肥皂泡沫中的星三角等价性

In two dimensional foams at equilibrium, triangular bubbles can be freely exchanged with 3-fold stars --three edges ending at a central vertex. This theorem is deduced here from Moukarzel's duality. Moreover, to probe the method, a few related properties are established: under slow gas diffusion, T2 processes are continuous for triangles but not for other types of bubbles. In general, the gas flow results in different configurations in the presence of a triangle than in the presence of a star. 在平衡二维泡沫中, 三角形气泡可以自由地与 3 度星形 --即三个边缘结束于中心顶点的结构 --进行交换。本文依据 Moukarzel 二元性推导出该定理。此外, 为检验该方法, 建立了一些相关性质: 在缓慢的气体扩散下, T2 过程对三角形是连续的, 但对其他类型的气泡则不是。一般而言, 在存在三角形的情况下, 气体流动导致的配置与在存在星形的情况下不同。