Critical Phonema In Composit Media

复合材料是一类在科学和技术上具有重要意义的材料，它们的材料和微观结构性能在某一临界点附近发生变化时表现出急剧转变。具有极其丰富行为的一个例子是电流变（ER）流体，它是一种具有高复杂介电常数的极化粒子的胶体悬浮液，典型的尺寸范围从微米到毫米不等，在低复杂介电常数的粘性流体（如油）中。在这种悬浮液上施加一个强电场，在几毫秒内就会从油性浆料急剧转变为固体状，并使悬浮液的粘度增加许多数量级。对于非导电介质球，转变的特点是形成链，这些链聚集成平行于场的列。对于金属球，形成具有分形特征的网状结构。最近，研究者介绍了一种将统计力学方法应用于复合介质宏观问题的方法，其长度尺度比传统统计力学领域大得多。在该奖项支持的研究中，研究人员将进一步发展这些方法，并开始将它们应用于研究ER流体的关键性质，特别是那些具有较大球体的流体，其中热效应可以忽略不计，而统计力学的经典应用产生的信息很少。电流变流体等材料表现出某种明显的过渡行为，在整个科学和工程中都很常见，在许多技术应用中都很重要。其他例子包括海冰、砂岩和土壤等多孔介质、用于智能设备和电磁应用的导电膜中的颗粒复合材料，以及由于断裂而导致的材料失效。内燃流体中的流固转变是这些材料所表现出的临界行为类型的一个特别有趣的例子。快速电气控制流变特性的潜力引起了人们对电流变流体的极大关注，其应用包括离合器、泵、制动器和减震器。然而，从理论的角度来看，关于过渡附近的材料行为和性质仍有许多有待了解的地方。在拟议的工作中，研究者将开发数学方法来理解ER流体中的转变，以及其他表现出临界行为的复合材料。

A scientifically and technologically important class ofcomposite materials are those which exhibit a sharp transition in theirmaterial and microstructural properties as some parameter isvaried near a critical point. One example with extremely richbehavior is an electrorheological (ER) fluid, which is a colloidal suspension of polarizable particles of high complexdielectric constant, with typical sizes ranging from micron tomillimeter scales, in a viscous fluid of low complex dielectricconstant such as oil. The application of a strong electric field to such a suspension produces within milliseconds a dramatictransition from an oily slurry to a solid-like state with anincrease in the viscosity of the suspension by many orders ofmagnitude. For non-conducting dielectric spheres, the transition is characterized by the formation of chains which aggregate intocolumns parallel to the field. For metal spheres, net-likestructures with fractal characteristics form. Recently theinvestigator has introduced a way of applying the methods ofstatistical mechanics to macroscopic problems in compositemedia, for length scales much larger than the in the traditionaldomain of statistical mechanics. In the research supported by this award, the investigator will develop these methods further and beginapplying them to study the critical properties of ER fluids,particularly those with larger spheres where thermal effectsare negligible, and classical application of statisticalmechanics yields little information.Materials such as electrorheological (ER) fluids which exhibit some type of marked transitional behavior appear throughout science and engineering, and are important in many technological applications. Other examples include sea ice, porous media such as sandstones and soils, particulate composites used insmart devices and in conducting films for electromagnetic applications, and material failure due to fracture. The fluid/solid transition in ER fluids is a particularly interesting example of the type of critical behavior exhibited by these materials. The potential for rapidelectrical control of rheological properties has attractedconsiderable attention to ER fluids, with applications includingclutches, pumps, brakes and shock absorbers. From a theoreticalstandpoint, however, there remains much to be understood about the material behavior and properties near the transition. In theproposed work the investigator will develop mathematical methodsfor understanding the transition in ER fluids, as well as othercomposite materials exhibiting critical behavior.