Instabilities and Solitons in Minimal Strips

Abstract

We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the Möbius 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 ${\varphi }^4$ 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.

7 pages, 4 figures. Videos can be found at http://www2.warwick.ac.uk/fac/sci/physics/staff/academic/galexander/research/soapfilm

References in corpus (3)

• Topological Boundary Modes in Isostatic Lattices
• Nonlinear conduction via solitons in a topological mechanical insulator
• Boundary Singularities Produced by the Motion of Soap Films

Cited by in corpus (6)

• Topological elasticity of non-orientable ribbons
• Mechanism to induce geometric constriction on kinks and domain walls
• Fractional solitons in non-Euclidian elastic plates
• Stable finite energy global vortices and asymptotic freedom
• A Björling Representation for Jacobi Fields on Minimal Surfaces and Soap Film Instabilities
• A novel connection between scalar field theories and quantum mechanics