Statistical Mechanics of Interfaces

一般来说，传统统计物理学的主要目的是根据材料的微观元素（如原子和分子）的特征来解释宏观现象。然而，在这些过程中，人们经常面临一个困难，特别是在长程相互作用起着重要作用的问题中，例如。G.相变现象在这样的问题中，采用粗粒度的描述通常是有用的。一个典型的例子是临界现象，在本研究中，我们从一个宏观连续介质模型出发，称为Ginzburg-Landau模型。通过粗糙的微观模型。这样的连续描述有时是不够的，应该通过考虑局部奇点（如界面）来补充。我们研究了下列问题，在每一个问题中，相互作用起着至关重要的作用：（1）细胞图形形成的统计力学;（2）凝胶的相共存;（3）含表面活性剂体系中的图形形成。这些问题不仅在基础物理领域，而且在应用科学领域都是重要的。我们的一些研究具有探索性的方面，在未来的研究中应该加以完善。

The main purpose of the traditional statistical physics has been, in general, to explain macroscopic phenomena in terms of features of microscopic elements of the material, like atoms and molecules. However, in these processes, one often faces a difficulty particularly in the problems where long-range interactions play an essential role, e. g. phase transition phenomena. In such problems, it is often useful to adopt coarse-grained descriptions. A typical example is the critical phenomena.In this study, we start from a macroscopic continuum model, called Ginzburg-Landau model, which can be derived. by coarse-graining microscopic models. Such a continuum description is sometimes inadequate and should be supplemented by taking account of localized singularities, like interfaces. We studied the following problems, in each of which interafces play a crucial role ;1) Statistical Mechanics of Cellular Pattern Formation2) Phase Coexistence of Gels3) Pattern Formation in Sytems Containing SurfactantsThese problems are important not only in the field of fundamental physics but also in the field of applied sciences. Some of our researches has exploratory aspects, which should be refined in the future studies.