Willmore flow for the radially symmetric case in in three space dimensions

A dumbbell with a very thin neck stays regular

Scale: Radius at neck = 0.01, radius of ends = 1, length of figure = 5.21.
Shape of neck: Modeled on y=x2.
Time step = 10-6.
Spatial resolution of generating curve = 0.01-0.05.
System: Toshiba 4015CDT Laptop with an Intel Pentium II 266 MHz.
Computation time: About 42 minutes.


After 0 time steps.
After 1,000 time steps.

After 10,000 time steps.
After 50,000 time steps.

After 200,000 time steps.
After 500,000 time steps.

After 1,000,000 time steps.
After 2,500,000 time steps.
[leftarrow]Back mayer@math.utah.edu
Posted on: Tue Apr 10 12:05:38 PDT 2001
Last updated: Thu Apr 12 09:23:50 PDT 2001