Stability and bifurcation of a soap film spanning a flexible loop

DOI10.1007/s10659-013-9458-xzbMath1298.49064arXiv1307.3521OpenAlexW2028967496MaRDI QIDQ457165

Eliot Fried, Yi-Chao Chen

Publication date: 26 September 2014

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.3521

zbMATH Keywords

stabilityEuler-Lagrange equationsbifurcationsurface tensionsoap filmflexural rigidityclosed-curve problemEuler-Plateau problemsecond variation conditionthread problem

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Stability in context of PDEs (35B35) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04) Differential line geometry (53A25) Bifurcations in context of PDEs (35B32)

Related Items (8)

Solution of the Kirchhoff-Plateau problem ⋮ Theoretical and experimental study of the stability of a soap film spanning a flexible loop ⋮ Instability paths in the Kirchhoff-Plateau problem ⋮ Influence of a spanning liquid film on the stability and buckling of a circular loop with intrinsic curvature or intrinsic twist density ⋮ On the anisotropic Kirchhoff-Plateau problem ⋮ Dimensional reduction of the Kirchhoff-Plateau problem ⋮ Regarding the Euler-Plateau problem with elastic modulus ⋮ Plateau’s Problem

Cites Work

• Singularities and groups in bifurcation theory. Volume I
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• On the differential geometry of closed space curves
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• Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids
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