Year: 2024
Author: Alexander Meiners, Hannes Uecker
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 555–606
Abstract
We describe some differential geometric bifurcation problems and their treatment in the Matlab continuation and bifurcation toolbox pde2path. The continuation steps consist in solving the PDEs for the normal displacement of an immersed surface $X ⊂\mathbb{R}^3,$ with bifurcation detection and possible subsequent branch switching. The examples include minimal surfaces such as Enneper’s surface and a Schwarz-P-family, some non-zero constant mean curvature surfaces such as liquid bridges, and some 4th order biomembrane models. In all of these we find interesting symmetry-breaking bifurcations. A few of these are (semi)analytically known and hence used as benchmarks.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2024-0005
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 555–606
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 52
Keywords: Numerical bifurcation constant mean curvature Helfrich functional discrete differential geometry.