Phase Transitions in Composite Media

GoldenDMS-1009704 研究人员和他的同事们对复合材料的相变进行了基础数学和数值研究，并将其应用于电流变（ER）流体和海冰，它们具有相似的微观结构特征。他们开发了一个统计力学框架，在其中可以研究这种转变，并探索复合材料微观结构的随机矩阵表征及其革命。 一个需要解决的中心问题是在电流变液中存在一个临界电场来诱导液/固相变。 他们预计，这种现象超越了统计力学中的经典相变，代表了一种新型的过渡机制，依赖于几何熵和电能之间的竞争。他们还研究海冰中的流体输送和相关的微结构转变，这在地球气候系统中起着关键作用。 这种微结构可以用随机矩阵来识别，研究人员用这种技术来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和大多数类型的工程。 这类问题的关键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）流体是颗粒在诸如油的粘性流体中的悬浮液。 如果施加的电场超过临界值，则颗粒形成链，并且悬浮液在毫秒内经历固态/固态转变。 这种电感应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。 另一个例子是海冰，一种纯冰与盐水包裹体的复合物，在地球气候系统中起着关键作用。 如果温度超过一个临界值，那么液体就可以流过冰。 这种转变介导了极地冰层中广泛的过程，这些过程对于更好地预测气候变化至关重要。 该研究员及其同事对电流变液和海冰中的这些转变进行了基础数学和数值研究。 他们运用复杂的理论物理学技术来更好地理解这类材料的行为。 通过这些研究，研究人员预计将应用于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。 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.