Modelling and Simulations of Multi-component Lipid Membranes and Open   Membranes via Diffusive Interface Approaches
  In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent experiments, it is demonstrated that the phase field models can capture the rich phenomena associated with the membrane transformation, thus it offers great functionality in the simulation and modeling of multicomponent membranes. 
Xiaoqiang Wang, and Qiang Du