Presidential Faculty Fellows/Presidential Early Career Awards for Scientists and Engineers (PFF/PECASE)

9629133 E这项工作得到了总统科学家和工程师早期职业奖的支持。研究部分将侧重于对复杂材料和复杂流体的理解和建模。这包括聚合物液体(液晶聚合物就是其中之一)、第二类超导体中的湍流和磁通流动等。关于液晶和聚合物的工作包括两个方面：(1)相分离过程和(2)液晶聚合物的流体动力学。第一个问题的主要问题是聚合驱动相变的动力学和形态，以及相分离和取向有序之间的相互作用。对于第二个问题，缺陷在大分子液晶流体动力学中的作用是令人感兴趣的。湍流研究的重点将放在湍流模型和大涡模拟上。要了解第二类半导体中磁通前沿和磁通流动的宏观不稳定性，需要一个磁通流动的宏观理论。结合一种新的界面边界条件，考虑了相互作用涡流的流体力学，建立了薄膜宏观理论。解决这三个问题的方法包括相似的步骤：(1)在非平衡热力学的指导下建立连续介质模型；(2)发展有效的数值方法；(3)利用简化情况的渐近分析提供洞察力；(4)识别典型问题以进行严格的数学分析。这位研究人员一直致力于通过开发计算不可压缩流体力学和材料科学的特别课程来加强他所在机构的课程，并积极参与暑期项目，以加强数学科学界不同群体(大学教师、高中教师、学生)之间的互动。科学家和工程师早期职业奖(PECASE)的设立是为了表彰在科学或工程研究中表现出的卓越表现和未来成功的前景，以及获奖者在各自领域最终发挥领导作用的潜力。这些奖项旨在培养一批杰出的科学家和工程师干部，并鼓励他们继续发展。

9629133 E This work is supported by a Presidential Early Career Award for Scientists and Engineers. The research component will focus on the understanding and modeling of complex materials and complex fluids. This includes polymeric liquids (of which liquid crystal polymers are one example), turbulent flows, and flux flows in type-II superconductors, etc. The work on liquid crystals and polymers includes two aspects: (1) the phase separation process and (2) the hydrodynamics of liquid crystal polymers. The main issues for the first problem are the dynamics and morphology for polymerization driven phase transition and the interplay between phase separation and orientational order. For the second problem, the role of defects in the hydrodynamics of large molecule liquid crystals is of interest. The focus of the work on turbulent flows will be on turbulence models and large eddy simulation. The understanding of macroscopic instabilities of flux fronts and flux flows in type-II semiconductors requires a macroscopic theory of flux flows. A macroscopic theory for thin films has been developed by considering the hydrodynamics of interacting vortices in combination with a novel interfacial boundary condition. The approaches to these three problems involve similar steps: (1) establishing continuum models under the guidelines of nonequilibrium thermodynamics, (2) developing effective numerical methods, (3) using asymptotic analysis of simplified situations to provide insight, and (4) identifying prototypical problems for rigorous mathematical analysis. The investigator has worked toward enhancing the curriculum at his institution through the development of special courses in computational incompressible fluid mechanics and materials science and has been actively engaged in summer programs to enhance interactions among different groups (university faculty, high school teachers, students) in the mathematical sciences community. The Presid ent Early Career Awards for Scientists and Engineers (PECASE) were created to recognize demonstrated excellence and promise of future success in scientific or engineering research, and the potential for eventual leadership of the awardees in their respective fields. These awards are designed to produce a prominent cadre of scientists and engineers and to encourage their continued development.