Interacting Particle Systems and Beyond

相互作用的粒子系统及其他

• 批准号: 2348756
• 负责人: Alisa Knizel
• 金额: $ 20.21万
• 依托单位: Barnard College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-11-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2348756&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晶格模型的研究。代数结构在此类模型中继承允许进行许多精确的计算，而它们的概率性质则提供了基础代数数据的新观点和解释。例如，这些系统可用于研究晶体如何融化，神经元如何在大脑中移动，火锋的进展，癌症的传播方式，浮游生物菌落在海洋中的生长方式。研究项目旨在更好地理解某些重要模型的宏观行为，因为系统的大小不断增长。所考虑的模型通常称为“可解决”或“完全可解决”。尽管完全可解决的系统非常特殊，但它们的不对称性能被认为是较大模型家族的代表性。这样，除了自己有趣之外，精确的可解决系统是他们猜想的大学阶级的典范，可用于建立直觉和做出预测。目的是获取各种健壮方法来研究普遍性类别。该研究计划旨在在某些相互作用的粒子系统的背景下更好地了解某些“普遍性”特征。研究计划由三个主要方向组成：对数字的研究（在线上的颗粒集合，受外部潜力彼此排斥的外部潜力，以对数为数），对kardar-parisi-zhang方程的固定措施的研究研究（非线性随机性部分微分方程（一种非线性的部分微分方程），该方程最初是统计的统计范围和统计范围的统计范围，并构成了一个模型的模型。使用基金会的智力优点和更广泛的影响标准，认为通过评估被认为是宝贵的支持。