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

A long straight tube becomes temporarily non-convex

Scale: Radius of end cap = 1, straight part in middle = 4.
Time step = 10-5.
Spatial resolution of generating curve = 0.01-0.05.
System: Toshiba 4015CDT Laptop with an Intel Pentium II 266 MHz.
Computation time: About 12 minutes.


After 0 time steps.
after 0 steps
After 5,000 time steps.
after 5,000 steps

After 10,000 time steps.
after 10,000 steps
After 25,000 time steps.
after 25,000 steps

After 50,000 time steps.
after 50,000 steps
After 100,000 time steps.
after 100,000 steps

After 200,000 time steps.
after 200,000 steps
After 1,000,000 time steps.
after 1,000,000 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