用Pinned格点上Potts模型重构的二维泡沫时间序列的动力学和拓扑性质
Dynamics and Topological Aspects of a Reconstructed Two-Dimensional Foam Time Series Using Potts Model on a Pinned Lattice
摘要：
我们讨论了一种方法来重建一个近似的二维泡沫结构，从一个不完整的图像使用扩展的Potts模式与钉扎晶格，我们在以前的文件中介绍。初始信息仅由顶点的位置组成。我们使用欧几里德距离映射构造定位气泡的中心，并在每个顶点位置分配一个连续的钉扎场，其势为$1/r$。我们使用扩展的Potts模型在每个中心处成核一个气泡，并让结构在缩放的目标区域的约束下演化，直到气泡彼此接触。目标区域约束和钉扎中心防止进一步粗化。然后，我们关闭面积约束，让边缘松弛到最小能量配置。结果是重建的结构非常接近模拟。我们重复这个过程的不同阶段的粗化相同的模拟泡沫和研究的模拟和重建动力学，拓扑结构和面积分布，发现他们同意良好的精度。
英文摘要：
We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomplete image using the extended Potts mode with a pinned lattice we introduced in a previous paper. The initial information consists of the positions of the vertices only. We locate the centers of the bubbles using the Euclidean distance-map construction and assign at each vertex position a continuous pinning field with a potential falling off as $1/r$. We nucleate a bubble at each center using the extended Potts model and let the structure evolve under the constraint of scaled target areas until the bubbles contact each other. The target area constraint and pinning centers prevent further coarsening. We then turn the area constraint off and let the edges relax to a minimum energy configuration. The result is a reconstructed structure very close to the simulation. We repeated this procedure for various stages of the coarsening of the same simulated foam and investigated the simulation and reconstruction dynamics, topology and area distribution, finding that they agree to good accuracy.
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