Collisional Kinetic Transport: Analysis and Numerical Methods

碰撞动力学输运：分析和数值方法

基本信息

批准号：
2009736
负责人：
Irene Gamba
金额：
$ 34.5万
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：
2020
资助国家：
美国
起止时间：
2020-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2009736&HistoricalAwards=false
关键词：
Collisional Kinetic Transport Analysis Numerical

项目摘要

The overall objective of this research is to develop accurate analytical modeling and simulation for a series of diverse phenomena of fundamental scientific interest, at the edge of various technological developments such as plasma evolution in fusion models, modeling of very cold gases in the intermediate transition to form Bose-Einstein condensation, hot-electron transport in semiconductor devices, nanostructures for solar generation of hydrogen, and reacting and polyatomic molecular mixtures associated with aerospace dynamics such as those in re-entry problems. Modeling and simulation will be based on data obtained by accurate crystallographic calculations, considering atomistic corrections, and the presence of rough media. Some of the techniques that will be developed are also pertinent to exciting new applications to non-linear dynamics modeling in bio-social sciences, such as modeling of self-organized flows where "particle" swarms, like birds or fish, couple to fluid dynamics, emerging consensus in population dynamics, multi-agent information transfer and social information dynamics in Internet, to name a few. Most significantly, this project provides research training opportunities for graduate students that prepare them to a job market that ranges from academia, to national labs, and industry.These research goals comprise a broad program in the development of analytical and numerical tools associated with statistical transport equations and systems at the core of applied mathematics in probability, statistics applied to chemistry, physics as well as to biological and 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 Smolukowski type. Computational schemes will be fully designed and analyzed to secure consistency, stability, error estimates control, and convergence rates to equilibrium. Many of these models appear in the collisional theory of semi-classical transport for short- and long-range particle interactions models that describe self-consistent phenomena at nano and meso-scales. New tools from non-linear 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.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.

这项研究的总体目标是在各种技术发展的边缘，为一系列具有基础科学意义的不同现象开发精确的分析模型和模拟，例如聚变模型中的等离子体演化、在中间过渡过程中对极冷气体的建模。形成玻色-爱因斯坦凝聚、半导体器件中的热电子传输、太阳能产生氢的纳米结构，以及与航空航天动力学（例如再入问题中的那些）相关的反应和多原子分子混合物。建模和模拟将基于通过精确晶体学计算获得的数据，考虑原子校正和粗糙介质的存在。将开发的一些技术也与生物社会科学中非线性动力学建模的令人兴奋的新应用相关，例如对自组织流进行建模，其中“粒子”群（如鸟类或鱼类）与流体动力学耦合，在人口动态、多智能体信息传递和互联网社会信息动态等方面正在形成共识。最重要的是，该项目为研究生提供研究培训机会，帮助他们为进入学术界、国家实验室和工业界的就业市场做好准备。这些研究目标包括开发与统计运输相关的分析和数值工具的广泛计划方程和系统是概率应用数学的核心，统计应用于化学、物理以及生物和社会动力学。他们关注复杂相互作用系统的建模，产生与出生-死亡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玻尔兹曼或斯莫卢科夫斯基类型的非线性积分微分方程组。计算方案将经过全面设计和分析，以确保一致性、稳定性、误差估计控制和平衡收敛速度。其中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。将开发非线性分析的新工具以及新的计算策略，以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。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。