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

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。Eicken 0934683阿拉斯加费尔班克斯大学提供资金用于开发电磁监测海冰内部状态，其微观结构的热演化及其控制的传输过程的方法。极地考察团将进行基础数学研究，并在北极和南极进行实地实验，目的是恢复冰群季节循环关键阶段的微观结构概况及其演变。他们将开发原位层析成像方法，以获得海冰低频的复杂介电常数剖面，并使用数学技术，利用这些数据重建复合微观结构的光谱测量演变，其中包含有关盐水几何形状和连通性的详细信息。他们将研究这一措施在渗流阈值附近的关键行为，即流体流动开启或关闭的地方。我们的工作将产生新的流体和热输运系数的谱表示，以及谱测量作为自由能量最小化的特征，就像在统计力学中一样。他们将分析光谱测量的特征值间隔分布的热演化，作为表征海冰盐水微观结构有序/无序转变的有力方法，这是由随机矩阵理论驱动的。他们还将从微观结构的随机图表示中开发复杂介电常数和其他输运性质的多尺度数值模型，以帮助重建计算。他们的研究结果将提供有关冰雪形成、融化过程和洪水-冻结循环的宝贵信息，并为气候和生物地球化学模型参数化这些过程提供见解。建议工作的主要特点包括：？岩心井间层析成像和直接测量技术的发展。在实验室和巴罗附近的北极进行初步测试、验证和改进，并进行南极测量。通过光谱测量建立连接EM、热和流体输运的交叉性质关系，以及海冰输运过程的EM成像相关方法。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Eicken 0934683University of Alaska FairbanksFunds 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.