Kinetic transport and dynamics in complex interacting systems: analysis and simulations

复杂相互作用系统中的动能传输和动力学：分析和模拟

• 批准号: 1109625
• 负责人: Irene Gamba
• 金额: $ 21万
• 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: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109625&HistoricalAwards=false
• 关键词: Kinetic; transport; dynamics; complex; interacting

The objective of this proposal focus on a broad program in analytical and numerical problems associated with the complex nature of non-conservative particle interactions in a kinetic (integro-differential Boltzmann type) framework of statistical transport equations. These models appear and the studies of semi-classical transport for short and long range interactions models that describe self-consistent phenomena at nano and mesoscales. More recently they have been appearing in the modeling of social interactions and the formation of networks such as Internet social dynamics and queuing in supply chains. New tools from non-linear analysis as well as new computational strategies need to be developed in order to address the linking from quantum to kinetic to fluid level of modeling. Of special interest is the understanding and developing of long time behaviour of the model, decay rates to stable modes, qualitative behavior of the solutions and optimal computational strategy. This area of research, essentially Applied Mathematics and Probability and Statistics, is related to Mathematical and Statistical Physics with remarkable new applications to non-linear dynamics modeling in Bio Sciences and Social Sciences as well. The investigated problems range into a broad area of statistical transport from modeling and prediction phenomena of rapid granular flows, reacting gas molecule mixtures, transport modeling at atomistic scale, particle swarms, opinion dynamics, multi-agent information transfer flow, and social information dynamics in Internet to name a few.

这项建议的目标是在统计输运方程的动力学(积分-微分Boltzmann类型)框架内，集中于与非保守粒子相互作用的复杂性质相关的分析和数值问题的广泛计划。这些模型的出现和对短程和长程相互作用的半经典输运的研究描述了纳米和介观尺度上的自洽现象。最近，它们出现在社会互动的建模和网络的形成中，如互联网、社会动态和供应链中的排队。需要开发非线性分析的新工具以及新的计算策略，以解决从量子到动力学再到流体层面的建模联系。特别令人感兴趣的是了解和发展模型的长期行为、衰减率到稳定模式、解的定性行为和最优计算策略。这一研究领域，主要是应用数学和概率统计，与数学和统计物理有关，在生物科学和社会科学中也有显著的非线性动力学建模的新应用。所研究的问题涉及到统计传输的广泛领域，从快速颗粒流的建模和预测现象、反应气体分子混合物、原子尺度的传输建模、粒子群、舆论动力学、多智能体信息传输流和互联网中的社会信息动力学等等。