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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Slow manifold structure in explosive kinetics. 1. Bifurcations of points-at-infinity in prototypical models
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Slow manifold structure in explosive kinetics. 1. Bifurcations of points-at-infinity in prototypical models

机译：爆炸性动力学中的歧管结构慢。 1.原型模型中无穷大点的分叉

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This article analyzes in detail the global geometric properties (structure of the slow and fast manifolds) of prototypical models of explosive kinetics (the Semenov model for thermal explosion and the chain-branching model). The concepts of global or generalized slow manifolds and the notions of heterogeneity and alpha-omega inversion for invariant manifolds are introduced in order to classify the different geometric features exhibited by two-dimensional kinetic schemes by varying model parameters and to explain the phenomena that may occur in model reduction practice. This classification stems from the definition of suitable Lyapunov-type numbers and from the analysis of normal-to-tangent stretching rates. In the case of the Semenov model, we show that the existence of a global slow manifold and its properties are controlled by a transcritical bifurcation of the points-at-infinity, which can be readily identified by analyzing the Poincare projected system. The issue of slow manifold uniqueness and the implications of the theory with regard to the practical definition of explosion limits are thoroughly addressed.
机译：本文详细分析了爆炸动力学的原型模型（用于热爆炸的Semenov模型和链分支模型）的全局几何特性（慢速歧管和快速歧管的结构）。引入了整体或广义慢流形的概念以及不变流形的异质性和α-ω反演的概念，以便通过改变模型参数来分类二维动力学方案所展示的不同几何特征，并解释可能发生的现象在模型简化实践中。这种分类源自对合适的Lyapunov型数的定义以及对法向切线拉伸率的分析。在Semenov模型的情况下，我们表明全局慢流形的存在及其性质受无穷多个点的跨临界分叉控制，这可以通过分析Poincare投影系统轻松确定。缓慢的歧管唯一性问题以及该理论在爆炸极限的实际定义方面的意义都得到了彻底解决。

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