Narrow Results

A model of fluid membrane, which is not self-avoiding, such as two-dimensional spherical random surface is studied by using Monte Carlo simulation. Spherical surfaces in R³ are discretized by piecewise linear triangle. Dynamical variables are the positions X of the vertices and the triangulation g. The action of the model is sum of area energy and bending energy times bending rigidity b. The bending energy and the specific heat are measured, and the critical exponents of the phase transitions are obtained by a finite-size scaling technique. We find that our model of fluid membrane undergoes a second order phase transition.

Some progresses in shape problems following the Helfrich model are reported. Based on the Helfrich model, we have predicted not only the exact solution for discoidal shape of red blood cells but also a special kind of toroidal vesicle with the ratio of two generation radii being . The Helfrich model can also be extended to investigate the complex structures in other soft matters such as the formation of focal conic domains in smectic liquid crystal, the tube-to-sphere transition in peptide nanostructures, and icosahedral configuration of small virus capsids.

Some progresses in shape problems following the Helfrich model are reported. Based on the Helfrich model, we have predicted not only the exact solution for discoidal shape of red blood cells but also a special kind of toroidal vesicle with the ratio of two generation radii being . The Helfrich model can also be extended to investigate the complex structures in other soft matters such as the formation of focal conic domains in smectic liquid crystal, the tube-to-sphere transition in peptide nanostructures, and icosahedral configuration of small virus capsids.