Mathematical Sciences: Interacting Particle Systems and Random Cellular Automata

这项研究工作将侧重于分析 具有简单动力学的相互作用粒子系统， 大规模的自组织行为 最初，研究 将集中在两个家庭的模型，在飞机和空间， 随机循环动力学：循环细胞自动机， 循环粒子系统 这些模型是 在某些化学物质中观察到空间相互作用波现象 反应、心房颤动、神经网络和其他地方。 在这些调查之后，研究将涉及其他 交互系统，如“反垫脚石模型”， 各种一维界面动力学。 这项研究是在概率论的一般领域 称为相互作用粒子系统。 这些系统，以及 相关的细胞自动机，模型复杂的随机动力学。 他们 已经在各种各样的科学背景中找到了应用， 包括物理，化学，生物和计算机科学。 的 特别重要是它们与统计数据的联系 物理学、群体遗传学和信息传递。

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.