Eigenmodes in a Knot

Specify a knot.

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\[CapitalOmega] = KnotData["Stevedore", "MeshRegion"]

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Compute 10 eigenfunctions of the Laplacian over the knot.

In[2]:=

{vals, funs} = NDEigensystem[-Laplacian[u[x, y, z], {x, y, z}], u, {x, y, z} \[Element] \[CapitalOmega], 10];

Visualize the 10^th eigenfunction as a set of heated nodes.

In[3]:=

nm = 10; c = Take[funs[[nm]]["ElementMesh"]["Coordinates"], {1, -1, 10}]; Graphics3D[ Point[c, VertexColors -> ColorData["Heat"] /@ Rescale[funs[[nm]] @@@ c]], Boxed -> False]

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