Studies in Interacting Particle Systems and Statistical Mechanics

相互作用粒子系统和统计力学研究

• 批准号: 9703814
• 负责人: Roberto Schonmann
• 金额: $ 7.6万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703814&HistoricalAwards=false
• 关键词: Studies; Interacting; Particle; Systems; Statistical

9703814 Schonmann The Principal Investigator will work on various projects in the areas of interacting particle systems, statistical mechanics, percolation, and other related subjects in Probability Theory. The main objects of interest in this proposal are the ergodic behavior and the relaxation patterns of several interacting particle systems, including Ising models and other lattice spin systems, contact processes on arbitrary graphs, growth models and cellular automata. Several of the proposed problems have their motivation in phenomena observed in nature as, for example, metastable states of systems in the vicinity of phase transition regions. The Principal Investigator will study problems in interacting particle systems. These are models for systems which contain a large number of similar components and in which each component interacts in a simple way with a few other ones. For instance one can think of the atoms in a crystal interacting when they are close enough, or individuals in a large population which may suffer or not from some infection with contamination occurring between neighbors. The local interaction may involve a substantial amount of randomness, but since the system as a whole is large, one expects and indeed observes a much more predictable behavior at the global level. A great deal of interest in such systems stems from the fact that the qualitative behavior of the whole system may depend in non-trivial ways on parameters which are built into the local interactions, but which only affect those in a smooth way (for example, the rate of infection between neighboring individuals in the second example above). The general issues of interest are then the understanding of which sort of equilibria can be reached by such types of stochastic dynamics, how an equilibrium state is reached, and how the parameters which affect the local rules may affect the answers to these questions.

小行星9703814 主要研究者将在相互作用粒子系统，统计力学，渗流和概率论的其他相关主题领域的各种项目中工作。 该方案的主要研究对象是几种相互作用粒子系统的遍历行为和弛豫模式，包括Ising模型和其他晶格自旋系统，任意图上的接触过程，生长模型和细胞自动机。 提出的几个问题有其动机的现象中观察到的性质，例如，在相变区附近的系统的亚稳态。 主要研究者将研究相互作用粒子系统中的问题。 这些模型适用于包含大量相似组件的系统，其中每个组件都以简单的方式与其他几个组件进行交互。 例如，人们可以想象晶体中的原子在足够接近时相互作用，或者大量人口中的个体可能会遭受或没有遭受邻居之间发生的污染的感染。 局部相互作用可能涉及大量的随机性，但由于系统作为一个整体是大的，人们期望并确实观察到一个更可预测的行为在全球范围内。 对这类问题的极大兴趣 系统的定性行为可能以非平凡的方式取决于参数，这些参数内置于局部相互作用中，但仅以平滑的方式影响那些参数（例如，上面第二个例子中相邻个体之间的感染率）。 感兴趣的一般问题，然后了解哪种平衡可以达到这种类型的随机动力学，如何达到平衡状态，以及如何影响局部规则的参数可能会影响这些问题的答案。