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

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资金。Eicken 0934683阿拉斯加大学费尔班克斯分校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运输过程的方法。首席研究员将进行基础数学研究，并在北极和南极进行实地实验，旨在恢复冰袋季节性循环关键阶段的微观结构特征及其演化。他们将开发原位断层扫描方法，以获得低频海冰的复杂介电常数剖面，并开发数学技术，使用这些数据来重建复合微结构的光谱测量的演化，其中包含有关盐水几何形状和连通性的详细信息。他们将研究该措施在渗透阈值（流体流动打开或关闭）附近的关键行为。我们的工作将为流体和热传输系数产生新颖的光谱表示，以及作为自由能最小化器的光谱测量的表征，如统计力学中那样。他们将分析光谱测量的特征值间距分布的热演化，作为表征海冰盐水微观结构中有序/无序转变的有效方法，这是由随机矩阵理论推动的。他们还将根据微观结构的随机图形表示来开发复介电常数和其他传输特性的多尺度数值模型，以帮助重建计算。他们的研究结果将产生有关冰雪形成、融化过程和洪水冰冻循环的宝贵信息，并为在气候和生物地球化学模型中参数化这些过程提供见解。拟议工作的主要特点包括：？开发跨钻孔断层扫描和岩心直接测量技术。在实验室和巴罗附近的北极以及南极测量中进行初步测试、验证和完善。通过光谱测量开发连接电磁、热和流体传输的跨属性关系，以及海冰传输过程电磁成像的相关方法。

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.