Analysis and Characterization of Multi-Phase Systems with Application to Optimal Design

小行星9700638 多相系统的分析和优化设计是本论文的核心内容。 开发用于电子、交通运输的先进材料 系统和航空航天应用。从人的角度来看， 生理学，理解复杂的运输现象是至关重要的， 生物系统。该项目涉及的领域， 多相系统的输运性质将对 技术.这个项目的一个重要部分集中在行为上， 不完全结合的复合材料。不完全键合 通常是规则。不完美的债券往往是 在使用过程中对结构造成的损坏。第一个项目对待 不完全粘结情况下纤维增强材料的设计 在纤维和基质材料之间。目标是提供严格的 非完全粘结纤维最佳性能的设计准则 加强结构。我们接下来考虑振荡的传输 通过具有不完全结合的结构材料的电信号 选民。我们寻找新的数学方法， 从传输的信号中提取结构信息。这些方法将依赖于 不完美的化学键的物理原理。第三 项目处理离子在生物系统中的传输。目标是 了解细胞几何形状对活体内离子运输的影响 组织.最后，非常大的布局所需的小几何形状 大规模集成电路引起电场沿着的高度集中 传导路径这些浓度往往导致一个 电子设备，如微处理器。导电路径通常 由三种或更多种材料的铝合金制成。我们追求最好的 以使电场最小化 浓度的 多相材料的分析和优化设计是多相材料设计的核心。 开发用于电子、交通运输的先进材料 系统和航空航天结构。从人的角度来看， 生理学，理解复杂的运输现象是至关重要的， 生物结构。该项目涉及改进的领域 多相结构的输运性质的知识将 对技术和医学的影响。纤维增强结构出现在 从高尔夫球杆到风车上的转子的许多应用。超过 纤维与周围材料之间的粘附力 因使用而受损。我们研究这种结构的优化设计 考虑到纤维和周围环境之间的不完美粘合 材料我们的目标是设计更耐用的产品， 传统的纤维增强产品。接下来，我们研究如何减少 微电子器件由于高浓度的电 电流集成电路布图中使用的小几何图形 需要非常窄的金属条来传导电流。这些条 经常因为它们携带的高电流量而失效。的 导电条通常由铝、铜和铝的混合物制成。 硅。我们寻求铜和硅的最佳部署， 金属条，以防止故障。最后，我们尝试改进表征 细胞间离子运输的过程从人体生理学的角度来看， 对人脑细胞这种运输的理解可能会提供早期的 检测中风造成的损伤程度。

9700638 Lipton The analysis and optimal design of multi-phase systems is central to the development of advanced materials for use in electronics, transportation systems, and aerospace applications. From the perspective of human physiology it is critical to understand transport phenomena in complex biological systems. This project addresses areas where improved knowledge of transport properties for multi-phase systems will have a large impact on technology. A significant part of this project focuses on the behavior of composites with imperfectly bonded components. Imperfect bonding between constituents is often the rule. Imperfect bonds are frequently the result of damage to the structure incurred during use. The first project treats the design of fiber reinforced materials in the presence of imperfect bonding between the fiber and the matrix material. The goal is to provide rigorous design rules for the optimal performance of imperfectly bonded fiber reinforced structures. We consider next the transmission of oscillating electric signals through structural materials possessing imperfectly bonded constituents. We look for new mathematical methods that will deliver structural information from the transmitted signal. These methods will rely on the physics of the imperfect bond separating the constituents. The third project treats the transport of ions in a biological system. The goal is to understand the effect of cell geometry on the ionic transport within living tissue. Last, the small geometries necessary for the layout of very large scale integrated circuits incur high concentrations of the electric field along conducting paths. These concentrations often result in the failure of an electronic devise such as a microprocessor. The conducting paths are often made from aluminum alloys of three or more materials. We seek the best geometries among multi- phase conductors so as to minimize electric field concentrations. The analysis and o ptimal design of multi-phase materials is central to the development of advanced materials for use in electronics, transportation systems, and aerospace structures. From the perspective of human physiology it is critical to understand transport phenomena in complex biological structures. This project addresses areas where improved knowledge of transport properties for multi-phase structures will have impact on technology and medicine. Fiber reinforced structures appear in many applications ranging from golf clubs to the rotors on windmills. Over time the adhesion between the fibers and the surrounding material is compromised by use. We investigate the optimal design of such structures taking into account the imperfect adhesion between fiber and surrounding material. Our goal is to design more durable products that last longer than conventional fiber reinforced products. Next, we investigate how to reduce the failure of microelectronic devices due to high concentrations of electric current. The small geometries used in the layout of integrated circuits require very narrow strips of metal to conduct electric currents. These strips often fail because of the high volume of current that they carry. The conducting strips are often made from a mixture of Aluminum, Copper , and Silicon. We seek the best deployment of the Copper and Silicon in the metal strip to prevent failure. Last, we attempt an improved characterization of inter cellular ionic transport. From the stand point of human physiology, an understanding of such transport for human brain cells may offer early detection of the extent of damage caused by stroke.