Boolean algebra of two-dimensional continua with arbitrarily complex topology
Boolean algebra of two-dimensional continua with arbitrarily complex topology
复制标题
具有任意复杂拓扑的二维连续体的布尔代数
DOI：
10.1090/mcom/3539
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Zhixuan Li
中科院分区：
文献类型：
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作者：
Qinghai Zhang;Zhixuan Li
我们提出了一个二维连续体的数学模型，以建立一个坚实的理论基础，为研究其复杂的拓扑结构，大的几何变形，拓扑结构的变化，如合并的背景下，多相流。我们的建模空间，命名为阴空间，包括经常开放的半解析集有界边界，并进一步配备了建设性和代数定义的布尔运算。我们的模型的主要特点包括：（a）流体的拓扑信息，如Betti数，可以很容易地在恒定的时间内提取，（B）流体的拓扑变化被捕获的非流形点的流体边界，和（c）布尔运算流体正确处理所有退化的情况下，并适用于任意复杂的拓扑结构。然而，它们是简单和有效的，因为它们仅涉及确定点与Jordan曲线的相对位置并与多个曲线段相交。最后，（a）和（c）的实用程序被证明是通过结合阴空间与最近的立方MARS方法跟踪一个复杂的流体在一个单一的涡流。引用
We propose a mathematical model for two-dimensional continua in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging in the context of multiphase flows. Our modeling space, named the Yin space, consists of regular open semianalytic sets with bounded boundaries, and is further equipped with constructive and algebraic definitions of Boolean operations. Major distinguishing features of our model include (a) topological information of fluids such as Betti numbers can be easily extracted in constant time,(b) topological changes of fluids are captured by nonmanifold points on fluid boundaries, and (c) Boolean operations on fluids correctly handle all degenerate cases and apply to arbitrarily complex topologies, yet they are simple and efficient in that they only involve determining the relative position of a point to a Jordan curve and intersecting a number of curve segments. Finally, utilities of (a) and (c) are demonstrated by combining the Yin space with the recent cubic MARS method to track a complex fluid in a single vortex flow. References
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DOI：
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发表时间：
2012
期刊：
三菱UFJビジネススクエア・SQUET
影响因子：
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作者：
朝倉哲郎
通讯作者：
朝倉哲郎