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  • Electronic Resource  (3)
  • 1985-1989  (3)
  • Chemistry  (2)
  • chaos  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 48 (1987), S. 151-199 
    ISSN: 1572-9613
    Keywords: Homoclinic tangency ; bifurcation theory ; periodic attractors ; chaos ; hyperbolic repellor ; symbolic dynamics ; chemical thermokinetics ; cool flame-ignition oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Nonlinear autonomous dynamical systems with ahomoclinic tangency to a periodic orbit are investigated. We study the bifurcation sequences of the mixed-mode oscillations generated by the homoclinicity, which are shown to belong to two different types, depending on the nature of the Liapunov numbers of the basic periodic orbit. A detailed numerical analysis is carried out to show how the existence of a tangent homoclinic orbit allows us to understand in a quantitative way a particular and regular sequence of cool flame-ignition oscillations observed in a thermokinetic model of hydrocarbon oxidation. Chaotic cool flame oscillations are also observed in the same model. When the control parameter crosses a critical value, this chaotic set of trajectories becomes globally unstable and forms a Cantor-like hyperbolic repellor, and the ignition mechanism generates ahomoclinic tangency to the Cantor set of trajectories. The complex bifurcation diagram may be globally reconstructed from a one-dimensional dynamical system, thanks to the strong contractivity of thermokinetics. It is found that a symbolic dynamics with three symbols is necessary to classify the periodic windows of the complex bifurcation sequence observed numerically in this system.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0030-493X
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Extensive networks of metastable ions link the major peaks in the electron impact mass spectra of two crown ethers containing 2,6-pyrido units. High-resolution mass measurements and the metastable peaks allow the elucidation of the fragmentation pathways. The spectra are influenced more by the presence of aromatic substituents than by the 2,6-pyrido units.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Brookfield, Conn. : Wiley-Blackwell
    Polymer Composites 9 (1988), S. 165-171 
    ISSN: 0272-8397
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of the crack layer theory to fatigue crack propagation (FCP) in epoxy is discussed. A crack tip damage evolution coefficient μ is introduced to assess the extent of damage as a fraction of the damage associated with critical crack propagation. The results can be expressed in the form \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{d\ell }}{{dN}} = \frac{{\beta G_1^2 }}{{\mu G_{1c} - G_1 }} $$\end{document} where dl/dN is the rate of FCP, G1 is the energy release rate whose critical value is G1c, and β is a phenomenological constant. Although no damage was detected from microscopic analyses, μ increases fivefold during stable crack propagation. Fractal analysis of fracture surface profiles provides a quantitative measure of the roughness associated with crack advance. The fractural measure d is found to evolve in a similar fashion as μ, suggesting the applicability of d to quantify crack tip damage evolution.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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