Large Scale Interface Dynamics in Energy-Driven Condensed Matter Systems

GlasnerDMS-0807423研究人员认为，流体和固体界面具有多尺度行为、时空相互作用和大尺度组织。该项目的一个组成部分侧重于粘性流体中重力和表面张力引起的自由表面不稳定性的演变，这些不稳定性导致了液滴、脊状和喷流等连贯结构。微扰技术和计算研究导致对大尺度凝结和地球物理过程的描述。该项目的第二个组成部分涉及材料微观结构的动态模型。从动力学发展的角度，利用形式和数值近似，以及产生统计描述的均匀化技术，从动态发展的角度研究了具有非局部相互作用的体系中的图样，例如嵌段共聚混合物。我们还研究了晶面演化方程中晶界的运动和图案形成方程，试图从能量学和几何学的角度描述出现的奇异结构。研究人员研究了在复杂的大型系统中，流体和固体界面如何移动和相互作用。开发的模型和模拟用于解释实验室观察，并具有预测和控制设计和制造动态的能力。所研究的流体流动的应用范围从工业涂料、地球物理形态，如洞穴形成。令人感兴趣的固体体系包括嵌段共聚物，这是一种在纳米工程中具有相当大前景的“设计型”材料。该项目还包括教育目标，让本科生接触建模和计算，并为科学职业培训毕业生。

GlasnerDMS-0807423 The investigator considers fluid and solid interfaces thathave multiscale behavior, spatiotemporal interaction and largescale organization. One component of this project focuses on theevolution of gravitational and surface tension induced freesurface instabilities in viscous fluids, which give rise tocoherent structures like fluid droplets, ridges and jets. Perturbative techniques and computational studies lead toward adescription of large-scale condensation and geophysicalprocesses. A second component of the project involves dynamicalmodels of material microstructures. Patterning in systems withnonlocal interactions, such as block copolymer mixtures, isstudied from the point of view of dynamical development,utilizing formal and numerical approximations, and homogenizationtechniques that yield statistical descriptions. The motion ofgrain boundaries in crystalline surface evolution and patternformation equations also is investigated, seeking to characterizethe singular structures that emerge both from energetic andgeometric perspectives. The investigator studies how fluid and solid interfaces moveand interact in complicated, large systems. Models andsimulations are developed that are used to explain laboratoryobservations and that have capabilities to predict and controldynamics for design and manufacturing. Fluid flows that arestudied have applications ranging from industrial coatings togeophysical morphology, such as cave formations. The solidsystems of interest include block copolymers, "designer"materials that hold considerable promise for nano-engineering. The project also includes educational aims that exposeundergraduates to modeling and computation and train graduatestudents for scientific careers.