Numerical simulations

The simulations herein were computed using a numerical scheme presented in several papers of mine:  about the general scheme,  about the surface diffusion flow,  about the Willmore flow in the radially symmetric case.

Model Static pages Dynamic pages
(play animations)
Averaged Mean Curvature Flow A limacon.  
Averaged Mean Curvature Flow A tetrahedron. A tetrahedron.
Averaged Mean Curvature Flow A long box. A long box.
Averaged Mean Curvature Flow A torus. A torus.
Averaged Mean Curvature Flow A dumbbell that stays regular. A dumbbell that stays regular.
Non-Averaged Mean Curvature Flow A dumbbell that becomes singular. A dumbbell that becomes singular.
Non-Averaged Mean Curvature Flow A spiral that shrinks to a point. A spiral that shrinks to a point.
Surface Diffusion Flow An erythrocyte. An erythrocyte.
Willmore Flow A torus. A torus.
Willmore Flow A dumbbell. A dumbbell.
Willmore Flow An erythrocyte. An erythrocyte.
Willmore Flow An immersed surface stays regular. An immersed surface stays regular.
Willmore Flow A long tube. A long tube.
Willmore Flow An immersed surface becomes singular. An immersed surface becomes singular.

The dynamic pages use JavaScript1.2, and work best with Firefox version 3 or higher, Netscape Communicator/Navigator version 4 or higher, or Microsoft Internet Explorer version 4 or higher, or Opera version 5 or higher. Playing of the animations does not work with Netscape Communicator/Navigator version 3.x, but at least the single-stepping works with those browsers.

[leftarrow] Back mayer@math.utah.edu
First posted: in Spring 1996
Last updated: Sun Jul 31 16:18:37 PDT 2016