Mathematical Prediction of the Physical Properties of Materials and Media

根据本奖项将进行的数学研究涉及偏微分方程组(PDE)的理论和计算方面，这是Bruno博士最近在材料科学、等离子体物理和电磁学中关于偏微分方程组问题的努力的自然延续。计算电磁学中的工作包括将最近引入的高阶散射解算器推广到应用中出现的各种复杂的三维系统--包括变形或侵蚀的物体、粗糙表面和海洋以及三维空间中的一般表面和非均匀物体。还展望了相关的复解析方法在等离子体物理的理论和计算方面的进一步推广。另一方面，在材料科学领域，将要开展的工作主要涉及金属合金、陶瓷和其他系统的弹性问题，这些系统的行为由潜在的微观结构决定。具体地说，布鲁诺博士将寻求计算微观不均匀变形和其他微观失配对宏观物体影响的方法。这些方法将被用来研究多晶的形状记忆效应，多晶陶瓷的热破碎，磁/电流变流体的硬化，晶界的微断裂等。该奖项将进行的数学研究的应用包括雷达、声纳、遥感、遥感应用中的杂波去除等，以及材料科学领域的现代材料设计、增韧陶瓷、智能结构、执行器和传感器等。将研究、开发和应用的新方法已经在各种配置中成功地进行了测试。它们已经带来了远远超过电磁散射和材料科学一般领域以前可用的理论进步和计算能力，现在将扩展到更复杂的情况和更广泛的材料和介质类别。这项工作将与学术界和工业界的同事和博士后同事以及研究生合作进行。学生的参与将旨在提供完善的应用数学普通教育，包括在设计最先进的模拟能力方面的丰富专业知识。学生将参与与上述领域相关的具体应用，此外，还将通过与来自工业或国家实验室的科学家直接互动。布鲁诺博士将为应用数学的广泛领域的研究人员的职业生涯做好准备，从更多的理论领域到以工程为导向的领域，并将为他们提供坚实的理论背景，具有模拟方面的天赋，并对科学和工程中的应用做出坚定的承诺。

The mathematical investigations to be conducted under the present award, which relate to theoretical and computational aspects of Partial Differential Equations (PDE), constitute a natural continuation of Dr. Bruno'srecent efforts on PDE problems in materials science, plasma physics and electromagnetism. The proposed work in computational electromagnetism involves generalization of high-order scattering solvers introduced recently to a variety of complex three-dimensional systems arising in applications -- including deformed or eroded bodies, rough surfaces and oceans as well as general surfaces and heterogeneous bodies in three dimensional space.Further generalizations of related complex-analytic approaches to theoretical and computational aspects of plasma physics are also envisioned. In the area of materials science, on the other hand, the work to be carried out relates mainly to problems of elasticity in metallic alloys, ceramics and other systems whose behavior is determined by an underlying microscopic structure. Specifically, Dr. Bruno will seek methods to compute the effects of microscopic inhomogeneous deformations and other microscopic misfits on a macroscopic body. These methods will then be used to study phenomena such as shape memory effect in polycrystals, thermal shatter in polycrystalline ceramics, hardening in magneto/electro-rheological fluids, microfracture at grain boundaries, etc.The mathematical research that will performed with this award has applications that include radar, sonar, remote sensing, clutter removal in remote sensing applications, amongst others in the area of electromagnetism, as well as design of modern materials, toughened ceramics, smart structures,actuators and sensors in the area of materials science. The novel approaches that will be studied, developed and applied have been successfullytested in a variety of configurations. They have already lead to theoretical advances and computational capabilities well beyond those available previously in the general areas of electromagnetic scattering and materials science andwill now be extended to more complicated situations and a wider class of materialsand media. This work is to be pursued in collaboration with colleagues and postdoctoral associates in academia and industry in addition to graduate students. The students' participation will be designed to provide a sound general education in applied mathematics, including substantial expertise in design of state-of-the-art simulation capabilities. Students will be involved in concrete applications in fields related to those mentioned above, and, in addition, by direct interaction with scientists from industry or national labs. Dr. Bruno will prepare researchers for careers in a wide range of areas of applied mathematics, ranging from the more theoretical to the engineering-oriented, and will provide them with a solid theoretical background, with a talent for simulation, and with a strong commitment to applications in science and engineering.