Microwave Processing of Ceramic Materials

研究人员将模拟和分析微波处理陶瓷中出现的一类物理问题。 这些问题引起了具有挑战性的非线性偏微分方程初边值问题。它们的数学公式涉及一个或多个非线性抛物方程，控制热扩散和化学浓度的扩散，以及麦克斯韦方程的时间谐波版本，控制电磁波的传播。 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将开发和使用渐近方法，由某些物理限制决定，以简化数学系统，并开发和使用数值方法来解决简化的问题。该奖项支持的工作目标是双重的。 第一个是对微波处理工作的基本物理机制的数学理解。 这样的理解将为从事陶瓷微波加工的科学家和工程师提供更多的基本科学依据，以判断和解释他们的实验结果。第二个目标是发展和应用渐近、数值和其他近似方法，以获得更真实和复杂过程的精确描述。计划研究的成功完成将使工程师和科学家能够设计更有效的陶瓷烧结和连接工艺，从而生产出更高质量的材料。 这也将有助于微波辅助气相沉积工艺的设计和实施，这在复合陶瓷材料的构建中具有很大的前景

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