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流体动力流动、晶体生长、磁性和波传播机制的理解。它还为具有可定制属性的材料提供了更智能的设计。该项目旨在利用各种状态空间（包括网络、树和分形）上的单粒子扩散拉普拉斯算子和狄利克雷能量形式的基本概念，对这些宏观现象有一个强有力的理解。这个项目的一个组成部分将包括通过PI对本科生的教学和研究来促进和训练概率和统计力学。本项目的重点是分析状态空间上的相互作用粒子系统，这些状态空间不需要具有空间对称性，而是以电阻确定的度量为界。PI将在这些阻力空间上进行非线性（随机）偏微分方程的严格推导，作为弱不对称排斥过程中经验观测值的标度极限。重点将放在控制体排斥和边界川崎动力学的参数所起的作用，导致宏观相变和非线性效应。PI将利用新的功能不等式、代数恒等式、粗粒度方法和(S)偏微分方程的分析来建立极限定理。总体目标是通过概率工具和非光滑全局分析的结合，获得对大规模网络上非平衡统计力学的自洽理解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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