Phase Transitions in Composite Media

戈登DMS-1009704研究员和他的同事们对复合材料中的相变进行了基本的数学和数值研究，并将其应用于具有相似微结构特征的电流变(ER)流体和海冰。他们建立了一个统计力学框架，可以在其中研究这种转变，并探索复合微结构及其革命的随机矩阵表征。一个需要解决的中心问题是电流变流体中诱导流体/固体相变所必需的临界电场的存在。他们预计，这一现象超越了统计力学中的经典相变，代表了一种依赖于几何熵和电能之间竞争的新型相变机制。他们还研究了在地球气候系统中起关键作用的海冰中的流体运输和相关的微结构转变。这样的微结构可以用随机矩阵来识别，研究人员用这种技术研究微结构特征的演变。复合材料出现在整个物理和生物科学以及大多数类型的工程中。这类问题的主要特征之一是有效材料性质对表征系统的参数的临界依赖性。例如，电流变(ER)流体是油等粘性流体中的颗粒悬浮液。如果外加电场超过临界值，则粒子形成链，悬浮液在毫秒内经历流体/固体转变。这种电诱导的转变已被用于下一代离合器、刹车、微流体阀和人体假肢等应用。另一个例子是海冰，它是纯冰和卤水包裹体的复合体，在地球气候系统中扮演着关键角色。如果温度超过一个临界值，那么液体就会流过冰层。这一转变调节了极地冰包中广泛的过程，这些过程是更好地预测气候变化的根本。研究人员和同事对电流变流体和海冰中的这些转变进行了基本的数学和数值研究。它们运用了理论统计物理的复杂技术，以更好地理解这些类型材料的行为。通过这些研究，研究人员期待着在其他高科技复合材料以及对我们理解极地气候变化至关重要的其他领域的应用发展。该项目由数学科学部和材料研究部共同资助。

GoldenDMS-1009704 The investigator and his colleagues conduct fundamentalmathematical and numerical studies of phase transitions incomposite materials, with applications to electrorheological (ER)fluids and sea ice, which share similar microstructural features. They develop a statistical mechanics framework in which suchtransitions can be studied, and explore random matrixcharacterizations of composite microstructures and theirevolution. One central problem to be addressed is the existenceof a critical electric field necessary to induce the fluid/solidtransition in ER fluids. They anticipate that this phenomenongoes beyond classical phase transitions in statistical mechanics,representing a new type of transitional mechanism that depends ona competition between geometrical entropy and electrical energy. They also study the fluid transport and related microstructuraltransition in sea ice, which plays a key role in Earth's climatesystem. Such microstructures can be identified with randommatrices, and the investigators study the evolution ofmicrostructural features with such techniques. Composite materials arise throughout the physical andbiological sciences and across most types of engineering. One ofthe key features of these types of problems is the criticaldependence of the effective material properties on the parameterscharacterizing the system. For example, an electrorheological(ER) fluid is a suspension of particles in a viscous fluid suchas oil. If an applied electric field exceeds a critical valuethen the particles form chains and the suspension undergoes afluid/solid transition within milliseconds. This electricallyinduced transition has been used in applications including nextgeneration clutches, brakes, micro-fluidic valves, and humanprosthetics. Another example is sea ice, a composite of pure icewith brine inclusions, which plays a key role in Earth's climatesystem. If the temperature exceeds a critical value, then fluidcan flow through the ice. This transition mediates a broad rangeof processes in the polar ice packs that are fundamental tomaking better predictions of climate change. The investigatorand colleagues conduct fundamental mathematical and numericalstudies of these transitions in ER fluids and sea ice. Theybring to bear sophisticated techniques of theoretical statisticalphysics to better understand the behavior of these types ofmaterials. Through these studies, the investigator anticipatesthe development of applications to other high-tech composites andto other areas critical to our understanding of polar climatechange. The project is cofunded by the Division of Mathematical Sciencesand the Division of Materials Research.