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

基本信息

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

项目摘要

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础科学意义的不同自然和工程过程开发精确的数学模型和数值模拟方法，例如聚变装置中等离子体的演化、极冷气体在中间过渡过程中的动力学。玻色-爱因斯坦凝聚体的形成、半导体器件中的热电子传输、太阳能产生氢的纳米结构的设计、与再入问题的航空航天动力学相关的反应分子混合物的动力学，所有这些现象都由其基础结构统一起来。涉及不同类型“粒子”相互作用的数学描述是该项目的主要主题，建模和模拟将基于精确的晶体学计算获得的数据，同时考虑到原子校正和粗糙度的存在。我们将开发的相同技术与生物和社会科学中令人兴奋的新应用相关，其中包括对鸟类或鱼类等“粒子”群中的自组织流进行建模，在种群动态、多态性方面形成共识。代理人仅举几例，该项目的研究目标包括开发与概率应用数学、化学统计中的统计传输方程相关的分析和数值工具的广泛计划。它们涉及复杂的相互作用系统的建模，产生与生灭动力学的马尔可夫过程相关的动力学框架，这种统计方法导致了碰撞经典或量子方程的非线性积分微分系统。玻尔兹曼或Smoluchowski 类型中的许多模型出现在短程和长程粒子相互作用模型的半经典输运碰撞理论中，这些模型描述了纳米和介观尺度的自洽现象。旨在解决稳态模式的长期行为、稳定性和衰减率，以及数值解和最佳计算策略的定性行为。

项目成果

期刊论文数量（11）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

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

基于拉格朗日的玻尔兹曼方程保守谱法的收敛性和误差估计

DOI：
10.1137/18m1173332
发表时间：
2016-11-13
期刊：
SIAM J. Numer. Anal.
影响因子：
0
作者：
R. Alonso;I. Gamba;S. H. Tharkabhushanam
通讯作者：
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：
2018-06
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 Existence and Uniqueness to Homogeneous Boltzmann Flows of Monatomic Gas Mixtures

单原子混合气体均匀玻尔兹曼流的存在唯一性

DOI：
10.1007/s00205-019-01428-y
发表时间：
2018-06-25
期刊：
Archive for Rational Mechanics and Analysis
影响因子：
2.5
作者：
I. Gamba;M. Pavić
通讯作者：
M. Pavić

Commentary: Three decades after Cathleen Synge Morawetz’s paper “The mathematical approach to the sonic barrier”

评论：Cathleen Synge Morawetz 论文“声屏障的数学方法”发表三十年后

DOI：
10.1090/bull/1620
发表时间：
2018-07
期刊：
Bulletin of the American Mathematical Society
影响因子：
1.3
作者：
Gamba; Irene M.
通讯作者：
Irene M.

Discontinuous Galerkin deterministic solvers for a Boltzmann–Poisson model of hot electron transport by averaged empirical pseudopotential band structures

通过平均经验赝势能带结构求解热电子输运玻尔兹曼泊松模型的不连续伽辽金确定性求解器

DOI：
10.1016/j.cma.2017.03.003
发表时间：
2017-07
期刊：
Computer Methods in Applied Mechanics and Engineering
影响因子：
7.2
作者：
Morales;Gamba, Irene M.;Cheng, Yingda;Majorana, Armando;Shu, Chi;Chelikowsky, James
通讯作者：
Chelikowsky, James