Mathematical Sciences: Percolation and Related Processes

数学科学：渗滤及相关过程

• 批准号: 9006395
• 负责人: Kenneth Alexander
• 金额: $ 5.36万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006395&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Percolation; Related; Processes

The principal investigator will conduct research concerning percolation theory, the random cluster model, and their relation to Ising and Potts models, mainly in two dimensions. Results to be sought concern (1) the formation of large rings of dual bonds in the random cluster model, which correspond to droplets of one phase immersed in another in a special construction of the Ising or Potts model; (2) the curve describing the typical shape of these rings, and its relation to properties of the function giving exponential rates of decay of correlations along rays emanating in various directions from the origin; and (3) percolation in half spaces. The principal investigator is working in the field of percolation theory and self avoiding random walk theory. The problems he will study are motivated by physical considerations. For example, percolation theory was motivated by the flow of a liquid through a porous material. Self avoiding random walks are used to model chemical polymers.

主要研究者将进行研究， 逾渗理论、随机簇模型及其相互关系 Ising和Potts模型，主要是二维的。 结果 （1）形成大环的双键 在随机簇模型中，其对应于一个微滴， 相沉浸在另一个在一个特殊的建设伊辛 或Potts模型;（2）描述典型形状的曲线， 这些环，以及它与函数性质的关系 给出了沿着射线的相关性的指数衰减率 从原点向各个方向发散;以及（3） 半空间中的渗流 首席研究员在以下领域工作： 渗流理论和自避免随机游走理论。 的 他要研究的问题是出于物理考虑。 例如，渗透理论的动机是一个流动的， 液体通过多孔材料。 自回避随机游动 用于模拟化学聚合物。