Microwave Processing of Ceramic Materials

研究人员将模拟和分析一类在陶瓷微波加工中出现的物理问题。这些问题导致了偏微分方程具挑战性的非线性初边值问题。他们的数学公式包括一个或多个控制热扩散和化学浓度扩散的非线性抛物方程，以及控制电磁波传播的麦克斯韦方程的时间谐和版本。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。Kriegsmann将开发和使用受某些物理限制的渐近方法来简化数学系统，并开发和使用数值方法来解决简化的问题。首先是对使微波处理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更基本的科学基础，以判断和解释他们的实验发现。第二个目标是发展和应用渐近、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。计划中的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，从而使他们能够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。

The investigator will model and analyze a class of physicalproblems arising in microwave processing of ceramics. These problemsgive rise to challenging nonlinear initial boundary value problemsfor partial differential equations. Their mathematical formulation involves one or more nonlinear parabolic equations, governing the diffusion of heat andthe diffusion of a chemical concentration, and the time harmonicversion of Maxwells equations, governing the propagation of electromagnetic waves. 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. Kriegsmann will develop and use asymptotic methods, dictated by certain physical limits, to simplify the mathematical systems and develop and use numerical methods to solve the reduced problems.The goals of the work supported with this award are twofold. The first is the mathematical understanding of the basic physical mechanisms which make microwave processing work. Such an understanding will give scientists and engineers involved in microwave processing of ceramics more basic scientificunderpinnings to judge and interpret their experimental findings.The second goal is the development and application of asymptotic, numerical,and other approximate methods required to obtain an accurate descriptionof more realistic and complicated processes. The successful completionof the planned research will allow engineers and scientists to designmore efficient sintering and joining processes for ceramics which will allow them to produce higher quality materials. It will also help in the designand implementation of microwave assisted vapor deposition processeswhich are highly promising in the construction of composite ceramicmaterials