Nonlinear Dynamics and Pattern Formation in Combustion

NSF奖摘要-DMS-0072491数学科学：燃烧中的非线性动力学和图案形成这项研究涉及燃烧和火焰传播问题的分析和数值研究的协同。这种方法非常成功地阐明了所研究的高度非线性偏微分方程组的解的行为。人们的兴趣集中在气体燃烧、固体燃料燃烧和非均相燃烧(固体+气体)中表现出复杂的时空动力学问题，这些问题出现在先进材料的自蔓延高温合成过程中。这项研究的目标是描述向复杂解决方案行为的转变以及其结构。该项目解决具有顺序反应的火焰和充气管道中的火焰领域的气体燃烧问题。随着参数的变化，这些系统表现出向具有更大程度的时空复杂性的状态的转变。该项目还分析了固体燃料燃烧中的问题，在固体燃料燃烧中，高温燃烧波，即固体火焰，被用来合成先进材料。研究集中在固体火焰和过滤燃烧领域，这涉及到气固两相反应的非均相燃烧。分析研究基于分叉和非线性稳定性理论，利用渐近分析和奇异摄动理论在分叉或其他过渡点的邻域内给出解的局部描述。采用自适应伪谱方法进行大规模科学计算，对局部描述进行了全局扩展。解决方案呈现出层次化、局部化的区域，在这些区域中，解决方案变化迅速。自适应伪谱方法成功地解决了准确和有效地解决这种层型行为的挑战。这个项目涉及理解能源转换和材料合成这两个国家重要领域中发生的过程。能量转换的研究主要集中在火焰的结构和动力学方面，涉及到多种物理机制之间的相互作用。为了确定各种机制之间的因果关系，这项工作探索了参数依赖关系。材料合成的研究是利用燃烧波来生产具有所需性能的材料，例如，极高的硬度或对极端温度的不透气性。在这一创新的工艺过程中，燃烧波在样品中传播，将未反应的固体粉末混合物转化为固体产品，这似乎比传统技术更具优势。当这样合成时，材料可以具有优异的性能。

NSF Award Abstract - DMS-0072491Mathematical Sciences: Nonlinear Dynamics and Pattern Formation in CombustionAbstract0072491 MatkowskyThis research involves a synergism of analytical and numerical studies of problems in combustion and flame propagation. This approach is highly successful in elucidating behavior of solutions to the highly nonlinear systems of partial differential equations under study. Interest centers on problems exhibiting complex spatio-temporal dynamics in gaseous combustion as well as in solid fuel combustion and in heterogeneous combustion (solid plus gas), which arise in the self-propagating high-temperature synthesis process for advanced materials. The goal of the research is to describe transitions to, and the structure of, complex solution behavior. The project addresses gaseous combustion problems in the areas of flames with sequential reactions and flames in gas filled tubes. These systems exhibit transitions to states with greater degrees of spatio-temporal complexity as parameters are varied. The project also analyzes problems in solid fuel combustion, in which high temperature combustion waves, referred to as solid flames, are used to synthesize advanced materials. Research centers on the areas of solid flames and filtration combustion, which involves heterogeneous combustion, with reaction between gas and solid phases. The analytical studies are based on bifurcation and nonlinear stability theories, which employ asymptotic analysis and singular perturbation theory in the neighborhood of bifurcation or other transition points to yield a local description of the solution. An adaptive pseudo-spectral method is employed for large scale scientific computations, with which the local description is globally extended. The solutions exhibit layers, localized regions in which the solution varies rapidly. The adaptive pseudo-spectral method successfully meets the challenge of accurately and efficiently resolving such layer type behavior. This project is concerned with understanding processes that occur in energy conversion and materials synthesis, two areas of national importance. The research in energy conversion is focused on flame structure and dynamics, which involve interactions among many physical mechanisms. To determine cause and effect relations among the various mechanisms, this work explores parameter dependencies. The research in materials synthesis studies the use of combustion waves to produce materials having desired properties, for example, extreme hardness or imperviousness to temperature extremes. In this innovative technological process, which appears to enjoy advantages over conventional technology, the combustion wave propagates through the sample, converting an unreacted solid powder mixture to solid product. When so synthesized, materials can have superior properties.