Phase Transitions in Composite Media

研究者和他的同事们对复合材料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观结构特征的电流变（ER）流体和海冰。他们开发了一个统计力学框架，在这个框架中可以研究这种转变，并探索复合微观结构的随机矩阵特征及其演变。要解决的一个中心问题是存在必要的临界电场，以诱导电流变流体/固体转变。他们预测，这种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输送和相关的微观结构转变。这些微观结构可以用随机矩阵来识别，研究者们用这些技术来研究微观结构特征的演变。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。这类问题的一个关键特征是有效材料的性质对表征系统的参数的严重依赖。例如，电流变流体（ER）是一种悬浮在粘性流体（如油）中的颗粒。如果外加电场超过一个临界值，那么颗粒就会形成链，悬浮液在几毫秒内就会发生流体/固体转变。这种电诱导的过渡已被用于下一代离合器，制动器，微流体阀和人体假肢等应用中。另一个例子是海冰，它是纯冰和盐水包裹体的混合物，在地球的气候系统中起着关键作用。如果温度超过一个临界值，那么流体就可以流过冰。这种转变在极地冰盖中介导了一系列广泛的过程，这些过程对于更好地预测气候变化至关重要。研究者和他的同事们对ER流体和海冰中的这些转变进行了基本的数学和数值研究。他们运用了理论统计物理学的复杂技术来更好地理解这类材料的行为。通过这些研究，研究人员预计其他高科技复合材料和其他对我们了解极地气候变化至关重要的领域的应用的发展。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.