Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn-Hilliard model on an evolving hypersurface coupled to Navier-Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn-Hilliard type energy, modelling line energy effects. A stable semidiscrete finite element approximation is introduced and, with the help of a fully discrete method, several phenomena occurring for two-phase membranes are computed.
Finite element approximation for the dynamics of fluidic two-phase biomembranes / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 51:6(2017), pp. 2319-2366. [10.1051/m2an/2017037]
Finite element approximation for the dynamics of fluidic two-phase biomembranes
Nürnberg R.
2017-01-01
Abstract
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn-Hilliard model on an evolving hypersurface coupled to Navier-Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn-Hilliard type energy, modelling line energy effects. A stable semidiscrete finite element approximation is introduced and, with the help of a fully discrete method, several phenomena occurring for two-phase membranes are computed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione