| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 3, 2014 |
| Latest Amendment Date: | September 3, 2014 |
| Award Number: | 1460319 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Andrew Pollington
adpollin@nsf.gov (703)292-4878 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2014 |
| End Date: | August 31, 2016 (Estimated) |
| Total Intended Award Amount: | $123,857.00 |
| Total Awarded Amount to Date: | $123,857.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
801 UNIVERSITY BLVD TUSCALOOSA AL US 35401-2029 (205)348-5152 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
801 University Blvd. Tuscaloosa AL US 35487-0104 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
OPPORTUNITIES FOR RESEARCH CMG, MATHEMATICAL GEOSCIENCES |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
1. Major problem focused by this project
Contaminant transport through natural geological media 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. To address this issue, collaborative efforts in hydrogeology and mathematics are required to develop flexible, efficient, and faithful transport models, which is the major focus of this project.
2. Project outcomes addressing the intellectual merit
Outcomes of this project can be summarized into three groups: 1) Tempered stable models and a spatiotemporally nonlocal transport theory that can capture pre-asymptotic solute transport, or transient diffusion, in heterogeneous media varying from local to regional scales; 2) Mesh-less, particle-tracking based Lagrangian solvers that can efficiently approximate various tempered stable models with both early arrivals and solute retentions in irregular flow fields; and 3) Quantitative linkage between medium properties, especially the property of aquitards that were typically ignored by traditional hydrologic studies, and parameters in tempered stable models.
This project found that the generalized non-local transport model, namely the tempered stable model in both space and time, might serve a universal model for hydrologic processes occurring on land surface (i.e., sediment transport in rivers, and surface runoff along hillslopes), vadose zone (water moving in unsaturated soils), and subsurface (i.e., conservative or reactive pollutants transport in aquifer-aquitard systems, porous media, or fractured rock masses). The multi-scale heterogeneity embedded in natural geological media, which generates complex anomalous dynamics, is the hydrogeological reason motivating the application of spatiotemporal nonlocal transport models such as the stable model. We expect that this project (with a unique and extremely helpful combination of mathematicians and hydrologists) may eventually motivate the next generation mathematical models for real-world hydrologic dynamics.
3. Broader Impacts of this project
Results of this interdisciplinary research, which blends hydrology with probability and statistics, may provide suggestions for future research for fractional calculus. On one hand, fractional engine finds its home in statistical physics and applied mathematics. On the other hand, anomalous diffusion has been observed in many disciplines from the nanoscale in biological systems to very large-scale geophysical, environmental, and financial systems. The novel tempered stable laws with partially predictable parameters, the computational efficient grid-free Lagrangian solver, and the laboratory experiments conducted in this project may enhance the theoretical study and application of anomalous diffusion in the above disciplines, as shown by the fact that our works have been cited by scientists from part of the above disciplines. In addition, this project also supported and trained graduate students who gained both marketability and relevance.
Last Modified: 09/30/2016
Modified by: Yong Zhang
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