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模式形成摘要0072491 Matkowsky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作用。这种方法在研究高度非线性偏微分方程组的解的行为方面是非常成功的。 兴趣集中在气体燃烧以及固体燃料燃烧和非均相燃烧（固体加气体）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。该研究的目标是描述过渡到，和结构，复杂的解决方案的行为。 该项目解决了气体燃烧的问题，在火焰与顺序反应和火焰的气体填充管的领域。 这些系统表现出过渡到状态的时空复杂度更大程度的参数变化。 该项目还分析了固体燃料燃烧中的问题，其中高温燃烧波（称为固体火焰）用于合成先进材料。研究集中在固体火焰和过滤燃烧领域，其中涉及非均相燃烧，气相和固相之间的反应。分析研究的基础上的分歧和非线性稳定性理论，采用渐近分析和奇异摄动理论在附近的分歧或其他过渡点，以产生一个本地的描述的解决方案。 本文提出了一种自适应伪谱方法，用于大规模科学计算，并将局部描述扩展到全局。 溶液呈现出分层，局部区域，其中溶液迅速变化。 自适应伪谱方法成功地满足了准确和有效地解决这种层型行为的挑战。该项目涉及了解能源转换和材料合成中发生的过程，这两个领域具有国家重要性。 能量转换的研究主要集中在火焰结构和动力学方面，其中涉及许多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，这项工作探讨了参数依赖关系。 材料合成研究使用燃烧波来生产具有所需特性的材料，例如，极端硬度或对极端温度的不渗透性。在这种创新的技术过程中，它似乎比传统技术具有优势，燃烧波传播通过样品，将未反应的固体粉末混合物转化为固体产品。当如此合成时，材料可具有上级性质。

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.