FourierNoise

Generate noise from a fourier series

This object generates a Fourier series with random coefficients $var element = document.getElementById("moose-equation-e86d0aa2-8a97-42d0-9696-69eb052e71be");katex.render("s_{\\vec k}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-b76c9fee-92a4-452f-813a-52db12d95409");katex.render("c_{\\vec k}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and an amplitude factor $var element = document.getElementById("moose-equation-2fdb9367-60f9-4793-a2ca-0b756c6b3a24");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (scale). The series can be cut off at a given length scale $var element = document.getElementById("moose-equation-c540829c-26ad-4502-a63a-0c8ad2433978");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (lambda) resulting in a low pass filtered white noise. For efficiency lambda should be chosen larger than the smallest mesh element size.

$var element = document.getElementById("moose-equation-97fc046e-4336-4886-adf1-82dd64f504d7");katex.render("\\sigma \\sum_{\\vc k, |\\vec k| < \\frac 1\\lambda} s_{\\vec k}\\sin \\vec r\\cdot \\vec k + c_{\\vec k}\\cos \\vec r\\cdot \\vec k", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Alternatively the series can be constructed with an entirely random set of series terms by specifying the number of terms num_terms resulting in a non-periodic noise.

Input Parameters

lambdaWavelength cut off (set to about twice the interfacial width)
C++ Type:double
Options:
Description:Wavelength cut off (set to about twice the interfacial width)

Required Parameters

num_termsNumber of random fourier series terms (this will result in non-periodic noise). Omit this parameter to obtain a periodic noise distribution.
C++ Type:unsigned int
Options:
Description:Number of random fourier series terms (this will result in non-periodic noise). Omit this parameter to obtain a periodic noise distribution.
seed12455Random number generator seed
Default:12455
C++ Type:unsigned int
Options:
Description:Random number generator seed

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

modules/phase_field/test/tests/functions/fourier_noise.i
modules/phase_field/examples/fourier_noise.i

modules/phase_field/test/tests/functions/fourier_noise.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./c]
  [../]
[]

[Functions]
  [./fn]
    type = FourierNoise
    lambda = 0.2
  [../]
[]

[ICs]
  [./c]
    type = FunctionIC
    variable = c
    function = fn
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

modules/phase_field/examples/fourier_noise.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 100
[]

[Variables]
  [./c]
  [../]
[]

[Functions]
  [./fn]
    type = FourierNoise
    lambda = 0.1
  [../]
[]

[ICs]
  [./c]
    type = FunctionIC
    variable = c
    function = fn
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

References

Input Parameters
Input Files
References

Application Usage

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