ScalarBulkEnergyA

Overview

Sets up the RHS of the coupled Landau-Khalatnikov equation. Since we are working with ScalarKernels, this is effectively a single grid point, or homogeneous calculation. In the context of micromagnetics, this is the macrospin analog for ferroelectrics. This object concerns the bulk contribution from the antiphase oxygen octahedral tilts $var element = document.getElementById("moose-equation-2df7992e-ba31-4ff8-b769-ecb99d28b572");katex.render("\\mathbf{A}", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ (in the case of $var element = document.getElementById("moose-equation-c55a9030-26a7-4bd4-8920-dd608565c236");katex.render("\\mathrm{BiFeO}_3", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ ),

$var element = document.getElementById("moose-equation-f5822cb3-cafc-4d4f-bc46-6518feaaa81c");katex.render(" \\begin{aligned} \\frac{\\partial \\mathbf{A}}{\\partial t} = - \\Gamma_A \\frac{\\delta f_\\mathrm{A,bulk}}{\\delta \\mathbf{A}} \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$

Ignoring the LHS and working in index notation,

$var element = document.getElementById("moose-equation-c6ee740f-bca5-4134-bd75-85815cc6606d");katex.render(" \\begin{aligned} - \\Gamma_A \\frac{\\delta f_\\mathrm{A,bulk}}{\\delta A_\\eta} &= - \\Gamma_A \\frac{\\partial}{\\partial A_\\eta} \\left( \\beta_{ij} A_i A_j + \\beta_{ijkl} A_i A_j A_k A_l\\right) \\\\ &= - \\Gamma_A \\left( 2 \\beta_{i\\eta} A_i + 4 \\beta_{ijk\\eta} A_i A_j A_k\\right) \\\\ \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$

In Voight notation, many of these terms vanish due to symmetry of the parent phase.

Example Input File Syntax

Input Parameters

componentAn integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2.0 for z)
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2.0 for z)
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

Ar1the first coefficient
Default:1
C++ Type:double
Controllable:No
Description:the first coefficient
Br1the second coefficient
Default:1
C++ Type:double
Controllable:No
Description:the second coefficient
Cr1the third coefficient
Default:1
C++ Type:double
Controllable:No
Description:the third coefficient
G1the time constant
Default:1
C++ Type:double
Controllable:No
Description:the time constant
antiferrodis_A_xvariable antiferrodis_A_x coupled into this kernel
C++ Type:std::vector<VariableName>
Controllable:No
Description:variable antiferrodis_A_x coupled into this kernel
antiferrodis_A_yvariable antiferrodis_A_y coupled into this kernel
C++ Type:std::vector<VariableName>
Controllable:No
Description:variable antiferrodis_A_y coupled into this kernel
antiferrodis_A_zvariable antiferrodis_A_z coupled into this kernel
C++ Type:std::vector<VariableName>
Controllable:No
Description:variable antiferrodis_A_z coupled into this kernel

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(test/tests/landau_khalatnikov/LK_full_test.i)
(test/tests/landau_khalatnikov/LK_test.i)

(test/tests/landau_khalatnikov/LK_full_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]


[GlobalParams]
  polar_x = polar_x
  polar_y = polar_y
  polar_z = polar_z

  antiferrodis_A_x = antiferrodis_A_x
  antiferrodis_A_y = antiferrodis_A_y
  antiferrodis_A_z = antiferrodis_A_z

  e_xx = e_xx
  e_yy = e_yy
  e_zz = e_zz
  e_xy = e_xy
  e_yz = e_yz
  e_zx = e_zx

  Ap = -1.09028
  Bp = 6.68020e-1
  Cp = -4.67264e-1

  Ar = -5.33957e-3
  Br = 1.35373e-5
  Cr = -7.73973e-6

  Bpr = 6.99618e-3
  Cpr = -2.14508e-3
  Cprp = -1.40134e-2

  C11 = 114.409
  C12 = 45.5681
  C44 = 28.709

  q11 = -5.89457
  q12 = -0.971881
  q44 = -2.01751

  r11 = -7.35454e-3
  r12 = 7.23046e-4
  r44 = 7.21126e-3

  G = 1.0
[]


[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]


  # ODE variables
  [./polar_x]
    family = SCALAR
    order = FIRST
    initial_condition = 0.4
  [../]
  [./polar_y]
    family = SCALAR
    order = FIRST
    initial_condition = 0.4
  [../]
  [./polar_z]
    family = SCALAR
    order = FIRST
    initial_condition = 0.4
  [../]
  [./antiferrodis_A_x]
    family = SCALAR
    order = FIRST
    initial_condition = 7.0
  [../]
  [./antiferrodis_A_y]
    family = SCALAR
    order = FIRST
    initial_condition = 7.0
  [../]
  [./antiferrodis_A_z]
    family = SCALAR
    order = FIRST
    initial_condition = 7.0
  [../]

  [./e_xx]
    family = SCALAR
    order = FIRST
    initial_condition = 0.001
  [../]
  [./e_yy]
    family = SCALAR
    order = FIRST
    initial_condition = 0.001
  [../]
  [./e_zz]
    family = SCALAR
    order = FIRST
    initial_condition = 0.001
  [../]

  [./e_xy]
    family = SCALAR
    order = FIRST
    initial_condition = 0.0001
  [../]
  [./e_yz]
    family = SCALAR
    order = FIRST
    initial_condition = 0.0001
  [../]
  [./e_zx]
    family = SCALAR
    order = FIRST
    initial_condition = 0.0001
  [../]


[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td_px]
    type = ODETimeDerivative
    variable = polar_x
  [../]
  [./td_py]
    type = ODETimeDerivative
    variable = polar_y
  [../]
  [./td_pz]
    type = ODETimeDerivative
    variable = polar_z
  [../]

  [./td_Ax]
    type = ODETimeDerivative
    variable = antiferrodis_A_x
  [../]
  [./td_Ay]
    type = ODETimeDerivative
    variable = antiferrodis_A_y
  [../]
  [./td_Az]
    type = ODETimeDerivative
    variable = antiferrodis_A_z
  [../]

  [./td_exx]
    type = ODETimeDerivative
    variable = e_xx
  [../]
  [./td_eyy]
    type = ODETimeDerivative
    variable = e_yy
  [../]
  [./td_ezz]
    type = ODETimeDerivative
    variable = e_zz
  [../]

  [./td_exy]
    type = ODETimeDerivative
    variable = e_xy
  [../]
  [./td_eyz]
    type = ODETimeDerivative
    variable = e_yz
  [../]
  [./td_ezx]
    type = ODETimeDerivative
    variable = e_zx
  [../]


  [./bulk_px]
    type = ScalarBulkEnergyP
    variable = polar_x
    component = 0
  [../]
  [./bulk_py]
    type = ScalarBulkEnergyP
    variable = polar_y
    component = 1
  [../]
  [./bulk_pz]
    type = ScalarBulkEnergyP
    variable = polar_z
    component = 2
  [../]

  [./bulk_Ax]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_x
    component = 0
  [../]
  [./bulk_Ay]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_y
    component = 1
  [../]
  [./bulk_Az]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_z
    component = 2
  [../]


  [./roto_Px]
    type = ScalarRotopolarEnergy
    variable = polar_x
    component = 0
  [../]
  [./roto_Py]
    type = ScalarRotopolarEnergy
    variable = polar_y
    component = 1
  [../]
  [./roto_Pz]
    type = ScalarRotopolarEnergy
    variable = polar_z
    component = 2
  [../]
  [./roto_Ax]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_x
    component = 3
  [../]
  [./roto_Ay]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_y
    component = 4
  [../]
  [./roto_Az]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_z
    component = 5
  [../]

  [./estric_Px]
    type = ScalarElectrostrictiveEnergy
    variable = polar_x
    component = 0
  [../]
  [./estric_Py]
    type = ScalarElectrostrictiveEnergy
    variable = polar_y
    component = 1
  [../]
  [./estric_Pz]
    type = ScalarElectrostrictiveEnergy
    variable = polar_z
    component = 2
  [../]

  [./estric_exx]
    type = ScalarElectrostrictiveEnergy
    variable = e_xx
    component = 3
  [../]
  [./estric_eyy]
    type = ScalarElectrostrictiveEnergy
    variable = e_yy
    component = 4
  [../]
  [./estric_ezz]
    type = ScalarElectrostrictiveEnergy
    variable = e_zz
    component = 5
  [../]
  [./estric_exy]
    type = ScalarElectrostrictiveEnergy
    variable = e_xy
    component = 6
  [../]
  [./estric_eyz]
    type = ScalarElectrostrictiveEnergy
    variable = e_yz
    component = 7
  [../]
  [./estric_ezx]
    type = ScalarElectrostrictiveEnergy
    variable = e_zx
    component = 8
  [../]


  [./rstric_Ax]
    type = ScalarRotostrictiveEnergy
    variable = antiferrodis_A_x
    component = 0
  [../]
  [./rstric_Ay]
    type = ScalarRotostrictiveEnergy
    variable = antiferrodis_A_y
    component = 1
  [../]
  [./rstric_Az]
    type = ScalarRotostrictiveEnergy
    variable = antiferrodis_A_z
    component = 2
  [../]

  [./rstric_exx]
    type = ScalarRotostrictiveEnergy
    variable = e_xx
    component = 3
  [../]
  [./rstric_eyy]
    type = ScalarRotostrictiveEnergy
    variable = e_yy
    component = 4
  [../]
  [./rstric_ezz]
    type = ScalarRotostrictiveEnergy
    variable = e_zz
    component = 5
  [../]
  [./rstric_exy]
    type = ScalarRotostrictiveEnergy
    variable = e_xy
    component = 6
  [../]
  [./rstric_eyz]
    type = ScalarRotostrictiveEnergy
    variable = e_yz
    component = 7
  [../]
  [./rstric_ezx]
    type = ScalarRotostrictiveEnergy
    variable = e_zx
    component = 8
  [../]

  [./elast_exx]
    type = ScalarElasticEnergy
    variable = e_xx
    component = 0
  [../]
  [./elast_eyy]
    type = ScalarElasticEnergy
    variable = e_yy
    component = 1
  [../]
  [./elast_ezz]
    type = ScalarElasticEnergy
    variable = e_zz
    component = 2
  [../]
  [./elast_exy]
    type = ScalarElasticEnergy
    variable = e_xy
    component = 3
  [../]
  [./elast_eyz]
    type = ScalarElasticEnergy
    variable = e_yz
    component = 4
  [../]
  [./elast_exz]
    type = ScalarElasticEnergy
    variable = e_zx
    component = 5
  [../]

[]


[BCs]
  [./right]
    type = DirichletBC
    variable = diffused
    boundary = 1
    value = 0.0
  [../]

  [./left]
    type = DirichletBC
    variable = diffused
    boundary = 0
    value = 1.0
  [../]
[]

[Postprocessors]
  [./Px]
    type = ScalarVariable
    variable = polar_x
    execute_on = timestep_end
  [../]
  [./Py]
    type = ScalarVariable
    variable = polar_y
    execute_on = timestep_end
  [../]
  [./Pz]
    type = ScalarVariable
    variable = polar_z
    execute_on = timestep_end
  [../]

  [./Ax]
    type = ScalarVariable
    variable = antiferrodis_A_x
    execute_on = timestep_end
  [../]
  [./Ay]
    type = ScalarVariable
    variable = antiferrodis_A_y
    execute_on = timestep_end
  [../]
  [./Az]
    type = ScalarVariable
    variable = antiferrodis_A_z
    execute_on = timestep_end
  [../]


  [./exx]
    type = ScalarVariable
    variable = e_xx
    execute_on = timestep_end
  [../]
  [./eyy]
    type = ScalarVariable
    variable = e_yy
    execute_on = timestep_end
  [../]
  [./ezz]
    type = ScalarVariable
    variable = e_zz
    execute_on = timestep_end
  [../]

  [./exy]
    type = ScalarVariable
    variable = e_xy
    execute_on = timestep_end
  [../]
  [./eyz]
    type = ScalarVariable
    variable = e_yz
    execute_on = timestep_end
  [../]
  [./ezx]
    type = ScalarVariable
    variable = e_zx
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_gmres_restart -snes_atol  -snes_rtol -ksp_rtol -pc_type'
    petsc_options_value = '    121            1e-8          1e-8       1e-6     bjacobi'
  [../]
[]


[Executioner]
  type = Transient
  start_time = 0
  dt = 0.1

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
  num_steps = 50
[]

[Outputs]
  print_linear_residuals = false
  [./out]
    type = Exodus
    file_base = out_full_LK
  [../]
[]

(test/tests/landau_khalatnikov/LK_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]


[GlobalParams]
  polar_x = polar_x
  polar_y = polar_y
  polar_z = polar_z

  antiferrodis_A_x = antiferrodis_A_x
  antiferrodis_A_y = antiferrodis_A_y
  antiferrodis_A_z = antiferrodis_A_z

  Ap = -1.09028
  Bp = 6.68020e-1
  Cp = -4.67264e-1

  Ar = -5.33957e-3
  Br = 1.35373e-5
  Cr = -7.73973e-6

  Bpr = 6.99618e-3
  Cpr = -2.14508e-3
  Cprp = -1.40134e-2

[]


[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]


  # ODE variables
  [./polar_x]
    family = SCALAR
    order = FIRST
    initial_condition = 0.01
  [../]
  [./polar_y]
    family = SCALAR
    order = FIRST
    initial_condition = 0.01
  [../]
  [./polar_z]
    family = SCALAR
    order = FIRST
    initial_condition = 0.01
  [../]
  [./antiferrodis_A_x]
    family = SCALAR
    order = FIRST
    initial_condition = 0.1
  [../]
  [./antiferrodis_A_y]
    family = SCALAR
    order = FIRST
    initial_condition = 0.1
  [../]
  [./antiferrodis_A_z]
    family = SCALAR
    order = FIRST
    initial_condition = 0.1
  [../]



[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td_px]
    type = ODETimeDerivative
    variable = polar_x
  [../]
  [./td_py]
    type = ODETimeDerivative
    variable = polar_y
  [../]
  [./td_pz]
    type = ODETimeDerivative
    variable = polar_z
  [../]

  [./td_Ax]
    type = ODETimeDerivative
    variable = antiferrodis_A_x
  [../]
  [./td_Ay]
    type = ODETimeDerivative
    variable = antiferrodis_A_y
  [../]
  [./td_Az]
    type = ODETimeDerivative
    variable = antiferrodis_A_z
  [../]


  [./bulk_px]
    type = ScalarBulkEnergyP
    variable = polar_x
    component = 0
  [../]
  [./bulk_py]
    type = ScalarBulkEnergyP
    variable = polar_y
    component = 1
  [../]
  [./bulk_pz]
    type = ScalarBulkEnergyP
    variable = polar_z
    component = 2
  [../]

  [./bulk_Ax]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_x
    component = 0
  [../]
  [./bulk_Ay]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_y
    component = 1
  [../]
  [./bulk_Az]
    type = ScalarBulkEnergyA
    variable = antiferrodis_A_z
    component = 2
  [../]


  [./roto_Px]
    type = ScalarRotopolarEnergy
    variable = polar_x
    component = 0
  [../]
  [./roto_Py]
    type = ScalarRotopolarEnergy
    variable = polar_y
    component = 1
  [../]
  [./roto_Pz]
    type = ScalarRotopolarEnergy
    variable = polar_z
    component = 2
  [../]
  [./roto_Ax]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_x
    component = 3
  [../]
  [./roto_Ay]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_y
    component = 4
  [../]
  [./roto_Az]
    type = ScalarRotopolarEnergy
    variable = antiferrodis_A_z
    component = 5
  [../]

[]


[BCs]
  [./right]
    type = DirichletBC
    variable = diffused
    boundary = 1
    value = 0.0
  [../]

  [./left]
    type = DirichletBC
    variable = diffused
    boundary = 0
    value = 1.0
  [../]
[]

[Postprocessors]
  [./Px]
    type = ScalarVariable
    variable = polar_x
    execute_on = timestep_end
  [../]
  [./Py]
    type = ScalarVariable
    variable = polar_y
    execute_on = timestep_end
  [../]
  [./Pz]
    type = ScalarVariable
    variable = polar_z
    execute_on = timestep_end
  [../]

  [./Ax]
    type = ScalarVariable
    variable = antiferrodis_A_x
    execute_on = timestep_end
  [../]
  [./Ay]
    type = ScalarVariable
    variable = antiferrodis_A_y
    execute_on = timestep_end
  [../]
  [./Az]
    type = ScalarVariable
    variable = antiferrodis_A_z
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_gmres_restart -snes_atol  -snes_rtol -ksp_rtol -pc_type'
    petsc_options_value = '    121            1e-8          1e-8       1e-6     bjacobi'
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1.0

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
  num_steps = 50
[]

[Outputs]
  print_linear_residuals = true
  [./out]
    type = Exodus
    file_base = out_LK
  [../]
[]