- Vorführexperimente, Videos
short phenomenom demonstation
another demonstation video
- Wissenschaftliche Artikel
Instabilities and Solitons in Minimal Strips
We show that highly twisted minimal strips can undergo a nonsingular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is nonorientable, this transition is topologically frustrated, and the resulting surface contains a helicoidal defect. Demonstrations with soap films confirm these results and show how the position of the defect can be controlled through boundary deformation.
Problem solving with soap films: Part II
It was shown in the previous article that it was possible to solve some two dimensional minimization problems by building an analogue system consisting of plates and pins and dipping the system into soap solution. The soap film produced between the plates when the system is withdrawn from the soap solution has the property that its length is minimized once the soap film has reached thermodynamic equilibrium. This article extends the method in order to solve problems requiring the determination of the minimum surface area bounded by lines in three dimensions. The specific problems examined have been chosen that the boundaries have a high degree of symmetry.
Shapes of embedded minimal surfaces
It has been known that the right mathematical model for a soap film is a minimal surface: the soap film is in a state of minimum energy when it covers the least possible amount of area. There are several other fields where minimal surfaces are actively used in understanding the shapes of physical phenomena. The authors discuss here the answer to the following questions: What are the possible shapes of embedded minimal surfaces in R3, and why?
The Helicoid versus the Catenoid: Geometrically Induced Bifurcations
The minimal surfaces bounded by a frame formed of a double helix and two horizontal rods are studied. The vibration equation shows that the helicoid is the stable surface when its winding number is small. The catenoid is locally isometric to the helicoid so that their vibration spectra are strongly related. While the catenoid is known to undergo a discontinuous transition to two disks, the helicoid is shown to become unstable through a continuous transition to a ribbon-shaped surface obtained experimentally, numerically, and analytically in the limit of infinite height. The normal forms of the bifurcations confirm the analysis.