High Lewis Number Combustion Wavefronts: A Perturbative Melnikov Analysis
نویسندگان
چکیده
منابع مشابه
High Lewis Number Combustion Wavefronts: A Perturbative Melnikov Analysis
The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. A formula for the wavespeed is established by a non-standard application of Melnikov’s method and slow man...
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We study a mathematical model for high Lewis number combustion processes with the reaction rate of the form of an Arrhenius aw with or without an ignition cut-off. An efficient method for the proof of the existence and uniqueness of combustion fronts is rovided by geometric singular perturbation theory. The fronts supported by the model with very large Lewis numbers are small erturbations of th...
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A phase-field model of non-isothermal solidification in dilute binary alloys is used to study the variation of growth velocity, dendrite tip radius and radius selection parameter as a function of Lewis number at fixed undercooling. By the application of advanced numerical techniques we have been able, for the first time, to extend the analysis to Lewis numbers of order 10000, which are realisti...
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A phase-field model of nonisothermal solidification in dilute binary alloys is used to study the variation of growth velocity, dendrite tip radius, and radius selection parameter as a function of Lewis number at fixed undercooling. By the application of advanced numerical techniques, we have been able to extend the analysis to Lewis numbers of order 10 000, which are realistic for metals. A lar...
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We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order k of the Melnikov function. The generic case k = 1 was considered by Binyamini, Novikov and Yakovenko ( [BNY10]). The boun...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Mathematics
سال: 2007
ISSN: 0036-1399,1095-712X
DOI: 10.1137/050640849