Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Eliot Fried McGill University Title: Stability and bifurcation of a soap film spanning an elastic loop Abstract: The Euler--Plateau problem, proposed by Giomi $\&$ Mahadevan in 2013, concerns a soap film spanning a flexible loop. The shapes of the film and the loop are determined by the interactions between the two components. In the work described in this talk, which is joint with Yi-chao Chen, the Euler--Plateau problem is reformulated to yield a boundary-value problem for a vector field that parameterizes both the spanning surface and the bounding loop. Using the first and second variations of the relevant free-energy functional, detailed bifurcation and stability analyses are performed. For a spanning surface with energy density $\sigma$ and a bounding loop with length $2\pi R$ and bending rigidity $a$, the first bifurcation, during which the spanning surface remains flat but the bounding loop becomes noncircular, occurs at $\sigma R^3/a=3$, confirming a result obtained previously via an energy comparison. All other bifurcation solution branches emanating from the flat circular solution branch, including those to nonplanar solution branches, are found to be unstable. Finally, relevance to the modeling of discoidal high-density lipoproteins is discussed.Recording: http://mm.math.cmu.edu/recordings/cna/CNA-EliotFriedTape-Sep-26-2013.avi Recording: http://mm.math.cmu.edu/recordings/cna/CNA-EliotFriedTape-Sep-26-2013.mp4 Date: Thursday, September 26, 2013Time: 1:30 pmLocation: Wean Hall 7218Submitted by: David Kinderlehrer |