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早期职业奖的支持 和工程师。 研究部分将侧重于了解 以及复杂材料和复杂流体的建模。 这包括 聚合物液体（其中液晶聚合物是一个实例）， 湍流和磁通流在第二类超导体等的工作 对液晶和聚合物的研究包括两个方面：（1）相 分离过程和（2）液晶聚合物的流体力学。 第一个问题的主要问题是动力学和形态学， 聚合驱动的相变和相之间的相互作用 分离和取向有序。 对于第二个问题， 大分子液晶的流体力学中的缺陷是令人感兴趣的。 湍流工作的重点是湍流模型， 大涡模拟 宏观不稳定性的理解 第二类半导体中的通量前沿和通量流需要宏观的 通量流理论 薄膜的宏观理论一直是 通过考虑相互作用的涡流的流体动力学， 结合新的界面边界条件。 的方法 对这三个问题的研究涉及到类似的步骤：（1）建立连续统 在非平衡态热力学指导下的模型，（2） 发展有效的数值方法，（3）使用渐近分析， 简化的情况下，以提供洞察力，（4）确定原型 严格的数学分析问题。 调查员在工作中 通过发展， 计算不可压缩流体力学的特殊课程， 材料科学，并一直积极参与夏季计划， 加强不同群体之间的互动（大学教师、高中 教师，学生）在数学科学界。 President Early Career Awards for Scientists and Engineers（PECASE） 是为了表彰卓越的表现和未来的希望 科学或工程研究的成功，以及最终 获奖者在各自领域的领导地位。 这些奖项是 旨在培养一批杰出的科学家和工程师， 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.