Abstract

Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems constrained by fixed area \(A\) and fixed volume \(V\), whose geometry is presented in terms of scalar spherical harmonics. These constraints can be incorporated in the theory in different ways. After an introductory review of the two approaches: with an exactly fixed by delta-function membrane area \(A\) [Seifert, Z. Phys. B, 97, 299 (1995)] or approximatively by means of a Lagrange multiplier \(\sigma \) conjugated to \(A\) [Milner and Safran, Phys. Rev. A, 36, 4371 (1987)], we discuss the determined role of the stretching effects, that has been announced in the framework of a model containing stretching energy term, expressed via the membrane vesicle tension [Bivas an d Tonchev, Phys. Rev. E, 100, 022416 (2019)]. Since the fluctuation spectrum for the used Hamiltonian is not exactly solvable an approximating method based on the Bogoliubov inequalities for the free energy has been developed. The area constraint in the last approach appears as a self-consistent equation for the membrane tension. In the general case this equation is intractable analytically. However, much insight into the physics behind can be obtained either imposing some restrictions on the values of the model parameters, or studying limiting cases, in which the self-consistent equation is solved. Implications for the equivalence of ensembles have been discussed as well.

中文翻译：

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近似球形膜热涨落的统计力学：弯曲和拉伸弹性的影响

摘要

审查了近球形的囊泡和微乳液液滴的理论研究，这些研究提出了受约束的热激发系统的典型例子。我们考虑了由固定面积\（A \）和固定体积\（V \）约束的此类系统的形状波动，其几何形状以标量球谐函数表示。这些约束可以以不同的方式并入理论中。经过对这两种方法的介绍性回顾之后：用增量功能膜面积\（A \）精确固定[Seifert，Z. Phys。[B，97，299（1995）]或近似地借助于与\（A \）共轭的拉格朗日乘数\（\ sigma \）[Milner和Safran，物理学。Rev. A，36，4371（1987）]，我们讨论了拉伸作用的确定作用，该作用已在包含拉伸能量项的模型框架中宣布，通过膜囊泡张力表达[Bivas and d Tonchev，Phys 。Rev.E，100，022416（2019）]。由于所用哈密顿量的波动谱不能完全求解，因此已经开发了一种基于Bogoliubov不等式的自由能近似方法。在最后一种方法中，面积约束表现为膜张力的自洽方程。在一般情况下，该方程在分析上是棘手的。但是，可以通过对模型参数的值施加一些限制或研究解决自洽方程的极限情况来获得对背后物理学的深入了解。