Stochastic Dynamics on Large-Scale Networks

大规模网络上的随机动力学

• 批准号: 1855604
• 负责人: Joe Chen
• 金额: $ 14.29万
• 依托单位: Colgate University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1855604&HistoricalAwards=false
• 关键词: Stochastic; Dynamics; Large; Scale; Networks

Rigorous analysis of microscopic probabilistic models enhances our understanding of the mechanisms governing hydrodynamic flow, crystal growth, magnetism, and wave propagation. It also informs smarter design of materials with customizable properties. This project aims to develop a robust understanding of these macroscopic phenomena, using fundamental concepts from single-particle diffusion Laplacians and Dirichlet energy forms on a wide variety of state spaces, including networks, trees, and fractals. An integral part of this project will involve promotion of, and training in, probability and statistical mechanics through the PI's teaching and research with undergraduate students.This project focuses on the analysis of interacting particle systems on state spaces which need not possess spatial symmetries, but are bounded in the metric determined by electrical resistance. The PI will carry out, on these resistance spaces, rigorous derivations of nonlinear (Stochastic) Partial Differential Equations as scaling limits of empirical observables in the weakly asymmetric exclusion processes. Emphasis will be on the role played by the parameters governing the bulk exclusion as well as the boundary Kawasaki dynamics, leading to macroscopic phase transitions and nonlinear effects. The PI will utilize novel functional inequalities, algebraic identities, coarse-graining methods, and analysis of (S)PDEs to establish limit theorems. The overall goal is to obtain a self-consistent understanding of non-equilibrium statistical mechanics on large-scale networks, through a combination of probabilistic tools and non-smooth global analysis.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.

对微观概率模型的严格分析增强了我们对管理水动力流，晶体生长，磁性和波传播的机制的理解。它还为具有可自定义属性的材料设计更智能设计。该项目旨在利用来自单粒子扩散拉普拉斯主义者的基本概念对这些宏观现象进行强有力的理解，并在包括网络，树木和分形等各种状态空间上形成了各种状态空间。该项目的一个组成部分将涉及通过PI与本科生的教学和研究来促进和培训概率和统计力学。该项目重点介绍了不需要具有空间对称性的状态空间上相互作用粒子系统的分析，但在指标中由电力抗性确定。 PI将在这些电阻空间上执行非线性（随机）部分微分方程的严格派生，作为在弱不对称的排除过程中经验可观察物的缩放限制。重点将取决于管理批量排除的参数以及川崎动力学的作用，从而导致宏观相变和非线性效应。 PI将利用新型的功能不平等，代数身份，粗粒度方法和对PDE的分析来建立限制定理。总体目的是通过结合概率工具和非平滑全球分析的组合对大规模网络上的非平衡统计力学获得自洽的理解。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的评估审查审查的评论来通过评估来获得支持的。

项目成果

Spectral Decimation of the Magnetic Laplacian on the Sierpinski Gasket: Solving the Hofstadter–Sierpinski Butterfly

谢尔宾斯基垫片上磁性拉普拉斯的光谱抽取：解决霍夫施塔特 - 谢尔宾斯基蝴蝶问题

• DOI: 10.1007/s00220-020-03850-w
• 发表时间: 2020
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Chen, Joe P.;Guo, Ruoyu
• 通讯作者: Guo, Ruoyu

Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions

SierpiÅski 垫片上的拉普拉斯生长和沙堆：限制形状通用性和精确解

• DOI: 10.4171/aihpd/95
• 发表时间: 2020
• 期刊: Annales de l’Institut Henri Poincaré D
• 作者: Chen, Joe;Kudler-Flam, Jonah
• 通讯作者: Kudler-Flam, Jonah

Asymptotic Behavior of Density in the Boundary-Driven Exclusion Process on the Sierpinski Gasket

Sierpinski 垫片边界驱动排除过程中密度的渐近行为

• DOI: 10.1007/s11040-021-09392-4
• 发表时间: 2021
• 期刊: Analysis and Geometry
• 作者: Chen, Joe P.;Gonçalves, Patrícia
• 通讯作者: Gonçalves, Patrícia

Higher-order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems

相互作用粒子系统的高阶流体动力学和平衡涨落

• 发表时间: 2021
• 期刊: Markov processes and related fields
• 影响因子: 0.2
• 作者: Chen, Joe P.;Sau, Federico
• 通讯作者: Sau, Federico