This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

Lipid bilayer model membranes that contain a single lipid species can undergo transitions
between ordered and disordered phases, and membranes that contain a mixture of lipid …

In this paper, we study efficient numerical schemes of the classical phase field elastic
bending energy model that has been widely used to describe the shape deformation of …

We consider in this paper gradient flows with disparate terms in the free energy that cannot
be efficiently handled with the scalar auxiliary variable (SAV) approach, and we develop the …

We develop a thermodynamically consistent phase-field model to simulate the dynamics of
multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature …

Biomembranes consisting of multiple lipids may involve phase separation phenomena
leading to coexisting domains of different lipid compositions. The modeling of such …

We consider the numerical approximation of the flow-coupled multi-phase-field elastic
bending energy model of lipid vesicles. Based on the classical model with approximate …

Different from the classical phase-field elastic bending model of lipid vesicles that uses a
penalty term to conserve volume approximately, in this paper, a new model with accurate …

Cell motion is crucial in human health and development. Cells may migrate individually or in
highly coordinated groups. Cell motion results from complex intra-and extra-cellular …

In this paper, for the highly nonlinear hydrodynamically coupled elastic bending energy
model of vesicle membranes, based on the discontinuous Galerkin (DG) method for spatial …