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arXiv · 1212.6321

Perturbative stability of catenoidal soap films

Soumya Jana·Sayan Kar
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Abstract

The perturbative stability of catenoidal soap films formed between parallel, equal radii, coaxial rings is studied using analytical and semi-analytical methods. Using a theorem on the nature of eigenvalues for a class of Sturm--Liouville operators, we show that for the given boundary conditions, azimuthally asymmetric perturbations are stable, while symmetric perturbations lead to an instability--a result demonstrated in Ben Amar et. al [7] using numerics and experiment. Further, we show how to obtain the lowest real eigenvalue of perturbations, using the semi-analytical Asymptotic Iteration Method (AIM). Conclusions using AIM support the analytically obtained result as well as the results in [7]. Finally, we compute the eigenfunctions and show, pictorially, how the perturbed soap film evolves in time.

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Soumya Jana, Sayan Kar. 2012-12-27. Perturbative stability of catenoidal soap films. https://doi.org/10.1140/epjp%2Fi2013-13108-y

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