Non-local Kinetic Collisional Transport: Analysis and Numerical Methods

非局部动力学碰撞传输：分析和数值方法

• 批准号: 1715515
• 负责人: Irene Gamba
• 金额: $ 31万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715515&HistoricalAwards=false
• 关键词: Non; local; Kinetic; Collisional; Transport

The overall objective of this research is to develop accurate mathematical modeling and methods of numerical simulation for an array of diverse natural and engineering processes of fundamental scientific interest, such as evolution of plasmas in fusion devices, dynamics of very cold gases in the intermediate transition to form Bose-Einstein condensates,  hot-electron transport in semiconductor devices, design of nanostructures for the solar generation of hydrogen, dynamics of reacting molecular mixtures associated to aerospace dynamics of re-entry problems. All these phenomena are unified by the underlying structure of their mathematical description that involves "particles" interactions of different kinds. A study of these mathematical structures is the principal subject of this project. Modelling and simulation will be based on data obtained by accurate crystallographic calculations, taking into account atomistic corrections, the presence of rough media, etc. Same of the techniques that we will develop are pertinent to exciting new applications in biological and social sciences. They include modeling of self-organized flows in "particle" swarms like birds or fish, emerging consensus in population dynamics, multi-agent information transfer and social information dynamics in internet, to name a few. Research goals of the project comprise a broad program in the development of analytical and numerical tools associated with statistical transport equations at the core of applied mathematics in probability, statistics applied to chemistry, physics and to an extent, to social dynamics as well. They concern the modeling of complex interactions systems yielding kinetic frameworks associated to Markovian processes of birth-death dynamics. Such statistical approaches lead to nonlinear integro-differential systems of equations of collisional classical or quantum Boltzmann or Smoluchowski type. Many of these models appear in the collisional theory of semi-classical transport for short- and long-range particle interactions models that describing self-consistent phenomena at nano and mesoscales.  New tools from nonlinear analysis as well as new computational strategies will be developed to address long-time behavior, stability and decay rates to stationary modes, as well as qualitative behavior of numerical solutions and optimal computational strategies.

这项研究的总体目标是为一系列具有基本科学意义的各种自然和工程过程开发精确的数学建模和数值模拟方法，例如聚变装置中等离子体的演化，中间过渡中形成玻色-爱因斯坦凝聚体的非常冷的气体的动力学，半导体器件中的热电子输运，设计太阳能产生氢气的纳米结构，与重返大气层问题的航空航天动力学有关的分子混合物反应动力学。所有这些现象都是由它们的数学描述的基本结构统一起来的，这种数学描述涉及不同种类的“粒子”相互作用。对这些数学结构的研究是本项目的主要课题。建模和模拟将基于通过精确的晶体学计算获得的数据，同时考虑到原子校正，粗糙介质的存在等，我们将开发的技术与生物和社会科学中令人兴奋的新应用有关。它们包括“粒子”群（如鸟类或鱼类）中自组织流的建模，人口动力学中的新兴共识，多代理信息传输和互联网中的社会信息动力学，仅举几例。该项目的研究目标包括一个广泛的计划，在概率应用数学的核心，应用于化学，物理学的统计学，并在一定程度上，社会动力学以及与统计运输方程相关的分析和数值工具的开发。它们涉及复杂的相互作用系统的建模，产生与马尔可夫过程的生灭动力学相关的动力学框架。这样的统计方法导致碰撞经典或量子玻尔兹曼或Smoluchowski型方程的非线性积分微分系统。这些模型中的许多出现在描述纳米和介观尺度自洽现象的短程和长程粒子相互作用模型的半经典输运碰撞理论中。来自非线性分析的新工具以及新的计算策略将被开发来解决稳态模式的长时间行为、稳定性和衰减率，以及数值解和最优计算策略的定性行为。

项目成果

Convergence and Error Estimates for the Lagrangian-Based Conservative Spectral Method for Boltzmann Equations

• DOI: 10.1137/18m1173332
• 发表时间: 2016-11
• 期刊: SIAM J. Numer. Anal.
• 作者: R. Alonso;I. Gamba;S. H. Tharkabhushanam

Galerkin methods for Boltzmann–Poisson transport with reflection conditions on rough boundaries

粗糙边界反射条件下玻尔兹曼-泊松输运的 Galerkin 方法

• DOI: 10.1016/j.jcp.2018.02.041
• 发表时间: 2018
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Morales Escalante, José A.;Gamba, Irene M.
• 通讯作者: Gamba, Irene M.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

朗道动力学方程及相关模型的弛豫率研究

• DOI: 10.1007/s10955-017-1814-y
• 发表时间: 2017
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: Bobylev, Alexander;Gamba, Irene M.;Zhang, Chenglong
• 通讯作者: Zhang, Chenglong

A FAST SPECTRAL METHOD FOR THE BOLTZMANN COLLISION OPERATOR WITH GENERAL COLLISION KERNELS

• DOI: 10.1137/16m1096001
• 发表时间: 2017-01-01
• 期刊: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• 影响因子: 3.1
• 作者: Gamba, Irene M.;Haack, Jeffrey R.;Hu, Jingwei
• 通讯作者: Hu, Jingwei

Global Weak Solutions to Compressible Navier–Stokes–Vlasov–Boltzmann Systems for Spray Dynamics

• DOI: 10.1007/s00021-020-00505-7
• 发表时间: 2018-06
• 期刊: Journal of Mathematical Fluid Mechanics
• 影响因子: 1.3
• 作者: I. Gamba;Cheng Yu