Interacting Particle Systems and Beyond

相互作用的粒子系统及其他

• 批准号: 2153958
• 负责人: Alisa Knizel
• 金额: $ 20.21万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-15 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153958&HistoricalAwards=false
• 关键词: Interacting; Particle; Systems; Beyond

The project focuses on the study of lattice models in statistical mechanics. The algebraic structure inherent in such models allows for many exact computations, while their probabilistic nature provides a new point of view and interpretation of the underlying algebraic data. For instance, these systems can be used to study how crystals melt, how neurons move through the brain, how a fire front advances, how a cancer spreads, how a plankton colony grows in the ocean. The research project aims at achieving a better understanding of the macroscopic behavior of some important models as the size of the system grows.The models under consideration are usually referred to as “integrable” or “exactly solvable.” Though exactly solvable systems are very special, their asymptotic properties are believed to be representative for a larger family of models. In this way, besides being interesting themselves, exactly solvable systems are exemplars of their conjectured universality classes and can be used to build intuition and make predictions. The aim is to obtain a variety of robust methods to study the universality classes. This research program seeks to establish a better understanding of some “universality” features in the context of certain interacting particle systems. The research program consists of three main directions— the study of log-gases (ensemble of particles on the line confined by an external potential that repel each other logarithmically), the study of the stationary measures for the Kardar-Parisi-Zhang equation (a non-linear stochastic partial differential equation that was originally proposed as a model of surface growth), and the study of traffic models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目着重于统计力学中的晶格模型。用于研究晶体如何融化，神经元如何移动大脑，火灾前进，癌症如何扩散，海洋中的浮游生物菌落如何旨在更好地了解某些人的宏观行为随着系统的增长，重要的模型通常称为“可解决的”或“完全可解决”的模型。建立插图并进行预测。 （粒子s在线上的合奏，被外部电位相互排斥的外部电势），对最初作为表面生长模型的kardar-parisi-zhang方程的研究）NSF'Sf'Sf'Sf'Stututory使用Toundation的Revader的心想评估会影响W标准。