Mathematical Sciences: "Microwave Processing of Ceramic Materials"

9623543 Kriegsmann建议对陶瓷微波加工中出现的一类物理问题进行建模和分析。这些问题产生了具有挑战性的非线性初边值问题，其数学表述涉及一个或多个控制热扩散和化学浓度扩散的非线性抛物型方程，以及时间调和形式的麦克斯韦方程。这些方程以非线性方式耦合在一起，此外，在表面温度产生显著热辐射的某些应用中，需要非线性热平衡。建议发展和使用在一定物理限制下的渐近方法，以简化数学系统，并发展和使用数值方法来解决简化的问题。该项目的目标是双重的。首先是对使这些过程工作的基本物理机制的数学理解。这样的理解将为参与陶瓷微波加工的科学家和工程师提供基本的科学基础，以判断和解释他们的实验结果。第二是发展和应用渐近、数值和其他近似方法，以获得对更现实和更复杂的过程的准确描述。拟议研究的成功完成将使工程师和科学家能够为陶瓷设计更高效的烧结和连接工艺，从而生产更高质量的材料。它还将有助于微波辅助气相沉积工艺的设计和实施，这些工艺在复合陶瓷材料的构造中具有很高的前景。

9623543 Kriegsmann It is proposed to model and analyze a class of physical problems arising in microwave processing of ceramics. These problems give rise to challenging nonlinear initial boundary value problems, the mathematical statements of which involve one or more nonlinear parabolic equations, governing the diffusion of heat and the diffusion of a chemical concentration, and the time harmonic version of Maxwell's equations. These equations are coupled together in a nonlinear fashion and, in addition, nonlinear heat balances are required in certain applications where surface temperatures produce significant thermal radiation. It is proposed to develop and use asymptotic methods, dictated by certain physical limits, to simplify the mathematical systems and to develop and use numerical methods to solve the reduced problems. The goals of the project are twofold. The first is the mathematical understanding of the basic physical mechanisms which make the processes work. Such an understanding would give scientists and engineers involved in microwave processing of ceramics the basic scientific underpinnings to judge and interpret their experimental findings. The second is the development and application of asymptotic, numerical, and other approximate methods required to obtain an accurate description of more realistic and complicated processes. The successful completion of the proposed research would allow engineers and scientists to design more efficient sintering and joining processes for ceramics which would produce higher quality materials. It would also help in the design and implementation of microwave assisted vapor deposition processes which are highly promising in the construction of composite ceramic materials.