Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons

A compartmentalized surface model of Nambu and Goto is studied on triangulated spherical surfaces by using the canonical Monte Carlo simulation technique. One-dimensional bending energy is defined on the skeletons and at the junctions, and the mechanical strength of the surface is supplied by the one-dimensional bending energy defined on the skeletons and junctions. The compartment size is characterized by the total number L^\prime of bonds between the two-neighboring junctions and is assumed to have values in the range from L^\prime=2 to L^\prime=8 in the simulations, while that of the previously reported model is characterized by L^\prime=1, where all vertices of the triangulated surface are the junctions. Therefore, the model in this paper is considered to be an extension of the previous model in the sense that the previous model is obtained from the model in this paper in the limit of L^\prime\to1 The model in this paper is identical to the Nambu-Goto surface model without curvature energies in the limit of L^\prime\to \infty and hence is expected to be ill-defined at sufficiently large L^\prime. One remarkable result obtained in this paper is that the model has a well-defined smooth phase even at relatively large L^\prime just as the previous model of L^\prime\to1. It is also remarkable that the fluctuations of surface in the smooth phase are crucially dependent on L^\prime; we can see no surface fluctuation when L^\prime\leq2, while relatively large fluctuations are seen when L^\prime\geq3.Comment: 7 pages, 8 figure

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.Comment: 18 pages, 11 figure