CMG COLLABORATIVE RESEARCH: Mathematics and Electromagnetics for Monitoring Transport Processes in Sea Ice

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Golden 0934721University of UtahFunds are provided to develop methods of electromagnetically monitoring the internal state of sea ice, the thermal evolution of its microstructure, and the transport processes it controls. The PIs will conduct fundamental mathematical studies, as well as field experiments in the Arctic and Antarctic, directed at recovering microstructual profiles and their evolution at critical phases in the seasonal cycle of the ice pack. They will develop in situ tomographic methods to obtain the complex permittivity profile o sea ice at low frequency, and mathematical techniques to use this data to reconstruct the evolution of the spectral measure of the composite microstructure, which contains detailed information about brine geometry and connectedness. They will investigate the critical behavior of this measure near the percolation threshold, where fluid flow turns on or off. Our work will yield novel spectral representations for fluid and thermal transport coefficients, and characterizations of the spectral measure as a free energy minimizer, as in statistical mechanics. They will analyze the thermal evolution of the distribution of eigenvalue spacings for the spectral measure as a powerful way of characterizing the order/disorder transition in the brine microstructure of sea ice, as motivated by the theory of random matrices. They will also develop multiscale numerical models of the complex permittivity and other transport properties from random graph representations of the microstructure to aid reconstruction calculations. Their results will yield valuable information on snow-ice formation, melt processes, and flood-freeze cycling, and provide insights on parameterizing these processes in climate and biogeochemical models. Key features of the proposed work include:? Development of cross-borehole tomography and direct measurement techniques on cores. Initial testing, validation and refinement in the lab and the Arctic near Barrow, with Antarctic measurements.? Development of cross-property relations connecting EM, thermal, and fluid transport via the spectral measure, and related methods for EM imaging of transport processes in sea ice.