Finsler geometry modeling of phase separation in multi-component membranes

Finsler geometric surface model is studied as a coarse-grained model for membranes of three-component such as DOPC, DPPC and Cholesterol. To understand the phase separation of liquid ordered (DPPC rich) $L_o$ and the liquid disordered (DOPC rich) $L_d$, we introduce a variable $\sigma (\in \{1,-1\})$ in the triangulated surface model. We numerically find that there appear two circulars and stripe domains on the surface and that these two morphologies are separated by a phase transition. The morphological change from the one to the other with respect to the variation of the area fraction of $L_o$ is consistent with existing experimental results. This gives us a clear understanding of the origin of the line tension energy, which has been used to understand those morphological changes in the three-component membranes. In addition to these two circulars and stripe domains, raft-like domain and budding domain are also observed, and the corresponding several phase diagrams are obtained. Technical details of the Finsler geometry modeling are also shown.