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Combustion Science and Technology Volume 34, 1983 - Issue 1-6
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Original Articles

Nonlinear Stability and Bifurcation in the Transition from Laminar to Turbulent Flame Propagation

Stephen B. Margolis Applied Mathematics Division, Sandia National Laboratories, Livemore
&
Bernard J. Matkowsky Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60201
Pages 44-77 | Received 27 May 1983, Published online: 02 May 2007

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N. Yokev & J.B. Greenberg. (2019) Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames. Combustion Theory and Modelling 23:2, pages 310-336.
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M.L. Kelley & D.A. Schult. (2006) Modeling extinction in forced opposed-flow smolder. Combustion Theory and Modelling 10:1, pages 133-143.
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TOSHISUKE HIRANO. (2000) Generation of Flame Front Turbulence∗ . Combustion Science and Technology 158:1, pages 35-51.
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MOHAMED el-HAMDI, MICHAEL GORMAN & KAYA. ROBBINS. (1993) Deterministic Chaos in Laminar Premixed Flames: Experimental Classification of Chaotic Dynamics. Combustion Science and Technology 94:1-6, pages 87-101.
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John K. Bechtold & Stephen B. Margolis. (1989) Hydrodynamic Stability of Solid and Liquid Propellant Combustion. Combustion Science and Technology 68:1-3, pages 49-84.
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STEPHENB. MARGOLIS & SHERIDANC. JOHNSTON. (1989) Multiplicity and Stability of Supercritical Combustion in a Nonadiabatic Tubular Reactor. Combustion Science and Technology 65:1-3, pages 103-136.
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Stephen B. Margolis & Forman A. Williams. (1988) Diffusional/Thermal Coupling and Intrinsic Instability of Solid Propellant Combustion. Combustion Science and Technology 59:1-3, pages 27-84.
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M. El-Hamdi, M. Gorman, J. W. Mapp & J. I. Blackshear$suffix/text()$suffix/text(). (1987) Stability Boundaries of Periodic Models of Propagation in Burner-Stabilized Methane-Air Flames. Combustion Science and Technology 55:1-3, pages 33-40.
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WM. T. ASHURST, N. PETERS & M. D. SMOOKE. (1987) Numerical Simulation of Turbulent Flame Structure with Non-unity Lewis Number. Combustion Science and Technology 53:4-6, pages 339-375.
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Stephen B. Margolis & Robert C. Armstrong. (1986) Two Asymptotic Models for Solid Propellant Combustion. Combustion Science and Technology 47:1-2, pages 1-38.
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J. W. Mapp, J. I. Blackshear$suffix/text()$suffix/text() & M. Gorman. (1985) Short Communication. Combustion Science and Technology 43:3-4, pages 217-225.
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Stephen B. Margolis, Hans G. Kaper, Gary K. Leaf & Bernard J. Matkowsky. (1985) Bifurcation of Pulsating and Spinning Reaction Fronts in Condensed Two-Phase Combustion. Combustion Science and Technology 43:3-4, pages 127-165.
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ALANR. KERSTEIN. (1984) Pulsating Instability in a Planar Diffusion Flame. Combustion Science and Technology 40:5-6, pages 293-302.
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Stephen B. Margolis & Alan R. Kerstein. (1983) Flame Stabilization in a Layered Medium. Combustion Science and Technology 35:5-6, pages 255-275.
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Articles from other publishers (51)

N. Yokev & J.B. Greenberg. (2018) Linear stability analysis of laminar premixed water-in-fuel emulsion spray flames. Fuel 222, pages 733-742.
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Vadim N. Kurdyumov, Vladimir V. Gubernov & Roman V. Fursenko. (2017) Controlling of flame propagation in a composite solid energetic material: From stabilization to chaotic regimes. Combustion and Flame 182, pages 167-178.
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JB Greenberg, LS Kagan & GI Sivashinsky. (2016) A numerical study of the propagation of organic gellant-based fuel-rich premixed spray flames. International Journal of Spray and Combustion Dynamics 8:3, pages 165-172.
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Noam Weinberg & J. Barry Greenberg. (2014) Linear Stability Analysis of Laminar Premixed Fuel-Rich Double-Spray Flames. International Journal of Spray and Combustion Dynamics 6:1, pages 87-112.
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Anna Ghazaryan, Jeffrey Humpherys & Joshua Lytle. (2013) Spectral Behavior of Combustion Fronts with High Exothermicity. SIAM Journal on Applied Mathematics 73:1, pages 422-437.
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Vladimir V. Gubernov, Andrei V. Kolobov, Andrei A. Polezhaev & Harvinder S. Sidhu. (2012) Stability of combustion waves in the Zeldovich–Liñán model. Combustion and Flame 159:3, pages 1185-1196.
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Vladimir Gubernov, Andrei Kolobov, Andrei Polezhaev, Harvinder Sidhu & Geoffry Mercer. (2010) Period doubling and chaotic transient in a model of chain-branching combustion wave propagation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466:2121, pages 2747-2769.
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M. Gorman, M. el-Hamdi & B. Pearson. (2009) The characteristics of four ratcheting states in cellular flames. Chaos: An Interdisciplinary Journal of Nonlinear Science 19:3.
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Changrong Cui, Moshe Matalon & Thomas L. Jackson. (2005) Pulsating Mode of Flame Propagation in Two-Dimensional Channels. AIAA Journal 43:6, pages 1284-1292.
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V. V. Gubernov, H. S. Sidhu & G. N. Mercer. (2005) The effect of ambient temperature on the propagation of nonadiabatic combustion waves. Journal of Mathematical Chemistry 37:2, pages 149-162.
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V. V. GubernovG. N. MercerH. S. SidhuR. O. Weber. (2004) Evans function stability of non-adiabatic combustion waves. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460:2048, pages 2415-2435.
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G. N. Mercer, H. S. Sidhu, R. O. Weber & V. Gubernov. (2003) Evans Function Stability of Combustion Waves. SIAM Journal on Applied Mathematics 63:4, pages 1259-1275.
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Stephen B. Margolis. (2001) Viscous Analysis of Pulsating Hydrodynamic Instability and Thermal Coupling in Liquid-Propellant Combustion. AIAA Journal 39:2, pages 233-241.
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A. Bayliss, B. J. Matkowsky, C. W. Wahle & T. K.MaMa. (2001) The Reactive Rayleigh--Bénard Problem with Throughflow. SIAM Journal on Applied Mathematics 61:4, pages 1103-1142.
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Satoshi Kadowaki & Shin-ichirow Goma. 2001. Computational Fluid Dynamics 2000. Computational Fluid Dynamics 2000 201 206 .
Stephen Margolis. (2000) Viscous and thermal effects on hydrodynamic instability in liquid-propellant combustion. Viscous and thermal effects on hydrodynamic instability in liquid-propellant combustion.
Satoshi Kadowaki. (1999) The lateral movement of the three-dimensional cellular flame at low Lewis numbers. International Journal of Heat and Fluid Flow 20:6, pages 649-656.
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Pavel K Brazhnik & John J Tyson. (1999) Travelling waves and static structures in a two-dimensional exactly solvable reaction-diffusion system. Journal of Physics A: Mathematical and General 32:46, pages 8033-8044.
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De S. Zhang, Guo W. Wei, Donald J. Kouri, David K. Hoffman, Michael Gorman, Antonio Palacios & Gemunu H. Gunaratne. (1999) Integrating the Kuramoto-Sivashinsky equation in polar coordinates: Application of the distributed approximating functional approach. Physical Review E 60:3, pages 3353-3360.
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Daniel A. Schult. (1999) Matched Asymptotic Expansions and the Closure Problem for Combustion Waves. SIAM Journal on Applied Mathematics 60:1, pages 136-155.
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A. Bayliss, B. J. Matkowsky & D. A. Schult. (1998) Traveling Waves in Natural Counterflow Filtration Combustion and Their Stability. SIAM Journal on Applied Mathematics 58:3, pages 806-852.
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Alvin Bayliss, Andreas Class & Bernard J. Matkowsky. (1998) Localized Flickering Cellular Flames. SIAM Journal on Applied Mathematics 59:3, pages 942-964.
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Satoshi Kadowaki. 1998. Sixteenth International Conference on Numerical Methods in Fluid Dynamics. Sixteenth International Conference on Numerical Methods in Fluid Dynamics 494 499 .
Alexander G. Merzhanov, William A. Sirignano & Luigi De Luca. 1997. Advances in Combustion Science: In Honor of Ya. B. Zel'dovich. Advances in Combustion Science: In Honor of Ya. B. Zel'dovich 157 177 .
L�o Glangetas & Jean -Michel Roquejoffre. (1996) Bifurcations of travelling waves in the thermo-diffusive model for flame propagation. Archive for Rational Mechanics and Analysis 134:4, pages 341-402.
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A. Bayliss, B.J. Matkowsky & H. Riecke. (1994) Structure and dynamics of Modulated Traveling Waves in cellular flames. Physica D: Nonlinear Phenomena 74:1-2, pages 1-23.
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Stephen B. Margolis. (2006) Nonlinear stability of combustion-driven acoustic oscillations in resonance tubes. Journal of Fluid Mechanics 253:-1, pages 67.
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. 1993. Dynamics of Gaseous Combustion. Dynamics of Gaseous Combustion 3 24 .
Alvin Bayliss, Bernard J. Matkowsky & Hermann Riecke. 1993. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters 137 162 .
Alvin Bayliss & Bernard J. Matkowsky. (1992) Nonlinear Dynamics of Cellular Flames. SIAM Journal on Applied Mathematics 52:2, pages 396-415.
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A.K. Hobbs & P. Metzener. (1992) Directional solidification: interface dynamics and weak remote flow. Journal of Crystal Growth 118:3-4, pages 319-332.
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Stephen B. Margolis. (1992) Stability of acoustic oscillations in a model helmholtz-type pulse combustor. Symposium (International) on Combustion 24:1, pages 19-27.
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Michael L. Frankel. (1991) Qualitative Approximation of Oscillatory Flames in Premixed Gas Combustion by a Local Equation of Front Dynamics. SIAM Journal on Applied Mathematics 51:3, pages 673-683.
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Stephen B. Margolis & Forman A. Williams. (1991) Flame propagation in solids and high-density fluids with Arrhenius reactant diffusion. Combustion and Flame 83:3-4, pages 390-398.
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Stephen B. Margolis. (1991) The transition to nonsteady deflagration in gasless combustion. Progress in Energy and Combustion Science 17:2, pages 135-162.
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Alvin Bayliss & Bernard J. Matkowsky. 1991. Dynamical Issues in Combustion Theory. Dynamical Issues in Combustion Theory 1 35 .
David Terman. (1990) Stability of Planar Wave Solutions to a Combustion Model. SIAM Journal on Mathematical Analysis 21:5, pages 1139-1171.
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Stephen B. Margolis & Forman A. Williams. (1990) Stability of homogeneous-solid deflagration with two-phase flow in the reaction zone. Combustion and Flame 79:2, pages 199-213.
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David O. Olagunju & Bernard J. Matkowsky. (1990) Burner-stabilized cellular flames. Quarterly of Applied Mathematics 48:4, pages 645-664.
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A. Bayliss, B. J. Matkowsky & M. Minkoff. (1989) Cascading Cellular Flames. SIAM Journal on Applied Mathematics 49:5, pages 1421-1432.
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Stephen B. Margolis & Forman A. Williams. (1989) Diffusional/Thermal Instability of a Solid Propellant Flame. SIAM Journal on Applied Mathematics 49:5, pages 1390-1420.
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M. R. Booty, M. Matalon & B. J. Matkowsky. (1988) A Nonlinear Wave Equation in Nonadiabatic Flame Propagation. SIAM Journal on Applied Mathematics 48:3, pages 519-535.
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N. Peters. (1988) Laminar flamelet concepts in turbulent combustion. Symposium (International) on Combustion 21:1, pages 1231-1250.
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Michael R. Booty, Stephen B. Margolis & Bernard J. Matkowsky. (1987) Interaction of Pulsating and Spinning Waves in Nonadiabatic Flame Propagation. SIAM Journal on Applied Mathematics 47:6, pages 1241-1286.
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Luis F. Razón & Roger A. Schmitz. (1987) Multiplicities and instabilities in chemically reacting systems — a review. Chemical Engineering Science 42:5, pages 1005-1047.
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. 1986. Dynamics of Reactive Systems Part I: Flames and Configurations; Part II: Modeling and Heterogeneous Combustion. Dynamics of Reactive Systems Part I: Flames and Configurations; Part II: Modeling and Heterogeneous Combustion 131 151 .
Stephen B. Margolis & Bernard J. Matkowsky. (1985) Flame Propagation in Channels: Secondary Bifurcation to Quasi-Periodic Pulsations. SIAM Journal on Applied Mathematics 45:1, pages 93-129.
Crossref
Alan R. Kerstein. (1985) Pulsating instability in stagnation combustion. Symposium (International) on Combustion 20:1, pages 1915-1923.
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ROBERT J. KEE, LINDA R. PETZOLD, MITCHELL D. SMOOKE & JOSEPH F. GRCAR. 1985. Multiple Time Scales. Multiple Time Scales 113 144 .
Robert J. Kee & James A. Miller. (1984) Computational modeling of flame structure. Physica D: Nonlinear Phenomena 12:1-3, pages 198-211.
Crossref
Thomas Erneux, Bernard J. Matkowsky & Edward L. Reiss. 1984. Modelling of Patterns in Space and Time. Modelling of Patterns in Space and Time 67 72 .

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