but this: 
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Shaped Layer Interfaces
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| · | Figures must maintain an extruded shape, with sidewalls and layer interfaces (the sidewalls cannot grow or shrink)
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| · | Layer interface surfaces must be continuous across region boundaries. If a surface has a vertical jump, it must be divided into layers, with a region interface at the jump boundary and a layer spanning the jump. (Not this: but this: )
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| · | Layer interface surfaces may merge, but may not invert. Use a MAX or MIN function in the surface definition to block inversion.
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| Using these rules, we can convert the canister of our example into a sphere by placing spherical caps on the cylinder.
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| The equation of a spherical end cap is
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| Z = Zcenter + sqrt( R^2 – x^2 – y^2)
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| Or,
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| Z = Ztop – R + sqrt(R^2 – x^2 – y^2)
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| · | To avoid grazing contact of this new sphere with the top and bottom of our former box, we will extend the extrusion from –1 to 1.
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| · | To avoid arithmetic errors, we will prevent negative arguments of the sqrt.
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| TITLE 'Heat flow around an Insulating Sphere'
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| COORDINATES
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| Cartesian3
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| VARIABLES
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| Phi { the temperature }
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| DEFINITIONS
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| K = 1 { default conductivity }
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| R = 0.5 { sphere radius }
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| { shape of hemispherical cap: }
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| Zsphere = sqrt(max(R^2-x^2-y^2,0))
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| EQUATIONS
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| Div(-k*grad(phi)) = 0
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| EXTRUSION
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| SURFACE 'Bottom' z=-1
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| LAYER 'underneath'
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| SURFACE 'Sphere Bottom' z = -max(Zsphere,0)
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| LAYER 'Can'
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| SURFACE 'Sphere Top' z = max(Zsphere,0)
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| LAYER 'above'
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| SURFACE 'Top' z=1
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| BOUNDARIES
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| REGION 1 'box'
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| START(-1,-1)
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| VALUE(Phi)=0 LINE TO (1,-1)
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| NATURAL(Phi)=0 LINE TO (1,1)
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| VALUE(Phi)=1 LINE TO (-1,1)
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| NATURAL(Phi)=0 LINE TO CLOSE
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| LIMITED REGION 2 'blob' { the embedded blob }
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| LAYER 2 K = 0.001
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| START 'ring' (RSphere,0) ARC(CENTER=0,0) ANGLE=360
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| TO CLOSE
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| PLOTS
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| GRID(y,z) on x=0
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| CONTOUR(Phi) on x=0
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| VECTOR(-k*grad(Phi)) on x=0
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| ELEVATION(Phi) FROM (0,-1,0) to (0,1,0)
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| END
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