The Formation of Voronoi Diagrams in Chemical and Physical Systems: Experimental Findings and Theoretical Models
The Formation of Voronoi Diagrams in Chemical and Physical Systems: Experimental Findings and Theoretical Models
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化学和物理系统中沃罗诺伊图的形成：实验结果和理论模型
DOI：
10.1142/s021812740401059x
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Hans
中科院分区：
文献类型：
--
作者：
B. D. L. Costello;N. Ratcliffe;A. Adamatzky;A. L. Zanin;A. Liehr;Hans
该工作结合实验和理论结果讨论了空间扩展非线性系统中Voronoi图的形成。关于实验系统的一些化学系统以前使用的原型化学处理器和阻挡气体放电系统进行了研究。虽然基本的微观过程是非常不同的，这两种类型的系统显示自组织Voronoi图的适当的参数。事实上，某些化学系统表现出Voronoi图作为两组不同参数的输出状态，一组对应于稳定的强制触发波的相互作用，另一组对应于由于系统中的点不稳定性引起的波的自发引发和相互作用。在化学系统的情况下，前端的启动，传播和相互作用（湮灭）是Voronoi图形成的主要机制，在阻挡气体放电系统的情况下，消失的电场区域定义的Voronoi图的中轴。在元胞自动机模型的基础上，阐述了Voronoi图形成的一般概念，并对相关机理进行了模拟。另一种直观的方法对自组织Voronoi图的理解已经给出了反应扩散模型的基础上解释的Voronoi图的形成作为一个结果的相互作用的触发前沿。表现为定态的Voronoi图的各种系统表明，Voronoi图是一种通用的和自然的模式形成现象。
The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical processors and a barrier gas-discharge system are investigated. Although the underlying microscopic processes are very different, both types of systems show self-organized Voronoi diagrams for suitable parameters. Indeed certain chemical systems exhibit Voronoi diagrams as an output state for two distinct sets of parameters one that corresponds to the interaction of stable forced trigger waves and the other that corresponds to the spontaneous initiation and interaction of waves due to point instabilities in the system. In the case of the chemical systems front initiation, propagation and interaction (annihilation) are the primary mechanisms for Voronoi diagram formation, in the case of the barrier gas-discharge system regions of vanishing electric field define the medial axes of the Voronoi diagram. On the basis of cellular automata models the general concept of the formation of Voronoi diagrams has been explained, and related mechanisms have been simulated. Another intuitive approach towards the understanding of self-organized Voronoi diagrams has been given on the basis of reaction–diffusion models explaining the formation of Voronoi diagrams as a result of the mutual interactions of trigger fronts. The variety of systems exhibiting Voronoi diagrams as stationary states indicates that Voronoi diagrams are a generic and natural pattern formation phenomenon.