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: 9300612
• 负责人: David Griffeath
• 金额: $ 18万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-05-15 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300612&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interacting; Particle; Systems

Professors Bramson and Griffeath propose to further the rigorous theory of various random and deterministic complex systems in the area of interacting particle systems and random cellular automata. These include systems of annihilating random walks and billiards, random and deterministic growth models, and random and deterministic interface dynamics. The methodology for studying these processes often combines traditional rigorous mathematical analysis with interactive computer visualization. Professors Bramson and Griffeath study random processes known as interacting particle systems and random cellular automata. These are "toy universe" models that evolve over time, e.g. on a computer graphics display, offering insights into the behavior of complex dynamics from many areas of applied science. The investigators have two main objectives: to understand the kinds of aggregate behavior that such dynamics manifest, and to explain how these behaviors arise by using the traditional analytical techniques, theorems and proofs of mathematics. The phenomena they study include such fundamental physical processes as contagion, clustering, turbulence, and nucleation.

Bramson和Griffeath教授建议进一步研究 各种随机和确定性复杂的严格理论 相互作用粒子系统和随机系统领域的系统 细胞自动机 这些系统包括零化随机 散步和台球，随机和确定性增长模型， 随机和确定性界面动力学。 的方法论 研究这些过程通常结合传统的严格的 数学分析与交互式计算机可视化。 Bramson和Griffeath教授研究随机过程 称为相互作用粒子系统和随机细胞 自动机这些是随着时间的推移而演变的“玩具宇宙”模型， 例如，在计算机图形显示器上，提供对 应用科学许多领域的复杂动力学行为。 调查人员有两个主要目标：了解 这种动态表现出的各种聚合行为， 解释这些行为是如何通过使用传统的 分析技巧、定理和数学证明。的 他们研究的现象包括这样的基本物理过程 如传染、聚集、湍流和成核。