Studies in Interacting Random Systems

相互作用随机系统的研究

• 批准号: 0402231
• 负责人: Timo Seppalainen
• 金额: --
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0402231&HistoricalAwards=false
• 关键词: Studies; Interacting; Random; Systems

0402231Seppalainen This project studies stochastic processes that model complex, interacting behavior, such as interacting particle systems and interface models. The goal is to obtain mathematical results that describe behavior over large space and time scales in terms of limit theorems, and roughness of interfaces or fluctuations in particle flow by order-of-magnitude exponents, limit distributions, and large deviation rate functions. The emphasis is on finding new phenomena, and on capturing the overall picture of connections between different classes of microscopic rules and the associated large-scale behavior. One particular problem of interest in the context of asymmetric systems is the fluctuations of the current across a characteristic of the partial differential equation that describes the macroscopic evolution of the system. The objective of this research is precise mathematical understanding of certain kinds of macroscopic phenomena that result from interactions among a large number of microscopic components. The project studies mathematical models that include randomness in the behavior of the individual components. These models are abstractions of basic principles of organization and behavior common to many types of complex systems. The goal is to describe the typical large scale behavior of the model, and also to quantify the chances of deviations from the typical behavior. Complex interactions occur all around us in natural and man-made processes. Examples include cars on a freeway, customers in a queue, packets making their way through a communication network, or fluid particles in a tube. Consequently understanding the mathematics of complex interactions has potentially wide implications for science and engineering. Models of the types described in the proposal and others related to them are concurrently studied by mathematicians, natural scientists, social scientists, and engineers.

0402231Seppalainen该项目研究模拟复杂的相互作用行为的随机过程，例如相互作用的粒子系统和界面模型。我们的目标是获得数学结果，描述行为在大的空间和时间尺度上的极限定理，粗糙度的界面或波动的粒子流的数量级指数，极限分布，和大偏差率函数。重点是发现新的现象，并捕捉不同类别的微观规则和相关的大规模行为之间的联系的整体画面。在非对称系统的背景下感兴趣的一个特别的问题是在描述系统的宏观演化的偏微分方程的特性的电流的波动。 这项研究的目的是精确的数学理解某些种类的宏观现象，导致大量的微观成分之间的相互作用。该项目研究的数学模型包括各个组件行为的随机性。这些模型是许多类型的复杂系统所共有的组织和行为的基本原则的抽象。目标是描述模型的典型大规模行为，并量化偏离典型行为的可能性。复杂的相互作用发生在我们周围的自然和人为过程中。例子包括高速公路上的汽车、排队的顾客、通过通信网络的数据包或管道中的流体颗粒。因此，理解复杂相互作用的数学可能对科学和工程产生广泛的影响。数学家、自然科学家、社会科学家和工程师同时研究提案中描述的模型和其他与之相关的模型。