CMG Collaborative Research: Tempered Stable Models for Preasymptotic Pollutant Transport in Natural Media

CMG 合作研究：自然介质中渐进前污染物传输的稳定模型

• 批准号: 1025417
• 负责人: Yong Zhang
• 金额: $ 31.58万
• 依托单位: Nevada System of Higher Education, Desert Research Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025417&HistoricalAwards=false
• 关键词: CMG; Collaborative; Research; Tempered; Stable

Contaminant transport through natural aquifers typically exhibits pre-asymptotic or transient anomalous behavior on the space and time scale critical to most environmental concerns. Complex and usually unpredictable medium heterogeneity at all relevant scales motivates the application of non-local transport theories. The proposed work will develop tempered stable models, which generalize standard non-local transport theories by adjusting fractal power-laws, to simulate pre-asymptotic transport and reveal the nature of real-world dispersion missed previously. There will be three major outcomes, including (1) a novel non-local transport theory and model based on tempered power laws that can efficiently simulate transient anomalous diffusion, (2) a quantitative linkage between the observable statistics of natural heterogeneous media and the model parameters built by a systematic Monte Carlo study, and (3) a convenient software suite with open source codes that solve and apply the model. This collaborative research will also test the model, the solver and the model predictability, by using historical tracer data and well-studied aquifer information. A careful consideration of the physical meaning of model components, and connections to statistical aquifer properties, will ensure that the resulting model is not limited to curve fitting applications.Accurate prediction of contaminant migration in real-world aquifers is critical to groundwater protection and cleanup. The proposed work will develop appropriate transport theory and build effective modeling components to address this problem. Hence this research is both highly theoretical and applied. In particular, the proposed work more accurately represents the underlying link between fractional calculus and power-law statistics in real aquifer material. The PI team includes mathematicians and hydrologists, forming interdisciplinary cooperation in cutting edge research.

通过天然含水层的污染物输送通常在空间和时间尺度上表现出渐近前或短暂的异常行为，这对大多数环境问题至关重要。所有相关尺度上复杂且通常不可预测的介质异质性激发了非局域传输理论的应用。拟议的工作将开发调和稳定模型，该模型通过调整分形幂律来推广标准非局域传输理论，以模拟渐进前传输并揭示之前遗漏的现实世界色散的本质。将产生三个主要成果，包括（1）基于缓和幂律的新型非局域传输理论和模型，可以有效地模拟瞬态异常扩散，（2）自然异质介质的可观测统计数据与模型之间的定量联系通过系统的蒙特卡罗研究建立的参数，以及 (3) 一个方便的软件套件，其中包含用于求解和应用模型的开源代码。这项合作研究还将利用历史示踪数据和经过充分研究的含水层信息来测试模型、求解器和模型的可预测性。仔细考虑模型组成部分的物理意义以及与统计含水层属性的联系，将确保所得模型不限于曲线拟合应用。准确预测现实含水层中污染物的迁移对于地下水保护和清理至关重要。拟议的工作将开发适当的运输理论并构建有效的建模组件来解决这个问题。因此，本研究具有很强的理论性和应用性。特别是，所提出的工作更准确地代表了真实含水层材料中分数阶微积分和幂律统计之间的潜在联系。 PI团队包括数学家和水文学家，在前沿研究方面形成跨学科合作。