Distributed obstruction finding and fullerene research

分布式阻塞发现和富勒烯研究

• 批准号: 360290-2008
• 负责人: Myrvold, Wendy
• 金额: $ 2.79万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Research Tools and Instruments - Category 1 (<$150,000)
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=364751
• 关键词: Distributed; obstruction; finding; fullerene; research

The equipment requested includes workstations for graduate and undergraduate students which will be publically available in our theory lab and some processors without monitors to enable extensive distributed computations for two research problems.One of the most famous theorem in graph theory is Kuratowski's theorem: if a graph cannot be drawn on a plane with no crossing lines then it must contain a subgraph homeomorphic to one of two graphs. One major ongoing goal of my research program is to find a similar theorem for a torus (a surface shaped like a doughnut). Extra computational resources would greatly facilitate searching for these and the ultimate goal of finding a computer-aided proof that the set of obstructions we have found is complete. Having a complete set of obstructions could be used to prove theorems about toroidal graphs and would give insight as to how to design simple, fast algorithms for drawing pictures of them.Fullerenes are all-carbon molecules whose structures are 3-regular planar graphs with face sizes five or six. We have developed a program, FuiGui to aid in the visualization of these molecules and their parameters. Our goal is to amass a large database of parameter information for all the small fullerenes in order to investigate correlations between these parameters and important chemical properties of fullerenes. Extra computational facilities are critical for collecting this data in a reasonable amount of time.

所要求的设备包括供研究生和本科生使用的工作站，这些工作站将在我们的理论实验室公开提供，以及一些没有监视器的处理器，以便为两个研究问题进行广泛的分布式计算。图论中最著名的定理之一是库拉托斯基定理：如果一个图不能画在没有交叉线的平面上，那么它必须包含一个同胚于两个图之一的子图。我的研究计划的一个主要目标是为环面（形状像甜甜圈的表面）找到一个类似的定理。额外的计算资源将极大地促进对这些障碍的搜索，最终目标是找到计算机辅助证明，证明我们发现的障碍集是完整的。拥有一组完整的障碍物可以用来证明关于环面图的定理，并将为如何设计简单，快速的算法来绘制它们的图片提供洞察力。富勒烯是一种全碳分子，其结构是面尺寸为5或6的3规则平面图。我们开发了一个程序FuiGui来帮助可视化这些分子及其参数。我们的目标是为所有小富勒烯积累一个大型的参数信息数据库，以便研究这些参数与富勒烯重要化学性质之间的相关性。额外的计算设施对于在合理的时间内收集这些数据至关重要。