Nonlinear Dynamics and Pattern Formation in Combustion

马特科夫斯基 9705670 我们从事非线性动力学和模式形成的研究项目 在燃烧中。该计划涉及分析和数值的协同作用 燃烧和火焰传播问题的研究， 成功地阐明了高度非线性系统的解的行为 我们所研究的偏微分方程。特别是，兴趣集中在问题上， 气体燃烧和固体燃料中的复杂时空动力学 燃烧在气体燃烧中，我们考虑四个不同的问题领域： (a)具有顺序反应的火焰，（B）拉伸流中的火焰， (c)在燃烧器上稳定的火焰，和（d）在充气管中的火焰。 我们还考虑了固体燃料燃烧中的问题，其中燃烧波用于合成先进材料。在这种相对较新和创新的技术过程中，它似乎比传统技术具有许多优点，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。我们的分析研究是基于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，导致在当地的描述的解决方案在附近的适当的临界点。然后提出了一种自适应拟谱方法，该方法是由提出者和A。贝利斯，受雇于大规模 科学计算，局部描述是全局的 延长所考虑的问题的解决方案表现出层型行为，即，局部区域，其中溶液变化非常迅速。如何准确、准确地计算出这些问题， 有效解决此类问题。自适应伪谱方法已被证明成功地满足这一挑战。当超过问题的关键参数时， 出现具有连续更大程度的空间-时间复杂性的状态。 我们的目标是描述过渡以及由此产生的 时空模式分析研究，除了阐明系统行为，例如，参数依赖性也用作随后的数值计算的基准。因此，代码 它不仅适用于简单的解决方案，也适用于复杂的时空行为。除了研究具体的 燃烧问题，我们有助于发展分析和 研究这些问题和其他问题的数值方法。最后，在可能的情况下，将与相关的实验观察进行比较。 我们研究描述燃烧过程的数学问题。的 这些研究的主要关注点是对基本机制的理解， 包括原因和结果，影响燃烧，这是必要的 这是控制燃烧过程的先决条件。特别是， 我们研究这些特征，例如，结构，传播速度，稳定性， 等等，燃烧波。 考虑的问题的一个例子是使用 来合成高级材料。以常规 技术，将成分的粉末混合物放入炉中并“烘烤” 直到它做好。在燃烧合成中，混合物被压成 固体并在一端点燃。然后燃烧波传播通过固体，将其转化为所需的产物。这一过程比传统技术更快、更便宜。产物的性质由燃烧波的传播方式决定，这是我们研究的主题。

Matkowsky 9705670 We pursue a research program in nonlinear dynamics and pattern formation in combustion. The program involves a synergism of analytical and numerical studies of problems in combustion and flame propagation, which has been successful in elucidating solution behavior of the highly nonlinear systems of PDEs which we study. In particular, interest centers on problems exhibiting complex spatiotemporal dynamics in gaseous combustion as well as in solid fuel combustion. In gaseous combustion, we consider four different problem areas: (a) flames with sequential reactions, (b) flames in stretched flows, (c) flames stabilized on a burner, and (d) flames in gas filled tubes. We also consider problems in solid fuel combustion, in which combustion waves are used to synthesize advanced materials. In this relatively new and innovative technological process, which appears to enjoy many advantages over conventional technology, the combustion wave propagates through the sample, converting unreacted solid powder mixture to solid product. Our 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, resulting in a local description of the solution in a neighborhood of the appropriate critical point. Then an adaptive pseudo-spectral method, developed by the proposer and A. Bayliss, is employed for large scale scientific computations, with which the local description is globally extended. The solutions of the problems considered exhibit layer type behavior, i.e., localized regions in which the solution varies very rapidly. It is a challenge to numerical methods to accurately and efficiently resolve such behavior. The adaptive pseudo-spectral method has been shown to successfully meet this challenge. As critical parameters of the problem are exceeded, transitions to states with successively greater degrees of spatio-temporal complexity occur. Our goal is to describe the transitions as well as the resulting spatio-temporal patterns. The analytical studies, in addition to elucidating system behavior, e.g., parameter dependencies, also serve as benchmarks for the ensuing numerical computations. Codes are thus validated not only for simple solutions, but for complex spatio-temporal behavior as well. In addition to studying specific combustion problems, we contribute to the development of both analytical and numerical methodology for the investigation of these and other problems. Finally, where possible, comparisons to relevant experimental observations will be made. We investigate mathematical problems describing combustion processes. The primary concern in these studies is the understanding of basic mechanisms, including cause and effect, influencing combustion, which is a necessary prerequisite to any attempt to control the combustion process. In particular, we study the characteristics, e.g., structure, propagation speed, stability, etc., of combustion waves. An example of the problems considered is the use of combustion waves to synthesize advanced materials. In the conventional technology, a powder mixture of components is placed in a furnace and "baked" until it is well done. In combustion synthesis the mixture is pressed into a solid and ignited at one end. A combustion wave then propagates through the solid converting it to desired product. The process is significantly faster and cheaper than the conventional technology. The nature of the product is determined by the manner of propagation of the combustion wave, which is the subject of our investigation.