Instabilities and Solitons in Minimal Strips

TL;DR

This paper investigates the behavior of highly twisted minimal strips, revealing non-singular transitions and the formation of topologically protected defect solitons, supported by theoretical analysis and soap film experiments.

Contribution

It introduces a novel topological defect in minimal surfaces, modeled as a kink soliton in a scalar field theory, and demonstrates experimental control over defect positioning.

Findings

Highly twisted minimal strips undergo non-singular transitions.

Topologically frustrated defects form as kink solitons.

Experimental soap films confirm theoretical predictions.

Abstract

We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the M\"obius strip and the catenoid. If the strip is non-orientable this transition is topologically frustrated, and the resulting surface contains a helical defect. Through a controlled analytic approximation the system can be mapped onto a scalar $\phi^4$ theory on a non-orientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, thus establishing their existence in minimal surfaces. Experimental studies of soap films confirm these results and demonstrate how the position of the defect can be controlled through boundary deformation.