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Geology project list

Computational Structural Geology

Deformation in 2D and 3D

An opportunity for students to create their own deformations, visualising affine and non-affine, isochoric and non-isochoric transformations in 2D and 3D with various sliders, coupled with the full 3D result, which would be the geological structure observed in the field.

Goals (deliverables)

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  • Interactive software for exploring
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  • undeformed and deformed states for any user-chosen affine and/or non-affine transformation
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  • the various deformation and strain tensors associated with any user-chosen deformation gradient F
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  • deformation plus strain ellipses for any user-chosen deformation
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  • all the above and include volume changes
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  • eigenvectors in 2D and 3D

    • Resources

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  • Geometry: The Concept of Deformation. Chapter 2, Hobbs, B.E. and Ord, A., 2015. Structural Geology: The Mechanics of Deforming Metamorphic Rocks. Elsevier Inc., Netherlands. 665 pp.
    ​
    • Chapter 7 Nonlinear Dynamics

    7.4 Linear Stability Analysis

    Table 7.1

    Stable node

    In[]:=
    imagescale={Automatic,500,128};​​LineIntegralConvolutionPlot[{{-x,-0.5y},imagescale},{x,-10,10},{y,-10,10},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]

    Stable focus

    In[]:=
    imagescale={Automatic,500,128};​​LineIntegralConvolutionPlot[{{-x-y,x-y},imagescale},{x,-10,10},{y,-10,10},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]
    Out[]=

    Unstable focus

    In[]:=
    imagescale={Automatic,500,128};​​LineIntegralConvolutionPlot[{{x-y,x+y},imagescale},{x,-10,10},{y,-10,10},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]
    Out[]=

    Unstable node

    In[]:=
    imagescale={Automatic,500,128};​​LineIntegralConvolutionPlot[{{x,0.5y},imagescale},{x,-10,10},{y,-10,10},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]
    Out[]=

    Saddle point

    In[]:=
    imagescale={Automatic,500,128};​​LineIntegralConvolutionPlot[{{x,-y},imagescale},{x,-10,10},{y,-10,10},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]
    Out[]=

    Hopf bifurcation

    In[]:=
    mum=0.1;
    In[]:=
    imagescale={Automatic,500,128};
    In[]:=
    licplot=LineIntegralConvolutionPlot[{{y+mumx-xy^2,mumy-x-y^3},imagescale},{x,-1,1},{y,-1,1},VectorPoints10,VectorStyleRed,ColorFunction"BeachColors",LightingAngle0,LineIntegralConvolutionScale10,ImageSize{250,250}]
    Out[]=

    7.6 Bifurcations
    

    References

    Lynch 2007