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

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

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

After 1,000,000 time steps.
after 1000,000 steps
After 2,500,000 time steps.
after 2500,000 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