Mathematical Sciences: Interacting Particle Systems and Random Cellular Automata

数学科学：相互作用的粒子系统和随机元胞自动机

• 批准号: 8922876
• 负责人: David Griffeath
• 金额: $ 18.84万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8922876&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interacting; Particle; Systems

This research effort will focus on the analysis of interacting particle systems with simple dynamics that exhibit large-scale self-organized behavior. Initially, the research will focus on two families of models, in the plane and in space, with random cyclic dynamics: the cyclic cellular automata, and the cyclic particle system. The models are prototypes for spatial interactive wave phenomena observed in certain chemical reactions, atrial fibrillation, neural networks, and elsewhere. Following these investigations, the research will involve other interacting systems such as 'anti-stepping stone models' and various one-dimensional interface dynamics. This research is in the general area of probability theory known as interacting particle systems. Such systems, and related cellular automata, model complex random dynamics. They have found application in a wide variety of scientific contexts, including physics, chemistry, biology, and computer science. Of special importance are their connections with statistical physics, population genetics, and information transmission.

这项研究工作将集中于分析具有简单动力学的相互作用粒子系统，这些系统表现出大规模的自组织行为。最初，研究将集中在平面和空间中具有随机循环动力学的两类模型：循环元胞自动机和循环粒子系统。这些模型是在某些化学反应、心房颤动、神经网络和其他地方观察到的空间相互作用波现象的原型。在这些调查之后，研究将涉及其他相互作用系统，如“反踏脚石模型”和各种一维界面动力学。这项研究是概率论的一般领域，被称为相互作用粒子系统。这样的系统，以及相关的元胞自动机，模拟了复杂的随机动力学。它们在各种科学背景下都有广泛的应用，包括物理、化学、生物和计算机科学。特别重要的是它们与统计物理学、群体遗传学和信息传递的联系。