[WIP] Update anisotropic viscosity cookbook with new parameters

cookbooks/CPO_induced_anisotropic_viscosity/doc/CPO_induced_anisotropic_viscosity.md

@@ -16,9 +16,9 @@ This cookbook explains how to use the CPO-induced anisotropic viscosity material
 
 ## Introduction
 
-Individual crystals of the mineral olivine reorganize their orientations into crystal-preferred orientations (CPO) under deformation. The viscous properties of olivine crystals are direction-dependent (anisotropic), which suggests that the effective viscosity for olivine rocks/aggregates is different when deformations occur in different directions relative to the CPO. This cookbook model computes an anisotropic viscosity based on the CPO evolution predicted by D-Rex ({cite}`fraters_billen_2021_cpo`; {cite}`kaminski2004`) and includes this information in the subsequent modeling process.
+Individual crystals of the mineral olivine reorganize their orientations into crystal-preferred orientations (CPO) under deformation. The viscous properties of olivine crystals are direction-dependent (anisotropic), which suggests that the effective viscosity for olivine rocks/aggregates is different when deformations occur in different directions relative to the CPO. This cookbook model computes an anisotropic viscosity based on the CPO evolution predicted by D-Rex ({cite}`fraters_billen_2021_cpo`; {cite}`kaminski2004`) and includes this information in the subsequent modeling process based on the formulation of Király at al., (in rev.).
 
-Our constitutive equation for the relationship between the strain rate and stress using the anisotropic viscosity tensor is adapted from {cite:t}`signorelli:etal:2021`:
+The constitutive equation for the relationship between the strain rate and stress using the anisotropic viscosity tensor is adapted from {cite:t}`signorelli:etal:2021`:
 
 ```{math}
 :label: eqn:anisotropic_general_stress
@@ -36,7 +36,7 @@ $\gamma_0=1.1\times 10^{5}$ is the isotropic fluidity, $Q=530$ $kJ/mol$ is the a
 
 ```{math}
 :label: eqn:equivalent_yield_stress
-J(\sigma_{ij})=(F(\sigma_{11} - \sigma_{22})^2+G(\sigma_{22} - \sigma_{33})^2+H(\sigma_{33} - \sigma_{11})^2+2L\sigma_{23}^2+2M\sigma_{13}^2+2N\sigma_{12}^2)^{1/2}
+J(\sigma_{ij})=(F(\sigma_{22} - \sigma_{33})^2+G(\sigma_{33} - \sigma_{11})^2+H(\sigma_{11} - \sigma_{22})^2+2L\sigma_{23}^2+2M\sigma_{13}^2+2N\sigma_{12}^2)^{1/2}
 ```
 
 and $A_{ij}$ is the anisotropic tensor of fluidity in Kelvin notation:
@@ -45,24 +45,24 @@ and $A_{ij}$ is the anisotropic tensor of fluidity in Kelvin notation:
 :label: eqn:anisotropic_fluidity
 A_{ij}=\frac{2}{3} \left[
 \begin{matrix}
-F+H & -F & -H & 0 & 0 & 0 \\
--F & G+F & -G & 0 & 0 & 0 \\
--H & -G & H+G & 0 & 0 & 0 \\
+G+H & -H & -G & 0 & 0 & 0 \\
+-H & H+F & -F & 0 & 0 & 0 \\
+-G & -F & F+G & 0 & 0 & 0 \\
 0 & 0 & 0 & L & 0 & 0 \\
 0 & 0 & 0 & 0 & M & 0 \\
 0 & 0 & 0 & 0 & 0 & N
 \end{matrix} \right]
 ```
 
-$J(\sigma_{ij})$ and $A_{ij}$ are computed using Hill coefficients $H, J, K, L, M,$ and $N$ {cite}`hill:1948`, which describe the anisotropic viscous properties of an olivine aggregate and depend on its CPO. We determine the mean CPO orientation from the eigenvectors associated with the largest eigenvalues of the second-order orientation tensor (or covariance matrix) for all three symmetry axes. The corresponding eigenvalues quantify the dispersion of orientations around these mean orientation {cite}`bingham:1974`. The relationship between the 9 eigenvalues (3 for each axis) and Hill coefficients is derived using regression analysis on a texture database constructed with olivine textures from laboratory experiments, shear box models, and subduction models (Kiraly et al., in rev.). The 9 coefficients and 1 constant for each of the Hill coefficients are given as input in the parameter file. The default values and the equation to compute the Hill coefficients from the eigenvalues (e.g. $a_1, a_2, a_3$ are the eigenvalues of the orientation tensor for a-axis, where $a_1$ is the largest eigen value) are shown below:
+$J(\sigma_{ij})$ and $A_{ij}$ are computed using Hill coefficients $H, J, K, L, M,$ and $N$ {cite}`hill:1948`, which describe the anisotropic viscous properties of an olivine aggregate and depend on its CPO. We determine the mean CPO orientation from the eigenvectors associated with the largest eigenvalues of the second-order orientation tensor (or covariance matrix) for all three symmetry axes. The corresponding eigenvalues quantify the dispersion of orientations around these mean orientation {cite}`bingham:1974`. The relationship between the 9 eigenvalues (3 for each axis) and Hill coefficients is derived using regression analysis on a texture database constructed with olivine textures from laboratory experiments, shear box models, and subduction models (Kiraly et al., in rev., the data used for this paper is published through Zenodo {cite}`kiraly:etal:2026`). The 9 coefficients and 1 constant for each of the Hill coefficients are given as input in the parameter file. The default values and the equation to compute the Hill coefficients from the eigenvalues (e.g. $a_1, a_2, a_3$ are the eigenvalues of the orientation tensor for a-axis, where $a_1$ is the largest eigen value) are shown below:
 ```{math}
 :label: eqn:hill_coefficients
-F = 1.039 a_1^2 - 0.767 a_2 - \frac{0.003}{a_3} + 0.197 b_1^2 + 0.413 b_2 + \frac{0.015}{b_3} - 0.936 c_1^2 - 2.393 c_2 + \frac{0.052}{c_3} + 1.08 \\
-G = -2.836 a_1^2 - 1.632 a_2 - \frac{0.001}{a_3} + 0.267 b_1^2 - 0.993 b_2 + \frac{0.003}{b_3} +1.969 c_1^2 + 2.314 c_2 - \frac{0.019}{c_3} + 0.69 \\
-H = 1.669 a_1^2 + 0.58 a_2 + \frac{0.003}{a_3} + 0.702 b_1^2 + 0.251 b_2 + \frac{0.000}{b_3} - 2.003 c_1^2 - 2.570 c_2 + \frac{0.071}{c_3} + 0.75 \\
-L = -0.325 a_1^2 + 0.728 a_2 + \frac{0.000}{a_3} - 0.665 b_1^2 + 0.515 b_2 + \frac{0.003}{b_3} - 1.027 c_1^2 - 1.263 c_2 + \frac{0.009}{c_3} + 1.60 \\
-M = 1.643 a_1^2 - 0.878 a_2 + \frac{0.005}{a_3} + 2.489 b_1^2 + 0.816 b_2 - \frac{0.011}{b_3} - 2.494 c_1^2 - 0.511 c_2 + \frac{0.009}{c_3} + 0.89 \\
-N = 0.812 a_1^2 - 0.157 a_2 + \frac{0.002}{a_3} - 1.649 b_1^2 + 0.194 b_2 - \frac{0.01}{b_3} + 1.68 c_1^2 - 0.104 c_2 + \frac{0.02}{c_3} + 1.21
+F = 0.592 a_1^2 - 0.832 a_1 - 0.001 a_2 - \frac{0.000}{a_3} + 0.380 b_1^2 - 0.533 b_1 + 0.468 b_2 - \frac{0.001}{b_3} - 1.249 c_1^2 + 1.075 c_1 - 0.168 c_2 + \frac{0.003}{c_3} + 0.52 \\
+G = -1.695 a_1^2 + 1.336 a_1 - 0.184 a_2 + \frac{0.000}{a_3} + 0.750 b_1^2 + 0.691 b_1 + 0.377 b_2 - \frac{0.002}{b_3} - 0.670 c_1^2 - 0.552 c_1 - 0.428 c_2 + \frac{0.003}{c_3} + 0.26 \\
+H = -1.140 a_1^2 + 1.353 a_1 + 0.751 a_2 - \frac{0.002}{a_3} - 0.256 b_1^2 - 1.006 b_1 - 0.116 b_2 + \frac{0.003}{b_3} + 0.648 c_1^2 - 0.031 c_1 - 0.080 c_2 + \frac{0.006}{c_3} + 0.75 \\
+L = -3.511 a_1^2 + 2.686 a_1 + 0.360 a_2 - \frac{0.001}{a_3} + 3.948 b_1^2 - 3.816 b_1 - 0.779 b_2 + \frac{0.004}{b_3} + 4.122 c_1^2 - 2.483 c_1 - 1.320 c_2 + \frac{0.002}{c_3} + 2.00 \\
+M = 4.537 a_1^2 - 3.228 a_1 + 0.276 a_2 + \frac{0.007}{a_3} - 7.447 b_1^2 + 5.764 b_1 - 1.403 b_2 - \frac{0.032}{b_3} + 2.968 c_1^2 - 3.435 c_1 - 2.266 c_2 + \frac{0.122}{c_3} + 2.44 \\
+N = 7.873 a_1^2 - 7.934 a_1 - 2.588 a_2 + \frac{0.030}{a_3} + 7.606 b_1^2 - 5.469 b_1 - 0.348 b_2 + \frac{0.064}{b_3} - 1.788 c_1^2 + 2.255 c_1 + 3.023 c_2 - \frac{0.103}{c_3} + 3.70
 ```
 
 In this material model plugin, strain rate, density, temperature, and other parameters are taken as input to compute the anisotropic viscosity, which is passed into the Stokes system to compute the stress. As a result, we adapt {math:numref}`eqn:anisotropic_general_stress` to be:

cookbooks/CPO_induced_anisotropic_viscosity/plugin/CMakeLists.txt

@@ -16,24 +16,25 @@
 # along with ASPECT; see the file LICENSE.  If not see
 # <http://www.gnu.org/licenses/>.
 
-CMAKE_MINIMUM_REQUIRED(VERSION 3.13.4)
+cmake_minimum_required(VERSION 3.13.4)
 
-FIND_PACKAGE(Aspect 2.4.0 QUIET HINTS ${Aspect_DIR} ../ ../../ $ENV{ASPECT_DIR})
+find_package(Aspect 2.4.0 QUIET HINTS ${Aspect_DIR} ../ ../../ $ENV{ASPECT_DIR})
 
-IF (NOT Aspect_FOUND)
-  MESSAGE(FATAL_ERROR "\n"
-  "Could not find a valid ASPECT build/installation directory. "
-  "Please specify the directory where you are building ASPECT by passing\n"
-  "   -D Aspect_DIR=<path to ASPECT>\n"
-  "to cmake or by setting the environment variable ASPECT_DIR in your shell "
-  "before calling cmake. See the section 'How to write a plugin' in the "
-        "manual for more information.")
-ENDIF ()
+if (NOT Aspect_FOUND)
+  message(FATAL_ERROR "\n"
+    "Could not find a valid ASPECT build/installation directory. "
+    "Please specify the directory where you are building ASPECT by passing\n"
+    "   -D Aspect_DIR=<path to ASPECT>\n"
+    "to cmake or by setting the environment variable ASPECT_DIR in your shell "
+    "before calling cmake. See the section 'How to write a plugin' in the "
+    "manual for more information.")
+endif ()
 
 DEAL_II_INITIALIZE_CACHED_VARIABLES()
 
-SET(TARGET "CPO_induced_anisotropic_viscosity")
-PROJECT(${TARGET})
 
-ADD_LIBRARY(${TARGET} SHARED  cpo_induced_anisotropic_viscosity.h cpo_induced_anisotropic_viscosity.cc anisotropic_stress.cc anisotropic_stress.h)
+set(TARGET "CPO_induced_anisotropic_viscosity")
+project(${TARGET})
+
+add_library(${TARGET} SHARED  cpo_induced_anisotropic_viscosity.h cpo_induced_anisotropic_viscosity.cc anisotropic_stress.cc anisotropic_stress.h)
 ASPECT_SETUP_PLUGIN(${TARGET})