Statistical transport of complex particle systems

复杂粒子系统的统计传输

• 批准号: 0807712
• 负责人: Irene Gamba
• 金额: $ 15万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0807712&HistoricalAwards=false
• 关键词: Statistical; transport; complex; particle; systems

This research project is an analytical and numerical study of statistical transport under complex, non-conservative particle interactions. The models under study include kinetic integro-differential equations of Boltzmann type and semiclassical quantum probability transport models. Modeling, analysis, and development of numerical methods will be conducted in three primary problem areas:(1) Statistical models related to energy-dissipative phenomena, including hard sphere equations for kinetic models of rapid granular flow and dynamics of gas mixtures. (2) Mesoscale kinetic systems modeled by Boltzmann-Poisson and Vlasov-Poisson systems under strong shear forces induced by electric fields or by boundary driving forces. (3) Semiclassical quantum trajectory models for flow of quantum probability distributions, with application to problems in nanoscale modeling.New tools from non-linear analysis as well as new computational strategies will be developed to establish links from quantum to kinetic to fluid levels of modeling.This research concerns the development and analysis of mathematical models for a number of important scientific problems. The models, which arise in biological, social, and physical sciences, describe statistically the transport of large numbers of interacting objects. Applications include modeling of rapid granular flows, chemically reacting gas mixtures, distribution of wealth in economic systems, opinion dynamics, and semiconductor behavior. This project will develop new mathematical tools that aid in the analysis of such models and their use in predicting the behavior of these complicated systems.

该研究项目是对复杂、非保守粒子相互作用下的统计输运的分析和数值研究。 正在研究的模型包括玻尔兹曼型动力学积分微分方程和半经典量子概率输运模型。 数值方法的建模、分析和开发将在三个主要问题领域进行：（1）与能量耗散现象相关的统计模型，包括快速颗粒流动力学模型和气体混合物动力学的硬球方程。 (2) 在由电场或边界驱动力引起的强剪切力下，由 Boltzmann-Poisson 和 Vlasov-Poisson 系统建模的中尺度动力学系统。 （3）量子概率分布流的半经典量子轨迹模型，应用于纳米级建模问题。将开发非线性分析的新工具以及新的计算策略，以建立从量子到动力学到流体水平建模的联系.这项研究涉及许多重要科学问题的数学模型的开发和分析。 这些模型出现在生物、社会和物理科学中，以统计方式描述大量相互作用物体的传输。 应用包括快速颗粒流建模、化学反应气体混合物、经济系统中的财富分配、舆论动态和半导体行为。 该项目将开发新的数学工具，帮助分析此类模型及其在预测这些复杂系统的行为中的应用。