </struct>
+ <struct name="gaussSwarm">
+ <param name="Type">IntegrationPointsSwarm</param>
+ <param name="CellLayout">cellLayout</param>
+ <param name="ParticleLayout">particleLayout</param>
+ <param name="FeMesh">mesh-Q2</param>
+ <param name="TimeIntegrator">timeIntegrator</param>
+ <param name="IntegrationPointMapper">nearestMapper</param>
+ </struct>
+ <struct name="nearestMapper">
+ <param name="Type">NearestNeighborMapper</param>
+ <param name="IntegrationPointsSwarm">gaussSwarm</param>
+ <param name="MappedSwarm">picIntegrationPoints</param>
+ </struct>
+ <struct name="timeIntegrator">
+ <param name="Type">TimeIntegrator</param>
+ <param name="order">timeIntegratorOrder</param>
+ <param name="simultaneous">f</param>
+ <param name="Context">context</param>
+ </struct>
+ <struct name="weights">
+ <param name="Type">PCDVC</param>
+ <param name="resolutionX">20</param>
+ <param name="resolutionY">20</param>
+ <param name="resolutionZ">20</param>
+ <param name="lowerT">0.6</param>
+ <param name="upperT">25</param>
+ <param name="maxDeletions">3</param>
+ <param name="maxSplits">3</param>
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+ </struct>
+ <struct name="localLayout">
+ <param name="Type">MappedParticleLayout</param>
+ </struct>
+ <struct name="picIntegrationPoints">
+ <param name="Type">IntegrationPointsSwarm</param>
+ <param name="CellLayout">cellLayout</param>
+ <param name="ParticleLayout">localLayout</param>
+ <param name="FeMesh">mesh-Q2</param>
+ <param name="WeightsCalculator">weights</param>
+ <param name="TimeIntegrator">timeIntegrator</param>
+ <param name="IntegrationPointMapper">mapper</param>
+ </struct>
+ <struct name="mapper">
+ <param name="Type">CoincidentMapper</param>
+ <param name="IntegrationPointsSwarm">picIntegrationPoints</param>
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+ </struct>
+ <struct name="materialSwarmParticleLayout">
+ <param name="Type">MeshParticleLayout</param>
+ <param name="cellParticleCount">particlesPerCell</param>
+ <param name="mesh">mesh-Q2</param>
+ </struct>
+ <struct name="pMovementHandler">
+ <param name="Type">ParticleMovementHandler</param>
+ </struct>
+ <struct name="pShadowSync">
+ <param name="Type">ParticleShadowSync</param>
+ </struct>
+ <struct name="materialSwarm">
+ <param name="Type">MaterialPointsSwarm</param>
+ <param name="CellLayout">cellLayout</param>
+ <param name="ParticleLayout">materialSwarmParticleLayout</param>
+ <param name="FeMesh">mesh-Q2</param>
+ <list name="ParticleCommHandlers">
+ <param>pMovementHandler</param>
+ <param>pShadowSync</param>
+ </list>
+ <param name="SplittingRoutine">splittingRoutine</param>
+ <param name="RemovalRoutine">removalRoutine</param>
+ <param name="EscapedRoutine">escapedRoutine</param>
+ </struct>
+ <struct name="materialSwarmAdvector">
+ <param name="Type">SwarmAdvector</param>
+ <param name="Swarm">materialSwarm</param>
+ <param name="TimeIntegrator">timeIntegrator</param>
+ <param name="VelocityField">VelocityField</param>
+ <param name="PeriodicBCsManager">periodicBCsManager</param>
+ <param name="allowFallbackToFirstOrder">True</param>
+ </struct>
+ <struct name="solutionVelocity">
+ <param name="Type">SolutionVector</param>
+ <param name="FeVariable">VelocityField</param>
+ </struct>
+ <struct name="solutionPressure">
+ <param name="Type">SolutionVector</param>
+ <param name="FeVariable">PressureField</param>
+ </struct>
+ <struct name="mom_force">
+ <param name="Type">ForceVector</param>
+ <param name="FeVariable">VelocityField</param>
+ <param name="ExtraInfo">context</param>
+ </struct>
+ <struct name="cont_force">
+ <param name="Type">ForceVector</param>
+ <param name="FeVariable">PressureField</param>
+ <param name="ExtraInfo">context</param>
+ </struct>
+ <struct name="k_matrix">
+ <param name="Type">StiffnessMatrix</param>
+ <param name="RowVariable">VelocityField</param>
+ <param name="ColumnVariable">VelocityField</param>
+ <param name="RHS">mom_force</param>
+ <param name="allowZeroElementContributions">False</param>
+ </struct>
+ <struct name="constitutiveMatrix">
+ <param name="Type">ConstitutiveMatrixCartesian</param>
+ <param name="Swarm">gaussSwarm</param>
+ <param name="StiffnessMatrix">k_matrix</param>
+ </struct>
+ <struct name="g_matrix">
+ <param name="Type">StiffnessMatrix</param>
+ <param name="RowVariable">VelocityField</param>
+ <param name="ColumnVariable">PressureField</param>
+ <param name="RHS">mom_force</param>
+ <param name="transposeRHS">cont_force</param>
+ <param name="allowZeroElementContributions">False</param>
+ </struct>
+ <struct name="gradientStiffnessMatrixTerm">
+ <param name="Type">GradientStiffnessMatrixTerm</param>
+ <param name="Swarm">gaussSwarm</param>
+ <param name="StiffnessMatrix">g_matrix</param>
+ </struct>
+ <struct name="preconditioner">
+ <param name="Type">StiffnessMatrix</param>
+ <param name="RowVariable">PressureField</param>
+ <param name="ColumnVariable">PressureField</param>
+ <param name="RHS">cont_force</param>
+ <param name="allowZeroElementContributions">True</param>
+ </struct>
+ <struct name="preconditionerTerm">
+ <param name="Type">UzawaPreconditionerTerm</param>
+ <param name="Swarm">gaussSwarm</param>
+ <param name="StiffnessMatrix">preconditioner</param>
+ </struct>
+ <struct name="uzawa">
+ <param name="Type">Stokes_SLE_UzawaSolver</param>
+ <param name="velocitySolver">matrixSolver</param>
+ <param name="Preconditioner">preconditioner</param>
+ <param name="tolerance">linearTolerance</param>
+ <param name="monitor">false</param>
+ <param name="maxIterations">5000</param>
+ <param name="minIterations">1</param>
+ </struct>
+ <struct name="stokesEqn">
+ <param name="Type">Stokes_SLE</param>
+ <param name="SLE_Solver">uzawa</param>
+ <param name="Context">context</param>
+ <param name="StressTensorMatrix">k_matrix</param>
+ <param name="GradientMatrix">g_matrix</param>
+ <param name="DivergenceMatrix"></param>
+ <param name="VelocityVector">solutionVelocity</param>
+ <param name="PressureVector">solutionPressure</param>
+ <param name="ForceVector">mom_force</param>
+ <param name="ContinuityForceVector">cont_force</param>
+ <param name="nonLinearMaxIterations">nonLinearMaxIterations</param>
+ <param name="nonLinearTolerance">nonLinearTolerance</param>
+ <param name="makeConvergenceFile">false</param>
+ </struct>
+ <struct name="buoyancyForceTerm">
+ <param name="Type">BuoyancyForceTerm</param>
+ <param name="ForceVector">mom_force</param>
+ <param name="Swarm">picIntegrationPoints</param>
+ <param name="gravity">gravity</param>
+ </struct>
+ <struct name="background">
+ <param name="Type">Everywhere</param>
+ </struct>
+ <struct name="escapedRoutine">
+ <param name="Type">EscapedRoutine</param>
+ <param name="idealParticleCount">0</param>
+ </struct>
+ <struct name="velocityRemesher">
+ <param name="Type">RegularRemesherCmpt</param>
+ <param name="mesh">mesh-Q2</param>
+ <list name="remeshDims">
+ <param>0</param>
+ <param>1</param>
+ <param>2</param>
+ </list>
+ </struct>
+
+ <struct name="storeViscosity">
+ <param name="Type">StoreVisc</param>
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+ </struct>
+ <struct name="storeStress">
+ <param name="Type">StoreStress</param>
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+ </struct>
+ </struct>
+
+ <list name="FieldVariablesToCheckpoint">
+ <param>VelocityField</param>
+ <param>PressureField</param>
+ </list>
+ <param name="timeIntegratorOrder">1</param>
+ <param name="maxTimeSteps">10</param>
+ <param name="outputEvery">1</param>
+ <param name="dumpEvery">1</param>
+ <param name="outputPath">./output</param>
+ <param name="dim">2</param>
+ <param name="shadowDepth">1</param>
+ <param name="minX">0.0f</param>
+ <param name="minY">0.0f</param>
+ <param name="minZ">0.0f</param>
+ <param name="maxX">2.0f</param>
+ <param name="maxY">0.35f</param>
+ <param name="maxZ">0.3f</param>
+ <param name="elementResI">16</param>
+ <param name="elementResJ">8</param>
+ <param name="elementResK">4</param>
+ <param name="allowUnbalancing">True</param>
+ <param name="buildNodeNeighbourTbl">True</param>
+ <param name="buildElementNeighbourTbl">True</param>
+ <param name="particlesPerCell">40</param>
+ <param name="seed">13</param>
+ <struct name="EulerDeform">
+ <list name="systems">
+ <struct>
+ <param name="mesh">mesh-Q2</param>
+ <param name="remesher">velocityRemesher</param>
+ <param name="velocityField">VelocityField</param>
+ <param name="wrapTop">True</param>
+ </struct>
+ </list>
+ </struct>
+ <struct name="velocityBCs">
+ <param name="type">CompositeVC</param>
+ <list name="vcList">
+ <struct>
+ <param name="type">WallVC</param>
+ <param name="wall">left</param>
+ <list name="variables">
+ <struct>
+ <param name="name">vx</param>
+ <param name="type">double</param>
+ <param name="value">0.0</param>
+ </struct>
+ </list>
+ </struct>
+ <struct>
+ <param name="type">WallVC</param>
+ <param name="wall">right</param>
+ <list name="variables">
+ <struct>
+ <param name="name">vx</param>
+ <param name="type">double</param>
+ <param name="value">0.0</param>
+ </struct>
+ </list>
+ </struct>
+ <struct>
+ <param name="type">WallVC</param>
+ <param name="wall">bottom</param>
+ <list name="variables">
+ <struct>
+ <param name="name">vy</param>
+ <param name="type">double</param>
+ <param name="value">0.0</param>
+ </struct>
+ </list>
+ </struct>
+ </list>
+ </struct>
+ <param name="checkpointEvery">1</param>
+ <param name="gravity">1.0</param>
+</StGermainData>
diff -r d2ffcc29d112 -r 864429d7016b UPGRADE
--- a/UPGRADE Thu Sep 29 12:11:45 2011 -0700
+++ b/UPGRADE Thu Sep 29 12:47:17 2011 -0700
@@ -1,3 +1,14 @@ Upgrading Gale from 1.5.0 to 1.6.0
+Upgrading Gale from 1.6 to 2.0
+------------------------------
+
+There is no strict need to convert input files from 1.6 to 2.0. All
+valid 1.6 input files should run without change in 2.0. However, the
+Q2 P-1 elements supported in 2.0 are much more suitable for general
+geodynamic modelling. In particular, there is no longer a need for a
+HydrostaticTerm.
+
+
+
Upgrading Gale from 1.5.0 to 1.6.0
----------------------------------
diff -r d2ffcc29d112 -r 864429d7016b doc/gale.lyx
--- a/doc/gale.lyx Thu Sep 29 12:11:45 2011 -0700
+++ b/doc/gale.lyx Thu Sep 29 12:47:17 2011 -0700
@@ -1,5 +1,5 @@
-#LyX 1.6.7 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
\begin_document
\begin_header
\textclass book
@@ -10,18 +10,26 @@
\renewcommand{\url}[1]{(\myUrl{#1})}
\end_preamble
\use_default_options false
+\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding auto
+\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_default_family default
+\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
@@ -29,9 +37,18 @@
\use_geometry true
\use_amsmath 1
\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
\cite_engine basic
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
\leftmargin 1in
\topmargin 1in
\rightmargin 1in
@@ -39,15 +56,16 @@
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
-\defskip medskip
+\paragraph_indentation default
\quotes_language swedish
\papercolumns 1
\papersides 2
\paperpagestyle headings
\tracking_changes false
\output_changes false
-\author ""
-\author ""
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
@@ -455,8 +473,10 @@ We start by decomposing the stress tenso
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\sigma_{ij}=\tau_{ij}-p\delta_{ij},\label{eq:stress}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\sigma_{ij}=\tau_{ij}-p\delta_{ij},\label{eq:stress}
+\end{equation}
\end_inset
@@ -469,8 +489,10 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\tau_{ij,j}-p_{,i}=0,\label{eq:simple momentum conservation}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{ij,j}-p_{,i}=0,\label{eq:simple momentum conservation}
+\end{equation}
\end_inset
@@ -478,8 +500,10 @@ subject to the (incompressible) continui
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-v_{i,i}=0,\label{eq:continuity}\end{equation}
+\begin_inset Formula
+\begin{equation}
+v_{i,i}=0,\label{eq:continuity}
+\end{equation}
\end_inset
@@ -497,8 +521,10 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-v_{i,i}\equiv v_{x,x}+v_{y,y}+v_{z,z}.\label{eq:implicit summation}\end{equation}
+\begin_inset Formula
+\begin{equation}
+v_{i,i}\equiv v_{x,x}+v_{y,y}+v_{z,z}.\label{eq:implicit summation}
+\end{equation}
\end_inset
@@ -536,8 +562,10 @@ Assuming a simple Newtonian fluid, we ca
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\tau_{ij}=2\eta\dot{\varepsilon}_{ij}\equiv\eta\left(v_{i,j}+v_{j,i}\right),\label{eq:stress strain}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{ij}=2\eta\dot{\varepsilon}_{ij}\equiv\eta\left(v_{i,j}+v_{j,i}\right),\label{eq:stress strain}
+\end{equation}
\end_inset
@@ -613,8 +641,10 @@ reference "eq:simple momentum conservati
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\tau_{ij,j}-p_{,i}=f_{i},\label{eq:body force}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{ij,j}-p_{,i}=f_{i},\label{eq:body force}
+\end{equation}
\end_inset
@@ -622,11 +652,14 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\begin{array}{ccc}
f_{x} & = & 0\\
f_{y} & = & -g\rho\\
-f_{z} & = & 0\end{array}.\label{eq:gravity body force}\end{equation}
+f_{z} & = & 0
+\end{array}.\label{eq:gravity body force}
+\end{equation}
\end_inset
@@ -676,8 +709,10 @@ reference "eq:continuity"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-v_{i,i}=d,\label{eq:divergence}\end{equation}
+\begin_inset Formula
+\begin{equation}
+v_{i,i}=d,\label{eq:divergence}
+\end{equation}
\end_inset
@@ -702,8 +737,10 @@ reference "eq:simple momentum conservati
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\eta\left(v_{i,jj}+v_{j,ij}\right)+p_{,i}=0.\label{eq:1D momentum}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\eta\left(v_{i,jj}+v_{j,ij}\right)+p_{,i}=0.\label{eq:1D momentum}
+\end{equation}
\end_inset
@@ -718,8 +755,10 @@ reference "eq:divergence"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-v_{x,x}=d,\label{eq:1D divergence}\end{equation}
+\begin_inset Formula
+\begin{equation}
+v_{x,x}=d,\label{eq:1D divergence}
+\end{equation}
\end_inset
@@ -727,8 +766,10 @@ v_{x,x}=d,\label{eq:1D divergence}\end{e
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-2\eta d_{,x}+p_{,x}=0.\label{eq:pressure_divergence_derivative}\end{equation}
+\begin_inset Formula
+\begin{equation}
+2\eta d_{,x}+p_{,x}=0.\label{eq:pressure_divergence_derivative}
+\end{equation}
\end_inset
@@ -808,8 +849,10 @@ reference "eq:body force"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\frac{\partial T}{\partial t}+v\cdot\nabla T=\kappa\nabla^{2}T+Q,\label{eq:energy}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\frac{\partial T}{\partial t}+v\cdot\nabla T=\kappa\nabla^{2}T+Q,\label{eq:energy}
+\end{equation}
\end_inset
@@ -872,8 +915,10 @@ key "Fast Solvers"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-v_{i,i}+Cp=d,\label{eq:stabilized}\end{equation}
+\begin_inset Formula
+\begin{equation}
+v_{i,i}+Cp=d,\label{eq:stabilized}
+\end{equation}
\end_inset
@@ -881,11 +926,14 @@ v_{i,i}+Cp=d,\label{eq:stabilized}\end{e
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
C & \equiv & \frac{1}{\nu}\left(M-D\right)\\
M & \equiv & \int_{\Omega_{e}}\psi(x)\psi^{T}(x)d\Omega_{e}\\
-D & \equiv & \int_{\Omega_{e}}d\Omega_{e}\end{array},\]
+D & \equiv & \int_{\Omega_{e}}d\Omega_{e}
+\end{array},
+\]
\end_inset
@@ -1076,10 +1124,13 @@ reference "eq:stabilized"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
s & \rightarrow & 10^{25}s,\\
-kg & \rightarrow & 10^{50}kg.\end{array}\]
+kg & \rightarrow & 10^{50}kg.
+\end{array}
+\]
\end_inset
@@ -1236,8 +1287,10 @@ reference "eq:body force"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\tau_{ij,j}-p_{0,i}-\delta p_{,i}=f_{0i}+\delta f_{i},\label{eq:hydrostatic}\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{ij,j}-p_{0,i}-\delta p_{,i}=f_{0i}+\delta f_{i},\label{eq:hydrostatic}
+\end{equation}
\end_inset
@@ -1277,10 +1330,13 @@ reference "eq:divergence"
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\begin{array}{ccc}
\tau_{ij,j}-\delta p_{,i} & = & \delta f_{i}\\
-v_{i,i}+C\delta p & = & d\end{array}.\label{eq:complete numerical stokes}\end{equation}
+v_{i,i}+C\delta p & = & d
+\end{array}.\label{eq:complete numerical stokes}
+\end{equation}
\end_inset
@@ -1310,14 +1366,19 @@ Using standard finite-element techniques
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\left(\begin{array}{cc}
K & G\\
-G^{T} & C\end{array}\right)\left(\begin{array}{c}
+G^{T} & C
+\end{array}\right)\left(\begin{array}{c}
v\\
-p\end{array}\right)=\left(\begin{array}{c}
+p
+\end{array}\right)=\left(\begin{array}{c}
f\\
-d\end{array}\right),\label{eq:matrix form}\end{equation}
+d
+\end{array}\right),\label{eq:matrix form}
+\end{equation}
\end_inset
@@ -1343,10 +1404,13 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\begin{array}{ccc}
Kv+Gp & = & f\\
-G^{T}v+Cp & = & d\end{array}.\label{eq:expanded matrix}\end{equation}
+G^{T}v+Cp & = & d
+\end{array}.\label{eq:expanded matrix}
+\end{equation}
\end_inset
@@ -1359,8 +1423,10 @@ In order to solve this, it turns out to
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\left(G^{T}K^{-1}G\right)z=r,\]
+\begin_inset Formula
+\[
+\left(G^{T}K^{-1}G\right)z=r,
+\]
\end_inset
@@ -1380,8 +1446,10 @@ In order to solve this, it turns out to
\end_inset
with
-\begin_inset Formula \[
-Q\equiv G^{T}\left[diag\left(K\right)\right]^{-1}G.\]
+\begin_inset Formula
+\[
+Q\equiv G^{T}\left[diag\left(K\right)\right]^{-1}G.
+\]
\end_inset
@@ -2417,8 +2485,10 @@ reference "fig:Two-blocks-sliding"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-L_{\eta_{min}}=\frac{\eta_{min}v}{C},\]
+\begin_inset Formula
+\[
+L_{\eta_{min}}=\frac{\eta_{min}v}{C},
+\]
\end_inset
@@ -2501,8 +2571,10 @@ So the other solution Gale provides is t
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-L_{\dot{\epsilon}_{max}}=\frac{v}{\dot{\epsilon}_{max}}.\]
+\begin_inset Formula
+\[
+L_{\dot{\epsilon}_{max}}=\frac{v}{\dot{\epsilon}_{max}}.
+\]
\end_inset
@@ -6471,7 +6543,7 @@ Add the components
\end_layout
\begin_layout LyX-Code
- <param>VelocityMagnitudeField</param>
+ <param>PressureField</param>
\end_layout
\begin_layout LyX-Code
@@ -6544,7 +6616,7 @@ status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
- filename images/tracers.png
+ filename images/tracers.eps
width 70col%
\end_inset
@@ -6574,224 +6646,6 @@ Particle tracks of tracers
\end_inset
-\end_layout
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Hydrostatic-Term"
-
-\end_inset
-
-Hydrostatic Term
-\end_layout
-
-\begin_layout Standard
-This example will add a HydrostaticTerm to the simple extension model (Section
-
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Viscous-Material-in"
-
-\end_inset
-
-) to improve its accuracy.
- So first copy
-\family typewriter
-myviscous_extension.xml
-\family default
- to
-\family typewriter
-myhydrostatic.xml
-\family default
-.
- Then add a
-\family typewriter
-HydrostaticTerm
-\family default
- and
-\family typewriter
-StressBC
-\family default
- just before the
-\family typewriter
-BuoyancyForceTerm
-\end_layout
-
-\begin_layout LyX-Code
-<struct name="hydrostaticTerm">
-\end_layout
-
-\begin_layout LyX-Code
- <param name="Type">HydrostaticTerm</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="density">step(.35-y)</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="pressure">step(.35-y)*(.35-y)</param>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\begin_layout LyX-Code
-<struct name="stressBC">
-\end_layout
-
-\begin_layout LyX-Code
- <param name="Type">StressBC</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="ForceVector">mom_force</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="Swarm">picIntegrationPoints</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="wall">top</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="y_type">HydrostaticTerm</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="y_value">hydrostaticTerm</param>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\begin_layout Standard
-Then, in the
-\family typewriter
-BuoyancyForceTerm
-\family default
-, add an entry for
-\family typewriter
-HydrostaticTerm
-\family default
- so that the
-\family typewriter
-BuoyancyForceTerm
-\family default
- now looks like
-\end_layout
-
-\begin_layout LyX-Code
-<struct name="buoyancyForceTerm">
-\end_layout
-
-\begin_layout LyX-Code
- <param name="Type">BuoyancyForceTerm</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="ForceVector">mom_force</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="Swarm">picIntegrationPoints</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="gravity">gravity</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="HydrostaticTerm">hydrostaticTerm</param>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:Hydro_sri"
-
-\end_inset
-
- shows the strain rate invariant with the same color scale as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:Strain-viscous-extension"
-
-\end_inset
-
-.
- With the
-\family typewriter
-HydrostaticTerm
-\family default
-, the artifacts seen at the top and bottom in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:Strain-viscous-extension"
-
-\end_inset
-
- disappear.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename images/Paraview_hydro.png
- lyxscale 50
- width 100col%
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:Hydro_sri"
-
-\end_inset
-
-Strain rate invariant for an extension model with the hydrostatic pressure
- subtracted out.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-A worked example is in
-\family typewriter
-input/cookbook/hydrostatic.xml
-\family default
-.
\end_layout
\begin_layout Section
@@ -7973,7 +7827,7 @@ Specify the background material's therma
\end_layout
\begin_layout LyX-Code
- <param name="Shape">boxShape</param>
+ <param name="Shape">nonSphereShape</param>
\end_layout
\begin_layout LyX-Code
@@ -8095,7 +7949,7 @@ Modify the buoyancy force term by adding
\end_layout
\begin_layout Standard
-with the line
+the line
\end_layout
\begin_layout LyX-Code
@@ -8240,8 +8094,10 @@ input/cookbook/temperature
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-1+0.05\cos(6x)\cos(10y).\]
+\begin_inset Formula
+\[
+1+0.05\cos(6x)\cos(10y).
+\]
\end_inset
@@ -8455,6 +8311,10 @@ Add the NonNewtonian rheology after NonS
\begin_layout LyX-Code
<param name="StrainRateInvariantField">StrainRateInvariantField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TemperatureField">TemperatureField</param>
\end_layout
\begin_layout LyX-Code
@@ -9640,7 +9500,7 @@ reference "sub:Plugins"
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="35" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -10468,11 +10328,26 @@ reference "sec:Deformed-Upper-Boundary"
\begin_layout Description
elementResI,elementResJ,elementResK The number of elements in each direction.
- Note that the number of grid points is one larger (e.g., 64 elements
+ Note that the number of grid points depends on the type of element.
+ Constant (
+\begin_inset Formula $P_{0}$
+\end_inset
+
+) elements have their grid points in the center of the element, so they
+ have the same number of grid points as elements.
+ Linear (
+\begin_inset Formula $Q_{1}$
+\end_inset
+
+) elements have their grid points on the corners, so the number of grid
+ points is one larger (e.g., 64 elements
\begin_inset Formula $\Rightarrow$
\end_inset
65 grid points).
+ Note that when numbering grid points, we start from 0.
+ So the index for 65 grid points runs from 0 to 64.
+
\end_layout
\begin_layout Description
@@ -12396,7 +12271,7 @@ reference "sec:Materials"
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -12458,11 +12333,89 @@ name "sec:Shapes"
\end_layout
\begin_layout Standard
-When setting up a simulation, Gale reads in shapes to determine what to
- put where.
- For example, you can create a simulation with different materials by creating
- different shapes and putting different materials in them.
- As a simple example, you can create a 3D box
+When setting up the simulation, Gale first creates the computational domain.
+ That domain may be irregular if you are using a
+\family typewriter
+SurfaceAdaptor
+\family default
+ (Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Deformed-Upper-Boundary"
+
+\end_inset
+
+).
+ Gale then starts putting down materials within that domain.
+ When putting down a material at a particular point, Gale asks all of the
+ materials (Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Materials"
+
+\end_inset
+
+) whether that point belongs to that material.
+ So it is perfectly fine to have material shapes that cover more than the
+ computational domain.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Computational_Domain"
+
+\end_inset
+
+ shows an example with irregular top and bottom materials.
+ Materials for the upper and lower lithosphere are defined in large, regular
+ boxes, but material is only created within the blue region.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename images/computational_domain.pdf
+ width 100col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:Computational_Domain"
+
+\end_inset
+
+Areas covered by material box shapes and the computational domain.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As a simple example, you can create a 3D box
\end_layout
\begin_layout LyX-Code
@@ -12559,7 +12512,7 @@ Note that the exclamation point ``!'' in
\family typewriter
simpleSphere
\family default
- means ``not.'' So
+ means ``not.'' So this
\family typewriter
Intersection
\family default
@@ -12684,11 +12637,14 @@ The Euler angles use the
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
R=\left(\begin{array}{ccc}
-\sin\alpha\sin\gamma+\cos\alpha\cos\beta\cos\gamma & \sin\alpha\cos\gamma+\cos\beta\sin\gamma\cos\alpha & -\cos\alpha\sin\beta\\
-\cos\alpha\sin\gamma-\cos\beta\cos\gamma\sin\alpha & \cos\alpha\cos\gamma-\cos\beta\sin\gamma\sin\alpha & \sin\alpha\sin\beta\\
-\sin\beta\cos\alpha & \sin\beta\sin\alpha & \cos\beta\end{array}\right).\]
+\sin\beta\cos\alpha & \sin\beta\sin\alpha & \cos\beta
+\end{array}\right).
+\]
\end_inset
@@ -12700,17 +12656,22 @@ R=\left(\begin{array}{ccc}
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left(\begin{array}{c}
x'\\
y'\\
-z'\end{array}\right)=\left(\left(\begin{array}{c}
+z'
+\end{array}\right)=\left(\left(\begin{array}{c}
x\\
y\\
-z\end{array}\right)-\left(\begin{array}{c}
+z
+\end{array}\right)-\left(\begin{array}{c}
CentreX\\
CentreY\\
-CentreZ\end{array}\right)\right)R,\]
+CentreZ
+\end{array}\right)\right)R,
+\]
\end_inset
@@ -12737,7 +12698,7 @@ invert
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -12912,8 +12873,10 @@ BelowCosinePlane
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-y<offset+delta*\cos\left(\frac{\pi period}{180}*x+phase\right)\]
+\begin_inset Formula
+\[
+y<offset+delta*\cos\left(\frac{\pi period}{180}*x+phase\right)
+\]
\end_inset
@@ -12929,7 +12892,7 @@ y<offset+delta*\cos\left(\frac{\pi perio
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13051,8 +13014,10 @@ BelowPlane
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-y<offset\]
+\begin_inset Formula
+\[
+y<offset
+\]
\end_inset
@@ -13096,7 +13061,7 @@ This shape also uses the variables
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13271,20 +13236,26 @@ Box
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{c}
startX<x<endX\\
startY<y<endY\\
-startZ<z<endZ\end{array}\]
+startZ<z<endZ
+\end{array}
+\]
\end_inset
Alternately, you can use widths, in which case
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{c}
|x|<widthX/2\\
|y|<widthY/2\\
-|z|<widthZ/2\end{array}.\]
+|z|<widthZ/2
+\end{array}.
+\]
\end_inset
@@ -13310,7 +13281,7 @@ You may mix and match these specificatio
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13492,12 +13463,15 @@ This shape uses a variable
\begin_layout Standard
\noindent
\align center
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{c}
radius^{2}>x^{2}+y^{2}\\
startX<x<endX\\
startY<y<endY\\
-startZ<z<endZ\end{array}.\]
+startZ<z<endZ
+\end{array}.
+\]
\end_inset
@@ -13508,7 +13482,7 @@ startZ<z<endZ\end{array}.\]
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13788,7 +13762,7 @@ You can extrude this shape into three di
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13863,8 +13837,10 @@ Sphere
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-x^{2}+y^{2}+z^{2}<radius^{2}\]
+\begin_inset Formula
+\[
+x^{2}+y^{2}+z^{2}<radius^{2}
+\]
\end_inset
@@ -13880,7 +13856,7 @@ x^{2}+y^{2}+z^{2}<radius^{2}\]
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -13939,8 +13915,10 @@ In two dimensions
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\left(\frac{x}{radiusX}\right)^{2/epsilon1}+\left(\frac{y}{radiusY}\right)^{2/epsilon1}<1,\]
+\begin_inset Formula
+\[
+\left(\frac{x}{radiusX}\right)^{2/epsilon1}+\left(\frac{y}{radiusY}\right)^{2/epsilon1}<1,
+\]
\end_inset
@@ -13950,8 +13928,10 @@ and in three dimensions
\begin_layout Standard
\noindent
\align center
-\begin_inset Formula \[
-\left(\left(\frac{x}{radiusX}\right)^{2/epsilon2}+\left(\frac{y}{radiusY}\right)^{2/epsilon2}\right)^{epsilon2/epsilon1}+\left(\frac{z}{radiusZ}\right)^{2/epsilon1}<1.\]
+\begin_inset Formula
+\[
+\left(\left(\frac{x}{radiusX}\right)^{2/epsilon2}+\left(\frac{y}{radiusY}\right)^{2/epsilon2}\right)^{epsilon2/epsilon1}+\left(\frac{z}{radiusZ}\right)^{2/epsilon1}<1.
+\]
\end_inset
@@ -13962,7 +13942,7 @@ and in three dimensions
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14220,7 +14200,7 @@ reference "sec:Shapes"
\end_layout
\begin_layout LyX-Code
- <param name="Shape">yieldingShape</param>
+ <param name="Shape">materialShape</param>
\end_layout
\begin_layout LyX-Code
@@ -14342,8 +14322,10 @@ At a given time
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-Qe^{-\lambda t}\]
+\begin_inset Formula
+\[
+Qe^{-\lambda t}
+\]
\end_inset
@@ -14362,7 +14344,7 @@ Qe^{-\lambda t}\]
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14533,7 +14515,7 @@ materialSwarm
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14614,7 +14596,7 @@ eta0
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14676,8 +14658,10 @@ Frank-Kamenetskii
\begin_layout Standard
This is a temperature-dependent viscosity
-\begin_inset Formula \[
-eta=eta0*\exp\left(-theta*T\right).\]
+\begin_inset Formula
+\[
+eta=eta0*\exp\left(-theta*T\right).
+\]
\end_inset
@@ -14693,7 +14677,7 @@ eta=eta0*\exp\left(-theta*T\right).\]
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14778,8 +14762,10 @@ This is another temperature dependent vi
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-eta=eta0*\exp\left(\left(activationEnergy+activationVolume*(height-y)\right)/\left(T+referenceTemperature\right)\right).\]
+\begin_inset Formula
+\[
+eta=eta0*\exp\left(\left(activationEnergy+activationVolume*(height-y)\right)/\left(T+referenceTemperature\right)\right).
+\]
\end_inset
@@ -14805,7 +14791,7 @@ eta=eta0*\exp\left(\left(activationEnerg
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -14931,8 +14917,10 @@ This is a strain rate dependent rheology
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\dot{\varepsilon}=A\tau^{n}\exp\left(-T_{0}/T\right),\]
+\begin_inset Formula
+\[
+\dot{\varepsilon}=A\tau^{n}\exp\left(-T_{0}/T\right),
+\]
\end_inset
@@ -14958,8 +14946,10 @@ This is a strain rate dependent rheology
are constants.
Using
-\begin_inset Formula \[
-\tau=2\eta\dot{\varepsilon},\]
+\begin_inset Formula
+\[
+\tau=2\eta\dot{\varepsilon},
+\]
\end_inset
@@ -14967,8 +14957,10 @@ This is a strain rate dependent rheology
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\eta=\frac{\dot{\varepsilon}^{\frac{1}{n}-1}\exp\left(T_{0}/nT\right)}{2A^{\frac{1}{n}}}.\]
+\begin_inset Formula
+\[
+\eta=\frac{\dot{\varepsilon}^{\frac{1}{n}-1}\exp\left(T_{0}/nT\right)}{2A^{\frac{1}{n}}}.
+\]
\end_inset
@@ -14999,7 +14991,7 @@ You may set maximum and minimum values f
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -15237,8 +15229,10 @@ materialSwarm
\begin_layout Description
healingRate With this parameter, accumulated strain can decrease.
Specifically, the time derivative of accumulated strain becomes
-\begin_inset Formula \[
-\frac{\sigma_{yield}}{\eta}\left(\frac{\beta}{1-\beta}-healingRate\right),\]
+\begin_inset Formula
+\[
+\frac{\sigma_{yield}}{\eta}\left(\frac{\beta}{1-\beta}-healingRate\right),
+\]
\end_inset
@@ -15361,7 +15355,7 @@ You can also define a strain weakening r
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -15611,8 +15605,10 @@ This is the simplest yielding rheology i
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\sqrt{J_{2}}=C'\]
+\begin_inset Formula
+\[
+\sqrt{J_{2}}=C'
+\]
\end_inset
@@ -15661,8 +15657,10 @@ True
True
\family default
, then the viscosity is set to
-\begin_inset Formula \[
-\eta_{new}=2C'^{2}\eta/\left(C'^{2}+J_{2}\right).\]
+\begin_inset Formula
+\[
+\eta_{new}=2C'^{2}\eta/\left(C'^{2}+J_{2}\right).
+\]
\end_inset
@@ -15673,8 +15671,10 @@ True
\begin_deeper
\begin_layout Standard
-\begin_inset Formula \[
-\eta_{new}=\eta C'/\sqrt{J_{2}},\]
+\begin_inset Formula
+\[
+\eta_{new}=\eta C'/\sqrt{J_{2}},
+\]
\end_inset
@@ -15694,7 +15694,7 @@ True
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -15818,8 +15818,10 @@ This rheology uses the same parameters a
This rheology uses the same parameters as Von Mises, but also adds a friction
coefficient that can soften.
Specifically, the yield condition is
-\begin_inset Formula \[
-\sqrt{J_{2}}=Ap+B,\]
+\begin_inset Formula
+\[
+\sqrt{J_{2}}=Ap+B,
+\]
\end_inset
@@ -15842,8 +15844,10 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\sigma_{MC}=C'+\sigma_{\bot}\tan\phi',\]
+\begin_inset Formula
+\[
+\sigma_{MC}=C'+\sigma_{\bot}\tan\phi',
+\]
\end_inset
@@ -15851,10 +15855,13 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
A & = & \sin\phi'\\
-B & = & C'\cos\phi'\end{array}.\]
+B & = & C'\cos\phi'
+\end{array}.
+\]
\end_inset
@@ -15867,10 +15874,13 @@ B & = & C'\cos\phi'\end{array}.\]
\end_inset
is more complicated
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
A & = & \frac{2\sin\phi'}{\sqrt{3}\left(3-\sin\phi'\right)}\\
-B & = & \frac{6C'\cos\phi'}{\sqrt{3}\left(3-\sin\phi'\right)}\end{array}.\]
+B & = & \frac{6C'\cos\phi'}{\sqrt{3}\left(3-\sin\phi'\right)}
+\end{array}.
+\]
\end_inset
@@ -15935,8 +15945,10 @@ maximumStrainRate
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\eta_{new}=\frac{Ap+B}{\sqrt{\dot{\epsilon}_{max}}}.\]
+\begin_inset Formula
+\[
+\eta_{new}=\frac{Ap+B}{\sqrt{\dot{\epsilon}_{max}}}.
+\]
\end_inset
@@ -15945,8 +15957,10 @@ maximumStrainRate
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\eta_{new}=\frac{Ap+B}{\sqrt{\dot{\epsilon}}}.\]
+\begin_inset Formula
+\[
+\eta_{new}=\frac{Ap+B}{\sqrt{\dot{\epsilon}}}.
+\]
\end_inset
@@ -16044,7 +16058,7 @@ reference "sec:HydrostaticTerm"
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="18" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -16521,7 +16535,7 @@ ignoreOldOrientation
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -17602,8 +17616,10 @@ This sets the height of the surface to
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-h=h_{0}+amplitude*\cos\left(x*frequency\right),\]
+\begin_inset Formula
+\[
+h=h_{0}+amplitude*\cos\left(x*frequency\right),
+\]
\end_inset
@@ -17763,11 +17779,14 @@ Gradient
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
h=\left\{ \begin{array}{cc}
h_{0} & x<BeginOffset\\
h_{0}+Gradient\left(x-BeginOffset\right) & BeginOffset<x<EndOffset\\
-h_{0}+Gradient\left(EndOffset-BeginOffset\right) & x>EndOffset\end{array}\right..\]
+h_{0}+Gradient\left(EndOffset-BeginOffset\right) & x>EndOffset
+\end{array}\right..
+\]
\end_inset
@@ -17808,10 +17827,13 @@ Sign
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{c}
x'\equiv\max\left(\min\left(x,MaxX\right),MinX\right)\\
-d\equiv\sqrt{Radius^{2}-(x-x')^{2}}\end{array},\]
+d\equiv\sqrt{Radius^{2}-(x-x')^{2}}
+\end{array},
+\]
\end_inset
@@ -17823,10 +17845,13 @@ then the height is set to
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
h=\left\{ \begin{array}{cc}
h_{0}+Y0+d & Sign=true\\
-h_{0}+Y0-d & Sign=false\end{array}\right..\]
+h_{0}+Y0-d & Sign=false
+\end{array}\right..
+\]
\end_inset
@@ -17999,8 +18024,10 @@ This plugin applies a diffusive operator
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\frac{\partial y}{\partial t}=-diffusionCoefficient\frac{\partial^{2}y}{\partial x^{2}}.\]
+\begin_inset Formula
+\[
+\frac{\partial y}{\partial t}=-diffusionCoefficient\frac{\partial^{2}y}{\partial x^{2}}.
+\]
\end_inset
@@ -18029,8 +18056,10 @@ key "HRS"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\alpha=\overline{a}_{old}+\tan^{-1}\left(2vTW^{-2}-\frac{\left(2Kk{}_{a}^{m}\right)W^{hm-1}S^{n}}{\left(hm+1\right)dt_{erosion}}\right),\]
+\begin_inset Formula
+\[
+\alpha=\overline{a}_{old}+\tan^{-1}\left(2vTW^{-2}-\frac{\left(2Kk{}_{a}^{m}\right)W^{hm-1}S^{n}}{\left(hm+1\right)dt_{erosion}}\right),
+\]
\end_inset
@@ -18042,9 +18071,11 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
S & \equiv & \tan^{-1}\left(\overline{a}_{old}\right),\\
-\overline{a} & \equiv & \left(y_{max}-y_{0}\right)/W,\end{eqnarray*}
+\overline{a} & \equiv & \left(y_{max}-y_{0}\right)/W,
+\end{eqnarray*}
\end_inset
@@ -18154,7 +18185,7 @@ Geometry for HRS Erosion
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -18445,7 +18476,7 @@ Stokes_SLE_UzawaSolver
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -18599,7 +18630,7 @@ Stokes_SLE
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -19069,7 +19100,7 @@ critical
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -19177,8 +19208,10 @@ If you add this component, then there wi
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=-\rho g.\]
+\begin_inset Formula
+\[
+F=-\rho g.
+\]
\end_inset
@@ -19190,8 +19223,10 @@ TemperatureField
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=-\rho g\left(1-\alpha T\right).\]
+\begin_inset Formula
+\[
+F=-\rho g\left(1-\alpha T\right).
+\]
\end_inset
@@ -19259,7 +19294,7 @@ BuoyancyForceTerm
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -19426,8 +19461,10 @@ If you add this component, then there wi
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=-\rho Ra_{C}.\]
+\begin_inset Formula
+\[
+F=-\rho Ra_{C}.
+\]
\end_inset
@@ -19439,8 +19476,10 @@ TemperatureField
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=Ra_{T}T-\rho Ra_{C}.\]
+\begin_inset Formula
+\[
+F=Ra_{T}T-\rho Ra_{C}.
+\]
\end_inset
@@ -19501,7 +19540,7 @@ HydrostaticTerm
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -19748,8 +19787,10 @@ is equivalent to the formula
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-e^{-2\left(x^{2}+y^{2}\right)}.\]
+\begin_inset Formula
+\[
+e^{-2\left(x^{2}+y^{2}\right)}.
+\]
\end_inset
@@ -19811,7 +19852,7 @@ http://muParser.sf.net
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -19932,7 +19973,7 @@ In addition, the available functions are
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="34" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -20719,7 +20760,7 @@ a
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -21560,7 +21601,7 @@ particleStepping
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -21659,7 +21700,7 @@ status open
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
@@ -21993,8 +22034,10 @@ reference "sec:Geomod-2008"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-error\propto h+O(h^{2}),\]
+\begin_inset Formula
+\[
+error\propto h+O(h^{2}),
+\]
\end_inset
@@ -22101,8 +22144,10 @@ has instructions on running this benchma
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=6\pi\eta ru,\]
+\begin_inset Formula
+\[
+F=6\pi\eta ru,
+\]
\end_inset
@@ -22123,8 +22168,10 @@ F=6\pi\eta ru,\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F=\frac{4}{3}\pi r^{3}g\delta\rho,\]
+\begin_inset Formula
+\[
+F=\frac{4}{3}\pi r^{3}g\delta\rho,
+\]
\end_inset
@@ -22141,8 +22188,10 @@ where
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-u=\frac{2}{9}r^{2}g\delta\rho/\eta.\]
+\begin_inset Formula
+\[
+u=\frac{2}{9}r^{2}g\delta\rho/\eta.
+\]
\end_inset
@@ -22170,8 +22219,10 @@ Setting
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-u=0.00222.\]
+\begin_inset Formula
+\[
+u=0.00222.
+\]
\end_inset
@@ -22192,8 +22243,10 @@ key "Landau & Lifschitz"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-u=\frac{1}{3}\frac{r^{2}g\delta\rho}{\eta}\frac{\eta+\eta'}{\eta+\frac{3}{2}\eta'},\]
+\begin_inset Formula
+\[
+u=\frac{1}{3}\frac{r^{2}g\delta\rho}{\eta}\frac{\eta+\eta'}{\eta+\frac{3}{2}\eta'},
+\]
\end_inset
@@ -22228,8 +22281,10 @@ key "Stokes Sphere"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F_{H}=6\pi\eta ru\frac{1-0.75857\cdot\left(\frac{r}{R}\right)^{5}}{1+f_{H}\left(\frac{r}{R}\right)},\]
+\begin_inset Formula
+\[
+F_{H}=6\pi\eta ru\frac{1-0.75857\cdot\left(\frac{r}{R}\right)^{5}}{1+f_{H}\left(\frac{r}{R}\right)},
+\]
\end_inset
@@ -22237,8 +22292,10 @@ F_{H}=6\pi\eta ru\frac{1-0.75857\cdot\le
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-f_{H}\left(\frac{r}{R}\right)=-2.1050(r/R)+2.0865(r/R)^{3}-1.7068(r/R)^{5}+0.72603(r/R)^{6}.\]
+\begin_inset Formula
+\[
+f_{H}\left(\frac{r}{R}\right)=-2.1050(r/R)+2.0865(r/R)^{3}-1.7068(r/R)^{5}+0.72603(r/R)^{6}.
+\]
\end_inset
@@ -22258,8 +22315,10 @@ For our case with
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-u=1.122747319\cdot10^{-3}.\]
+\begin_inset Formula
+\[
+u=1.122747319\cdot10^{-3}.
+\]
\end_inset
@@ -22278,8 +22337,10 @@ key "Stokes Sphere"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-F_{F}=6\pi\eta ru/\left(1+f_{F}(r/R)\right),\]
+\begin_inset Formula
+\[
+F_{F}=6\pi\eta ru/\left(1+f_{F}(r/R)\right),
+\]
\end_inset
@@ -22287,9 +22348,11 @@ F_{F}=6\pi\eta ru/\left(1+f_{F}(r/R)\rig
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
f_{f}(r/R) & = & -2.10444(r/R)+2.08877(r/R)^{3}-0.94813(r/R)^{5}\\
- & & -1.372(r/R)^{6}+3.87(r/R)^{8}-4.19(r/R)^{10}.\end{eqnarray*}
+ & & -1.372(r/R)^{6}+3.87(r/R)^{8}-4.19(r/R)^{10}.
+\end{eqnarray*}
\end_inset
@@ -22297,8 +22360,10 @@ For our case, this gives a speed of
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-u=1.12293603939\cdot10^{-3},\]
+\begin_inset Formula
+\[
+u=1.12293603939\cdot10^{-3},
+\]
\end_inset
@@ -22517,9 +22582,11 @@ d.
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
v_{x} & = & -\dot{\epsilon}y,\\
-v_{y} & = & \dot{\epsilon}x,\end{eqnarray*}
+v_{y} & = & \dot{\epsilon}x,
+\end{eqnarray*}
\end_inset
@@ -22562,8 +22629,10 @@ A characteristic of the analytic solutio
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-p_{m}=4\dot{\epsilon}\frac{\mu_{m}\left(\mu_{i}-\mu_{m}\right)}{\mu_{i}+\mu_{m}}\frac{r_{i}^{2}}{r^{2}}\cos\left(2\theta\right),\]
+\begin_inset Formula
+\[
+p_{m}=4\dot{\epsilon}\frac{\mu_{m}\left(\mu_{i}-\mu_{m}\right)}{\mu_{i}+\mu_{m}}\frac{r_{i}^{2}}{r^{2}}\cos\left(2\theta\right),
+\]
\end_inset
@@ -22849,8 +22918,10 @@ key "Folds"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-t_{r}=\frac{4\pi\eta}{gL},\]
+\begin_inset Formula
+\[
+t_{r}=\frac{4\pi\eta}{gL},
+\]
\end_inset
@@ -23107,10 +23178,13 @@ reference "fig:Divergence_v_sri"
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
v_{x} & = & x\cdot d/2\\
-v_{y} & = & y\cdot d/2\end{array}.\]
+v_{y} & = & y\cdot d/2
+\end{array}.
+\]
\end_inset
@@ -23118,11 +23192,14 @@ v_{y} & = & y\cdot d/2\end{array}.\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{array}{ccc}
v_{x} & = & x\cdot d/3\\
v_{y} & = & y\cdot d/3\\
-v_{z} & = & z\cdot d/3\end{array}.\]
+v_{z} & = & z\cdot d/3
+\end{array}.
+\]
\end_inset
@@ -23317,8 +23394,10 @@ For the Drucker-Prager rheology in 2D, w
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\sigma_{ns}=\sigma_{nn}\tan\varphi+C,\]
+\begin_inset Formula
+\[
+\sigma_{ns}=\sigma_{nn}\tan\varphi+C,
+\]
\end_inset
@@ -23355,8 +23434,10 @@ For the Drucker-Prager rheology in 2D, w
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\sin\left(2\Theta\right)\left(\sigma_{I}-\sigma_{III}\right)/2=\tan\varphi\left(\left(\sigma_{I}+\sigma_{III}\right)/2+\cos\left(2\Theta\right)\left(\sigma_{I}-\sigma_{III}\right)/2\right)+C,\]
+\begin_inset Formula
+\[
+\sin\left(2\Theta\right)\left(\sigma_{I}-\sigma_{III}\right)/2=\tan\varphi\left(\left(\sigma_{I}+\sigma_{III}\right)/2+\cos\left(2\Theta\right)\left(\sigma_{I}-\sigma_{III}\right)/2\right)+C,
+\]
\end_inset
@@ -23373,8 +23454,10 @@ For the Drucker-Prager rheology in 2D, w
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-\Theta=\pm\left(\frac{\pi}{4}+\frac{\varphi}{2}\right).\]
+\begin_inset Formula
+\[
+\Theta=\pm\left(\frac{\pi}{4}+\frac{\varphi}{2}\right).
+\]
\end_inset
@@ -25864,6 +25947,7 @@ This General Public License does not per
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1"
@@ -25883,6 +25967,7 @@ Geophys.
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "2"
@@ -25912,6 +25997,7 @@ ANZIAM J
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "3"
@@ -25935,6 +26021,7 @@ J.
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "4"
@@ -25956,6 +26043,7 @@ Philosophical Magazine, 86
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "5"
@@ -25982,6 +26070,7 @@ 7
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "6"
@@ -26011,6 +26100,7 @@ 32
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "7"
@@ -26036,6 +26126,7 @@ 105
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "8"
@@ -26059,6 +26150,7 @@ 155
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "9"
@@ -26075,6 +26167,7 @@ Fluid Mechanics
\end_layout
\begin_layout Bibliography
+\labelwidthstring Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "10"
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diff -r d2ffcc29d112 -r 864429d7016b doc/images/tracers.png
Binary file doc/images/tracers.png has changed
diff -r d2ffcc29d112 -r 864429d7016b doc/tracer.gp
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc/tracer.gp Thu Sep 29 12:47:17 2011 -0700
@@ -0,0 +1,6 @@
+# A simple gnuplot script to generate the tracer output file for the manual.
+
+set key off
+set term postscript eps color
+set output "tracers.eps"
+plot "./swarmOutput.00000.dat" using 3:4 w l lw 5 title "particle 0", "./swarmOutput.00001.dat" using 3:4 w l lw 5 title "particle 1", "./swarmOutput.00002.dat" using 3:4 w l lw 5 title "particle 2", "./swarmOutput.00003.dat" using 3:4 w l lw 5 title "particle 3", "./swarmOutput.00004.dat" using 3:4 w l lw 5 title "particle 4", "./swarmOutput.00005.dat" using 3:4 w l lw 5 title "particle 5", "./swarmOutput.00006.dat" using 3:4 w l lw 5 title "particle 6", "./swarmOutput.00007.dat" using 3:4 w l lw 5 title "particle 7"
diff -r d2ffcc29d112 -r 864429d7016b tools/generate_pvd.cxx
--- a/tools/generate_pvd.cxx Thu Sep 29 12:11:45 2011 -0700
+++ b/tools/generate_pvd.cxx Thu Sep 29 12:47:17 2011 -0700
@@ -3,7 +3,7 @@
You will need Boost (www.boost.org) to compile this. Almost any
version should do. On Debian, you compile it with
- g++ generate_pvd.cxx -o generate_pvd -lboost_filesystem
+ g++ generate_pvd.cxx -o generate_pvd -lboost_filesystem -lboost_system
To generate a static binary, compile it with
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