TY - JOUR
T1 - Interaction of pulsating and spinning waves in condensed phase combustion
AU - Booty, Michael R.
AU - Margolis, Stephen B.
AU - Matkowsky, Bernard J.
N1 - Funding Information:
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Publisher Copyright:
© 1986 Society for Industrial and Applied Mathematics.
PY - 1986/10
Y1 - 1986/10
N2 - We employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, we consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energylmelting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, we split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quaternary branching to various types of quasi-periodic combustion waves.
AB - We employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, we consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energylmelting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, we split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quaternary branching to various types of quasi-periodic combustion waves.
KW - Bifurcation
KW - Condensed phase combustion
KW - Double eigenvalues
KW - Multiple bifurcation point
KW - Nonlinear stability
KW - Nonsteady combustion
KW - Quasi-periodic combustion
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U2 - 10.1137/0146050
DO - 10.1137/0146050
M3 - Article
AN - SCOPUS:84955898236
SN - 0036-1399
VL - 46
SP - 801
EP - 843
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 5
ER -