Mathematical Sciences: Percolation in Composite Materials

9622367黄金我们建议开发新的分析和数值技术 用于研究许多渗流模型的行为 在高对比度复合材料的研究中出现。 一些发展方向包括：（i）探索随机电阻网络的临界行为，根据一种新的，直接对应于伊辛模型，（ii）分析连续渗流模型的多孔介质 和基质颗粒复合材料，（iii）开发诊断 一种非破坏性地判断 复合酸盐或没有，这可能有应用程序， 复合材料失效检测或质量控制 制造，以及（iv）模拟热量和盐水的传输 穿过海冰这种多孔介质 材料科学中的一系列问题都涉及到复合材料 其特征在于， 组件。对于这样的媒体，有效的行为往往是 由连通性或渗透性质主导， 特殊阶段。实例包括多孔介质、掺杂的半导体， 智能材料，如压敏电阻和压敏电阻，薄金属 薄膜（用于太阳能生产），含油砂岩， 岩石和金属的断裂模式，人类的许多结构 海冰（在气候中起着重要作用， 全球变化指标）。在拟议的工作中，我们将研究 这些材料的数学模型。我们预计这个项目 将进一步提高我们预测 天然存在的或人工制造的复杂随机材料， 以及帮助开发设计成获得新颖或最佳性能的复合材料。 ***

9622367 Golden We propose to develop new analytical and numerical techniques for investigating the behavior of a number of percolation models arising in the study of high contrast composite materials. Some of the directions for development include: (i) exploring the critical behavior of the random resistor network in light of a new, direct correspondence with the Ising model, (ii) analysis of continuum percolation models for porous media and matrix-particle composites, (iii) developing a diagnostic method for non-destructively telling whether one phase in a composite percolates or not, which could have applications to the detection of material failure or quality control for composite manufacturing, and (iv) modeling the transport of heat and brine through sea ice, a porous medium. %%% A broad range of problems in materials science involve composites which can be characterized by a high contrast in the properties of the components. For such media, the effective behavior is often dominated by the connectedness, or percolation properties of a particular phase. Examples include porous media, doped semiconductors, smart materials such as piezoresistors and thermistors, thin metal films (used in solar energy production), oil bearing sandstones, fracture patterns in rocks and metals, many structures in the human body, and sea ice (which plays a major role in climate and is an indicator of global change). In the proposed work we will study mathematical models of such materials. We anticipate that this project will further our capabilities to predict the effective behavior of naturally occurring or artificially made complex random materials, as well as aid the development of composites designed to achieve novel or optimal properties. ***