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

污染物通过天然含水层的迁移在空间和时间尺度上表现出典型的前渐近或瞬态异常行为，这对大多数环境问题至关重要。复杂的和通常不可预测的介质异质性在所有相关的尺度激励非本地传输理论的应用。拟议的工作将开发回火稳定模型，通过调整分形幂律来推广标准的非局域传输理论，以模拟前渐近传输并揭示以前错过的真实世界色散的性质。将有三个主要成果，包括（1）一个新的非局部传输理论和模型的基础上回火幂律，可以有效地模拟瞬态异常扩散，（2）之间的定量联系的可观察的统计数据的天然非均匀介质和模型参数建立了一个系统的蒙特卡洛研究，和（3）一个方便的软件套件与开源代码，解决和应用模型。这项合作研究还将通过使用历史示踪剂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，将确保所得到的模型不仅限于曲线拟合application.Accurate预测污染物迁移在现实世界的含水层是至关重要的地下水保护和清理。拟议的工作将开发适当的传输理论，并建立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，拟议的工作更准确地代表分数微积分和幂律统计之间的联系，在真实的含水层材料。PI团队包括数学家和水文学家，在前沿研究中形成跨学科合作。

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.