骨架支持的固定连接曲面模型中的形状变换过渡
Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons
摘要：
利用正则蒙特卡罗模拟技术，在三角化球面上研究了Nambu和Goto的分区曲面模型。一维弯曲能定义在骨架和连接处，并且表面的机械强度由定义在骨架和连接处的一维弯曲能提供。隔室大小的特征在于两个相邻连接之间的键的总数L^ \prime，并且在模拟中假定具有从L^ \prime =2到L^ \prime =8的范围内的值，而先前报道的模型的特征在于L^ \prime =1，其中三角形化表面的所有顶点都是连接。因此，我们认为，本文中的模型被认为是先前模型的延伸，在这个意义上，先前模型是从本文中的模型在L^ \prime \to 1的极限中获得的。本文中的模型与在L^ \prime \to \infty的极限中没有曲率能的Nambu-Goto表面模型相同，因此预期在足够大的L^\prime。本文中得到的一个显著结果是，即使在相对大的L^ \prime下，该模型也具有良好定义的光滑相位，正如先前的L^ \prime \to 1模型一样。同样值得注意的是，光滑相中表面的波动与L^ \prime密切相关;当L^ \prime \leq 2时，我们看不到表面波动，而当L^ \prime \geq 3时，我们看到相对较大的波动。
英文摘要：
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.
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