Numerical Studies of Phase Transitions in Fluid Membranes

流体膜相变的数值研究

• 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

(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，发现晶体模型如预期发生了二级相变。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涨落的二阶相变与膜的流动性无关。（3）我们研究了被视为Polyakov刚性弦离散模型的普通流体膜模型。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)对普通结晶模型进行了朗之万模拟和蒙特卡洛分析。 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。

项目成果

鯉渕弘資: "液体および結晶界面に関する数値的方法による研究"熱流体系および固体系のミクロシミュレーションに関する合同シンポジウム・第5回分子動力学シンポジウム講演論文集. 00-4. 43-44 (2000)

Hiroshi Koibuchi：“使用数值方法研究液体和晶体界面”第五届分子动力学研讨会论文集，热流体和固体系统微观模拟联合研讨会 00-4（2000）。

H.Koibuchi and M.Yamada: "Phase Transition of a Model of Fluid Membrane"International Journal of Modern Physics C. 11・3. 441-450 (2000)

H.Koibuchi 和 M.Yamada：“流体膜模型的相变”国际现代物理学杂志 C. 11・3（2000）。

鯉渕弘資: "液体界面の相転移に関する数値的研究"日本機械学会2000年次大会講演論文集. Vol.1. 773-774 (2000)

Hiroshi Koibuchi：“液体界面相变的数值研究”日本机械工程师学会 2000 年年会论文集，第 1 卷 773-774（2000 年）。

鯉渕弘資: "講演論文:MC法とランジュバン法による結晶界面の分子シミュレーション"第13回計算力学講演会講演論文集. 589-590 (2000)

Hiroshi Koibuchi：“讲座论文：使用 MC 方法和 Langevin 方法进行晶体界面的分子模拟”第 13 届计算力学会议记录 589-590 (2000)。

H.Koibuchi and M.Yamada: "Phase Transition of a Model of Fluid Membrane"International Journal of Modern Physics C. Vol.11, No.3. 441-450 (2000)

H.Koibuchi 和 M.Yamada：“流体膜模型的相变”国际现代物理学杂志 C. 第 11 卷，第 3 期。