2012/12/27 by Soumya Jana, Sayan Kar · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boundary (topology) #Boundary value problem #Class (philosophy) #Coaxial #Computer science #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Instability #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scientific Research and Discoveries #Soap film #Stability (learning theory) #physics.class-ph
paper · pdf · doi:10.1140/epjp/i2013-13108-y
published in The European Physical Journal Plus 128(9) (Springer Science+Business Media) · 19 pages, 7 figures
arxiv created 2012/12/27 · openalex publication_date 2013/09/01 · arxiv updated 2014/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.