Helfrich cylinders -- instabilities, bifurcations and amplitude equations

TL;DR

This paper investigates the stability and bifurcation behavior of Helfrich cylinders, revealing how spontaneous curvature and periodicity influence the emergence of various shape instabilities like pearling, coiling, buckling, and wrinkling.

Contribution

It combines bifurcation analysis, numerical continuation, and bifurcation methods to classify and analyze shape instabilities of Helfrich cylinders under constraints.

Findings

Different bifurcation types depend on spontaneous curvature and periodicity.

Bifurcating solutions include axisymmetric and non-axisymmetric shapes.

Stability and secondary bifurcations vary with parameters.

Abstract

Combining local bifurcation analysis with numerical continuation and bifurcation methods we study bifurcations from cylindrical vesicles described by the Helfrich equation with volume and area constraints, with a prescribed periodicity along the cylindrical axis. The bifurcating solutions are in two main classes, axisymmetric (pearling), and non-axisymmetric (coiling, buckling, and wrinkling), and depending on the spontaneous curvature and the prescribed periodicity along the cylinder axis we obtain different stabilities of the bifurcating branches, and different secondary bifurcations.