Mathematical Sciences: "Microwave Processing of Ceramic Materials"

数学科学：《陶瓷材料的微波加工》

• 批准号: 9623543
• 负责人: Gregory Kriegsmann
• 金额: $ 11.5万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623543&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microwave; Processing; Ceramic

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.

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。 这些问题引起了具有挑战性的非线性初始边值问题，其数学表述涉及一个或多个非线性抛物线方程，控制热量扩散和化学浓度扩散，以及麦克斯韦方程的时间谐波版本。 这些方程以非线性方式耦合在一起，此外，在表面温度产生显着热辐射的某些应用中需要非线性热平衡。 建议开发和使用由某些物理限制决定的渐近方法，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。 该项目的目标是双重的。 第一个是对使过程起作用的基本物理机制的数学理解。 这种理解将为参与陶瓷微波加工的科学家和工程师提供判断和解释实验结果的基本科学基础。第二个是渐近、数值和其他近似方法的开发和应用，以获得对更现实和复杂过程的准确描述。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。 它还将有助于设计和实施微波辅助气相沉积工艺，该工艺在复合陶瓷材料的构造中非常有前景。