二维泡沫的统计力学：模型的物理基础
Statistical mechanics of two-dimensional foams: Physical foundations of the model
摘要：
在最近的一系列论文[1- 3]中，提出了一个统计模型，该模型解释了二维混洗泡沫的拓扑和几何性质之间的相关性，并与实验和数值数据进行了比较。在这里，暴露和证明了模型所依据的各种假设：泡沫配置的等概率假设。气泡之间的相关性的范围进行了讨论，并在模型中使用的平均场近似进行了详细说明。与平均场描述相联系的两个自洽方程可以分别解释为边数守恒定律和气泡曲率守恒定律。最后，使用一个“大典范”的描述，其中的泡沫构成了一个水库的侧面和曲率，是有道理的。
英文摘要：
In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a '' Grand-Canonical '' description, in which the foam constitutes a reservoir of sides and curvature, is justified.
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