Numerical Studies of Phase Transitions in Fluid Membranes

流体膜相变的数值研究

基本信息

批准号：
10650191
负责人：
KOIBUCHI Hiroshi
金额：
$ 1.54万
依托单位：
Ibaraki College of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650191/
关键词：
Fluid Membranes Liquid Crystals Complex Fluids Second Order Phase Transition Lipid Bilayer Membranes Membrane Elasticity Fluidity Monte Carlo Simulation 結晶界面数値計算比熱面積エネルギー曲げエネルギー

项目摘要

(1) We defined a model of fluid membrane which has a surface tension, a bending elasticity and a fluidity. The Hamiltonian of the model is considered as a discrete action of Nambu string for a model of elementary particles. We found by MC that this model undergoes a second order phase transition.(2) We performed MC simulations for a model of crystalline membranes whose Hamiltonian is identical with that of (1), and found that the crystalline model undergoes a second order phase transition as expected. It is found from this result together with that of (1) that the second order phase transition of shape fluctuations in the membrane, which has a surface tension and a bending rigidity, is independent of the fluidity of membranes.(3) We studied the ordinary model of fluid membrane that is considered as a discrete model of Polyakov rigid string. We found by MC that there is a second order phase transition of shape fluctuations in the ordinary model of fluid membranes.(4) Performing MC simulations for the ordinary model of crystalline membranes, we studied the phase transitions of shape fluctuations. By comparing the results of crystalline model with those of (3), we found that the fluidity in membranes strengthen the phase transition and that the Hausdorff dimension of the fluid model is larger that that of the crystalline model at the phase transition.(5) Langevin simulations as well as the Monte Carlo were performed for the ordinary crystalline model. The critical exponent of the phase transition and the Housdorff dimension at the phase Transition were obtained by both Langevin and MC, and results of the two techniques were almost identical with each other. Thus it was confirmed that the both techniques we used are correct for simulations of crystalline membranes.

(1)我们定义了具有表面张力、弯曲弹性和流动性的流体膜模型。该模型的哈密顿量被认为是基本粒子模型的南部弦的离散作用。通过MC我们发现该模型发生了二级相变。(2)我们对哈密顿量与(1)相同的晶体膜模型进行了MC模拟，发现晶体模型发生了二级相变正如预期的那样。从该结果与（1）的结果一起发现，具有表面张力和弯曲刚度的膜中形状波动的二阶相变与膜的流动性无关。（3）我们研究了流体膜的普通模型被视为 Polyakov 刚性弦的离散模型。通过MC我们发现普通流体膜模型中存在形状涨落的二阶相变。(4)对普通晶体膜模型进行MC模拟,研究了形状涨落的相变。通过将结晶模型的结果与(3)的结果进行比较，我们发现膜中的流动性增强了相变，并且相变时流体模型的Hausdorff维数大于结晶模型的Hausdorff维数。(5)对普通晶体模型进行朗之万模拟和蒙特卡罗模拟。 Langevin和MC均获得了相变的临界指数和相变时的Housdorff维数，两种技术的结果几乎相同。因此，证实我们使用的两种技术对于晶体膜的模拟都是正确的。