CAREER: Applicable Kinetic Computation with Boundaries and Rough Media

职业：边界和粗糙介质的适用动力学计算

• 批准号: 1750488
• 负责人: Qin Li
• 金额: $ 40万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1750488&HistoricalAwards=false
• 关键词: CAREER; Applicable; Kinetic; Computation; Boundaries

Kinetic theory describes the dynamics of a large number of particles in a statistical manner. The theory is central to statistical mechanics and naturally connects the micro-world described by Newton's law and the macro-world described by the Navier-Stokes equations. Its applications arise from aerospace engineering, mechanical engineering, nuclear engineering, and atmospheric science. In all these engineering fields, rarified gas, photons, neutrons, and many other types of particles are modeled by kinetic equations. This research project aims to advance kinetic theory in both abstract and practical ways, developing novel theory that is widely applicable to systems of central interest in science and engineering. This research project concentrates on three main questions in kinetic theory: 1. theoretically and numerically understanding particles' interactions with boundaries/interfaces, with the focus placed on understanding the boundary layer behavior; 2. analytically and numerically relaxing homogeneity assumptions for the media, with both highly oscillatory and rough media considered; 3. studying uncertainties and sensitivities of the problem in both forward and backward manner, that is, tracing the propagation of perturbations in the forward setting to understand how error gets enlarged in the associated inverse problem. Due to the multi-scale multi-physics nature of kinetic theory, the theoretical results will largely be obtained from performing asymptotic analysis on the formal level and regularity theory on the rigorous level. To tackle the challenges in computation, the PI intends to incorporate solution structure given by partial-differential-equation analysis, and to explore randomized solvers that have seen success in data science and compressed sensing. Throughout the project, the PI intends to collaborate with engineers to ensure the techniques under development are truly applicable.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.

动力学理论以统计方式描述了大量粒子的动力学。该理论是统计力学的核心，自然地连接了牛顿定律所描述的微世界和Navier-Stokes方程所描述的宏观世界。它的应用来自航空工程，机械工程，核工程和大气科学。在所有这些工程领域，稀有气体，光子，中子和许多其他类型的颗粒都是通过动力学方程建模的。该研究项目旨在以抽象和实用的方式推进动力学理论，开发新的理论，该理论广泛适用于科学和工程学中的核心系统。该研究项目集中在动力学理论中的三个主要问题上：1。从理论和数字上理解粒子与边界/接口的相互作用，重点放在理解边界层行为上。 2。在分析和数值上放松的同质性假设对媒体进行了高度振荡和粗糙的培养基的假设； 3。以前和向后研究问题的不确定性和敏感性，也就是说，追踪在正向环境中扰动的传播，以了解如何在相关的逆问题中扩大误差。由于动力学理论的多尺度多物理性质，理论结果将在很大程度上通过对严格级别的正式水平和规律性理论进行渐近分析获得。为了应对计算中的挑战，PI打算结合通过部分差异方程分析给出的解决方案结构，并探索在数据科学和压缩传感方面取得成功的随机求解器。在整个项目中，PI打算与工程师合作，以确保正在开发的技术确实适用。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响评估标准，被认为值得通过评估来提供支持。

项目成果

Bridging and Improving Theoretical and Computational Electrical Impedance Tomography via Data Completion

通过数据补全桥接和改进理论和计算电阻抗断层扫描

• DOI: 10.1137/21m141703x
• 发表时间: 2022
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Bui-Thanh, Tan;Li, Qin;Zepeda-Nún͂ez, Leonardo
• 通讯作者: Zepeda-Nún͂ez, Leonardo

Applications of kinetic tools to inverse transport problems

动力学工具在逆输运问题中的应用

• DOI: 10.1088/1361-6420/ab59b8
• 发表时间: 2020
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: Li, Qin;Sun, Weiran
• 通讯作者: Sun, Weiran

Structured Random Sketching for PDE Inverse Problems

PDE 反问题的结构化随机草图

• DOI: 10.1137/20m1310497
• 发表时间: 2020
• 期刊: SIAM Journal on Matrix Analysis and Applications
• 影响因子: 1.5
• 作者: Chen, Ke;Li, Qin;Newton, Kit;Wright, Stephen J.
• 通讯作者: Wright, Stephen J.

Parameter Reconstruction for General Transport Equation

一般输运方程的参数重构

• DOI: 10.1137/19m1265739
• 发表时间: 2020
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Lai, Ru-Yu;Li, Qin
• 通讯作者: Li, Qin

Reconstructing the Thermal Phonon Transmission Coefficient at Solid Interfaces in the Phonon Transport Equation

重建声子输运方程中固体界面处的热声子传输系数

• DOI: 10.1137/20m1381666
• 发表时间: 2022
• 期刊: SIAM Journal on Applied Mathematics
• 影响因子: 1.9
• 作者: Gamba, Irene M.;Li, Qin;Nair, Anjali
• 通讯作者: Nair, Anjali