2023/09/07 by Alexander Meiners, Meiners, Alexander, Hannes Uecker +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #65P30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #Differential Geometry (math.DG) #FOS: Mathematics #Microtubule and mitosis dynamics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2309.03646
openalex publication_date 2023/09/07 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28
We describe how some differential geometric bifurcation problems can be treated with the MATLAB continuation and bifurcation toolbox pde2path. The basic setup consists in solving the PDEs for the normal displacement of an immersed surface X⊂ℝ3 and subsequent update of X in each continuation step, combined with bifurcation detection and localization, followed by possible branch switching. Examples treated include some minimal surfaces such as Enneper's surface and a Schwarz-P-family, some non-zero constant mean curvature surfaces such as liquid bridges and nodoids, and some 4th order biomembrane models. In all of these we find interesting symmetry breaking bifurcations. Some of these are (semi)analytically known and thus are used as benchmarks.