Second-Order Investigations in Particle and Trapping Systems

粒子和捕获系统的二阶研究

• 批准号: 0071504
• 负责人: Sunder Sethuraman
• 金额: $ 6.62万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071504&HistoricalAwards=false
• 关键词: Second; Order; Investigations; Particle; Trapping

The goal of this research is to investigate the fluctuation behaviors in two types of systems: Mass conservative particle systems, and Brownian trapping models. The first type includes the exclusion and zero-range processes, while the second type covers variants of the "Wiener Sausage" model. Three categories of problems are focused upon in these systems: Tagged particle problems in conservative particle systems, current fluctuations at a fixed location in the exclusion model, and localization structure of long time surviving Brownian paths in trap settings.Stochastic dynamical systems following the motion of a collection of particles have been successful in the modeling of diverse physical phenomena such as fluid and traffic flow, queuing, chemical trapping behavior, etc. Several theoretical studies have been made on "first-order" calculations, which describe the dominant modes of objects of interest, for instance, average velocities or trap survival probabilities. The intent of this project is to supply the "second-order" characteristics in these fluid and traffic models. The significance of second-order calculations is that they provide a measure of the robustness of the first-order approximations in applications. Aside from this general notion, the computations involved in this project would shed light on the intrinsic physics of the random media models studied. Also, from the mathematical view, the solution techniques of these challenging problems would be of great value themselves for future endeavors.

本研究的目的是探讨两类系统中的涨落行为：质量守恒的粒子系统和布朗俘获模型。 第一种类型包括排除和零范围过程，而第二种类型涵盖“维纳香肠”模型的变体。 在这些系统中，重点关注三类问题：保守粒子系统中的标记粒子问题，排斥模型中固定位置的电流波动，陷阱中长时间存活的布朗路径的局部化结构。随机动力学系统跟随粒子集合的运动已经成功地模拟了各种物理现象，如流体和交通流，排队，化学捕获行为等。已经对“一阶”计算进行了一些理论研究，该计算描述了感兴趣的对象的主导模式，例如平均速度或陷阱生存概率。 这个项目的目的是提供这些流体和交通模型的“二阶”特性。 二阶计算的重要性在于它们提供了一阶近似在应用中的鲁棒性的度量。 除了这个一般概念，这个项目中涉及的计算将揭示所研究的随机介质模型的内在物理。 同时，从数学的角度来看，这些具有挑战性的问题的解决技术将是非常有价值的，为未来的努力。