Mathematical Sciences: Interacting Particle Systems and Random Cellular Automata

Bramson和Griffeath教授建议在相互作用的粒子系统和随机细胞自动机领域进一步发展各种随机和确定性复杂系统的严格理论。其中包括消灭随机漫步和台球的系统，随机和确定性增长模型，以及随机和确定性界面动力学。研究这些过程的方法论通常将传统的严格数学分析与交互式计算机可视化相结合。布拉姆森和格里菲思教授研究被称为相互作用的粒子系统和随机细胞自动机的随机过程。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，提供了对应用科学许多领域的复杂动力学行为的洞察。研究人员有两个主要目标：了解这种动力学所表现出的聚合行为的种类，并使用传统的分析技术、定理和数学证明来解释这些行为是如何产生的。他们研究的现象包括传染、聚集、湍流和成核等基本物理过程。

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.