Workshop on: Modern Mathematical/Physical Tools That May Lead To Improved Models in Subsurface Hydrology

0314651库什曼从历史上看，地下水文学的主要进步或根本性的范式转变是从其他学科借鉴的思想或工具的结果。 在这些想法和工具是地质统计数据合成，随机模型，数值解偏微分方程的，广义尺度和粗粒化的概念。虽然在过去的几十年里，在模拟地下水流和输运方面取得了重大进展，但我们离能够定量预测更深地下（含水层）中可混溶和不混溶流体和胶体的运动以及近地表（土壤）中水和溶解成分的运动还有很长的路要走。 多相流理论、膨胀介质中的流动、空间非均匀性的描述和分支、滞后、化学老化、微生物传输和降解、多尺度过程等方面的困难比比皆是。将来自不同学科的研究人员聚集在一起（例如，数学、物理、化学、工程科学），讨论他们解决其他科学领域相关问题的方法，并使他们能够与水文学家交流。为NSF水文学撰写一份白色论文，介绍有可能大大推进水文建模的现代工具和方法。预计将讨论各种各样的主题和方法：其中包括混沌和非线性动力学，均匀化，CTRW和分数方法，随机动力学，非平衡统计力学，渗流，重整化，投影算子，随机扰动理论，复杂性理论，以及其他许多理论。 会议将不关注数值方法，而是关注描述多尺度物理，化学和微生物学的新方法。

0314651CushmanHistorically the major advances, or radical paradigm shifts, in subsurface hydrology have been the result of ideas or tools borrowed from other disciplines. Among these ideas and tools are geostatistical data synthesis, stochastic models, numerical solutions to PDE's, and generalized scaling and coarse graining concepts. Though significant progress has been made over the past few decades in modeling subsurface flows and transport, we are a long way from being able to quantitatively predict the movement of miscible and immiscible fluids and colloids in the deeper subsurface (aquifers), and of water and dissolved constituents in the near-surface (soils). Difficulties abound with theories of multiphase flow, flow in swelling media, descriptions and ramifications of spatial heterogeneity, hysteresis, chemical aging, microbial transport and degradation, multiscale processes, and etc. There are two purposes for the proposed workshop:i. To bring together researchers from disparate disciplines (e.g., math, physics, chemistry, engineering sciences) to discuss their approaches to related problems in other fields of science, and allow them to interface with hydrologists.ii. To write a white paper for NSF-hydrology on modern tools and approaches which have the potential to seriously advance hydrologic modeling.It is anticipated that a wide variety of topics and approaches will be discussed: Among these are chaos and nonlinear dynamics, homogenization, CTRW and fractional approaches, stochastic dynamics, nonequilibrium statistical mechanics, percolation, renormalization, projection operators, stochastic perturbation theories, complexity theory, as well as many others. The conference will not focus on numerical methods, but rather on novel approaches to describe multiscale physics, chemistry and microbiology.