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

该提案的目标集中在与非保守粒子相互作用的动力学（积分微分玻尔兹曼型）框架中的统计输运方程的复杂性质相关的分析和数值问题的广泛计划。这些模型的出现和半经典输运的研究，描述自洽现象在纳米和介观尺度的短程和长程相互作用模型。 最近，它们出现在社会互动的建模和网络的形成，如互联网社会动力学和供应链中的排队。 需要开发来自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到流体水平建模的联系。特别感兴趣的是理解和发展的长期行为的模型，衰减率稳定模式，定性行为的解决方案和最佳的计算策略。这一研究领域，基本上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着的非线性动力学建模的新应用。所调查的问题涉及统计运输的广泛领域， 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，意见动力学，多代理信息传输流，以及互联网中的社会信息动力学等等。

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.