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Wave Equation Sand Castle Mold

sandcast2_display_large.jpg Wave Equation Sand Castle Mold
sandcast1_display_large.jpg Wave Equation Sand Castle Mold
sandcast3_display_large.jpg Wave Equation Sand Castle Mold
image1-4_display_large.JPG Wave Equation Sand Castle Mold
sand1.stl Wave Equation Sand Castle Mold
sand3.stl Wave Equation Sand Castle Mold
sand2.stl Wave Equation Sand Castle Mold
sand4.stl Wave Equation Sand Castle Mold
sand5.stl Wave Equation Sand Castle Mold
sand3b.stl Wave Equation Sand Castle Mold
sand2b.stl Wave Equation Sand Castle Mold
sandcast2_display_large.jpg Wave Equation Sand Castle Mold
sandcast1_display_large.jpg Wave Equation Sand Castle Mold
sandcast3_display_large.jpg Wave Equation Sand Castle Mold
image1-4_display_large.JPG Wave Equation Sand Castle Mold
sand1.stl Wave Equation Sand Castle Mold
sand3.stl Wave Equation Sand Castle Mold
sand2.stl Wave Equation Sand Castle Mold
sand4.stl Wave Equation Sand Castle Mold
sand5.stl Wave Equation Sand Castle Mold
sand3b.stl Wave Equation Sand Castle Mold
sand2b.stl Wave Equation Sand Castle Mold
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7 files (STL) Close
  • sand1.stl
  • sand2.stl
  • sand2b.stl
  • sand3.stl
  • sand3b.stl
  • sand4.stl
  • sand5.stl

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Published to Thingiverse on:
Design number 41306
Balkhagal4D

Balkhagal4D

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3D model description

What goes better with the beach than waves? And what goes better with waves than the WAVE EQUATION??

We approximated the classic sand castle mold with a circle of 2-D Gaussian functions around a bump function. Setting this as our initial condition and imposing a Dirichlet boundary condition, we then simulated the wave equation PDE in Mathematica and sampled at a couple time points to get the different mold shapes.

How can we interpret these shapes? Imagine stretching a drumhead into the shape of a castle (like in the first mold) and then letting it go. The shapes of these molds are what vibrations in the membrane would look like as time evolves. You can even start to see them rebound into the drum in the last mold.

Check out a sweet GIF of the sandcastle's demise here and learn more about the math behind it here!

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