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Final Progress Reports: University of North Carolina-Chapel Hill: Mathematical and Statistical Analysis and Modeling Core

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Superfund Research Program

Mathematical and Statistical Analysis and Modeling Core

Project Leader: Cass T. Miller
Grant Number: P42ES005948
Funding Period: 2000 - 2011

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Final Progress Reports

Year:   2005 

The goal of this core is to provide quantitative support for all other components of the SBRP. These activities include experimental design, data analysis, hypothesis testing, and assistance with mechanistic model building and model solving for natural environmental and living systems. As such, the activities of the core range from applications of known quantitative tools to the development of new tools. Notable activities over the past year include: statistical and mechanistic modeling of exposure, spatial/temporal modeling of arsenic distribution, advances in multiphase porous medium model building, and development of new methods of solution for fate and transport models.  The core researchers comment briefly below on these four classes of activities.

The active collaboration in the area of biostatistical modeling of biomarkers of exposure has been continued. This work has increasingly focused on the development of more mechanistic models. Mechanistic dermal exposure modeling has also been initiated this year between the Core and Project 8. This work is starting with the construction of a diffusion model to evaluate the movement of contaminants through the skin. Core researchers anticipate extending this work to increasingly more realistic models that have a similarity with porous medium systems.

Together these activities will lead to more accurate and precise measures of contaminant exposure based upon quantitative biomedical measures.

The core has continued to collaborate with Project 7 to analyze multiple sources of arsenic data from New Jersey. The data set in hand involves several thousand measurements from three different classes of wells. One of these classes of data has privacy issues associated with it, which requires perturbing the actual location prior to use. This raises statistical estimation issues of a general nature that have not been evaluated or resolved with the Bayesian maximum entropy method of analysis being used. These results will be generalized to other related sets of data in which uncertainty in the location of the data exists.

Assessment and control of exposure and design of remediation systems at Superfund sites often rely upon models of how contaminants move in the environment. The core has been supporting ongoing fundamental work to develop rigorous multiscale models to describe fluid flow and contaminant transport in multiphase porous medium systems. The researchers have continued to develop pore-scale lattice Boltzmann simulation models for two-phase flow in a porous medium system and used these models to simulate dissolution of a nonaqueous phase liquid at the microscale, which has led to new mechanistic insights.

Mechanistic models of fate, transport, and exposure typically result in systems of differential equations that cannot be solved analytically and must be approximated numerically. Over the last year core researchers have made advancements to a variety of modeling approaches, such as Eulerian-Lagrangian methods, spatially and temporally adaptive methods, and evolving discrete approaches for spatially variable problems. These advances are expected to lead to increasingly higher fidelity simulations of natural systems and, therefore, more informed decisions.

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