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  • Cited by 53
  • Paul Clavin, Université d'Aix-Marseille, Geoff Searby, Centre National de la Recherche Scientifique (CNRS), Marseille, France
Publisher:
Cambridge University Press
Online publication date:
August 2016
Print publication year:
2016
Online ISBN:
9781316162453

Book description

Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also offering advanced material for scientists who wish to improve their knowledge.

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Contents

References
Abel, F.A. 1874. Contributions to the history of explosive agents. Philos. Trans. R. Soc. London, 164, 337–395.
Abramowitz, M., and Stegun, I. 1972. Handbook of mathematical functions. 9th edn. New York: Dover.
Abugov, D.I., and Obrezkov, O.I. 1978. Acoustic noise in turbulent flames. Combust. Expl. Shock Waves, 14, 606–612.
Akkerman, V., Law, C.K., Bychkov, V., and Eriksson, L.-E. 2010. Analysis of flame acceleration induced by wall friction in open tubes. Phys. Fluids, 22, 053606.
Albin, Y., and D'Angelo, Y. 2012. Assessment of the evolution equation modelling approach for three-dimensional expanding wrinkled premixed flames. Combust. Flame, 159, 1932–1948.
Aldredge, R.C., and Killingsworth, N.J. 2004. Experimental evaluation of Marksteinnumber influence on thermoacoustic instability. Combust. Flame, 137, 178–197.
Almarcha, C., Clavin, P., Duchemin, L., and Sanz, J. 2007. Ablative Rayleigh-Taylor instability with strong temperature dependence of the thermal conductivity. J. Fluid Mech., 579, 481–492.
Arnold, V.I. 1973. Ordinary differential equations. MIT Editions.
Ashurst, W.T. 1997. Darrieus–Landau instability, growing cycloids and expanding flame acceleration. Combust. Theor. Model., 1, 405–428.
Assier, R., and Wu, X. 2014. Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field. J. Fluid Mech., 758, 180–220.
Atzeni, S., and Meyer-Ter-Vehn, J. 2004. The physics of inertial fusion. 1st edn. Clarendon Press–Oxford Science Publications.
Audoly, B., Berestycki, H., and Pomeau, Y. 2000. Reaction diffusion in fast steady flows. C. R. Acad. Sci. Paris, 328(3), 255–262.
Bachelard, G. 1928. La psychanalise du feu. Gallimard.
Baillot, F., Durox, D., Ducruix, S., Searby, G., and Boyer, L. 1999. Parametric response of a conical flame to acoustic waves. Combust. Sci. Technol., 142, 91–109.
Baker, G., Meiron, D.I., and Orszag, S.A. 1980. Vortex simulation of the Rayleigh–Taylor instability. Phys. Fluids, 23, 1485–1490.
Balescu, R. 1975. Equilibrium and nonequilibrium statistical mechanics. John Wiley and Sons.
Barenblatt, G.I. 1996. Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press.
Bartenev, A.M., and Gelfand, B.E. 2000. Spontaneous initiation of detonations. Prog. Energy Combust. Sci., 26, 29–55.
Batchelor, G.K. 1967. An introduction to fluid dynamics. Cambridge University Press.
Bates, J.W. 2004. Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media. Phys. Rev. E, 69, 056313.
Bates, J.W. 2007. Instability of isolated planar shock waves. Phys. Fluids, 19, 094 102–1–6.
Bates, J.W. 2012. On the theory of shock wave driven by a corrugated piston in a non-ideal fluid. J. Fluid Mech., 691, 146–164.
Bechtold, J.K., and Matalon, M. 1987. Hydrodynamic and diffusion effects on the stability of spherical expanding flames. Combust. Flame, 67, 77–90.
Belliard, A. 1997. Etude experimental de l'émission sonore des flammes turbulentes. University thesis, Université d'Aix-Marseille-I.
Bender, M.C., and Orszag, S.A. 1984. Advanced mathematical methods for scientists and engineers. McGraw-Hill.
Bethe, H.A. 1990. Supernova mechanisms. Rev. Mod. Phys., 62(4), 801–866.
Bhatnagar, P.L., Gross, E.P., and Krook, M. 1954. A model for collision processes in gases. Phys. Rev., 94(3), 511–525.
Bhayyacharjee, R.R, Lau-Chapelaine, S.S.M., Maines, G., Maley, L., and Radulescu, M.I. 2013. Detonation re-initiationmechanism following theMach reflection of a quenched detonation. Proc. Comb. Inst., 34, 1893–1901.
Biamino, L., Jourdan, G., and Lazhar, H. 2011. Pattern of triple points on a shock wave reflected from an undulated wall. Private communication.
Bibliothèque des succès scolaires (ed). 1868. Histoire d'une chandelle. J. Hetzel et Cie.
Bilger, R.W., Pope, S.B., Bray, K.N.C., and Driscoll, J.F. 2005. Paradigms in turbulent combustion research. Proc. Comb. Inst., 30, 21–41.
Binney, J., and Tremaine, S. 1994. Galactic dynamics. Princeton University Press.
Bodner, S. 1974. Rayleigh–Taylor instability and laser-pellet fusion. Phys. Rev. Lett., 33, 761–764.
Boivin, P., Sanchez, A.L., and Williams, F.A. 2013. Four-step and three-step systematically reduced chemistry for a wide-range H2-air combustion problems. Combust. Flame, 160, 76–82.
Borghi, R. 1985. On the structure and morphology of turbulent premixed flames. Pages 117–138 of: Bruno, C., and Casci, C. (eds), Recent advances in aerospace sciences. Plenum.
Borghi, R. 1988. Turbulent combustion modelling. Prog. Energy Combust. Sci., 14(4), 245–292.
Borghi, R., and Champion, M. 2000. Modélisation et théorie des flammes. Édition Technip.
Boris, J.P., and Oran, E.S. 1987. Numerical simulation of reactive flow. New York: Elsevier.
Bosschaart, K.J., and De Goey, L.P.H. 2004. The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method. Combust. Flame, 136, 264–269.
Bourlioux, A., and Majda, A. J. 1992. Theoretical and numerical structure for unstable two-dimensional detonation. Combust. Flame, 90, 211–229.
Boury, G. 2003. Études théoriques et numériques de fronts de flammes plissées: Dynamiques non-linéaires libres ou bruités. Thesis, Université de Poitiers.
Boyer, L. 1980. Laser tomographic method for flame front movement studies. Combust. Flame, 39, 321–323.
Bradley, D., Chamberlain, G.A., and Drysdale, D.D. 2012. Large vapour cloud explosions, with particular reference to that at Buncefield. Philos. Trans. R. Soc. London Ser. A, 370, 544–566.
Bradley, D., Cresswell, M.T., and Puttock, J.S. 2001. Flame acceleration due to flameinduced instabilities in large-scale explosions. Combust. Flame, 124, 551–559.
Bradley, D., Gaskell, P.H., and Gu, X.J. 1996. Burning velocities, Markstein lengths, and flame quenching for spherical methane–air flames: A computational study. Combust. Flame, 104, 176–198.
Bradley, D., Sheppard, C.G.W., Woolley, R., Greenhalgh, D.A., and Lockett, R.D. 2000. The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions. Combust. Flame, 122(1–2), 195–209.
Brailovsky, I., and Sivashinsky, G.I. 2000. Hydraulic resistance as a mechanism for deflagration-to-detonation transition. Combust. Flame, 122, 492–499.
Brailovsky, I., Kagan, L., and Sivashinsky, G. 2012. Combustion waves in hydraulically resisted systems. Philos. Trans. R. Soc. London Ser. A, 370, 625–646.
Braudel, F. 1987. Grammaire des civilisations. Arthaud.
Bray, K.N.C., and Moss, J.B. 1977. Unified statistical model of premixed turbulent flame. Acta Astronaut., 4(3–4), 291–319.
Briscoe, M.G., and Kovitz, A.A. 1968. Experimental and theoretical study of the stability of planar shock waves reflected normally from perturbed flat walls. J. Fluid Mech., 31(3), 529–546.
Brush, S.G. 1966. Kinetic theory. Vols. 1 and 2. Pergamon Press.
Buckmaster, J. 1976. The quenching of deflagration waves. Combust. Flame, 26, 151–162.
Buckmaster, J., and Joulin, G. 1989. Radial propagation of premixed flames. Combust. Flame, 78, 275–289.
Buckmaster, J., and Mikolaitis, D. 1982. The premixed flame in a counterflow. Combust. Flame, 47, 191–204.
Buckmaster, J., and Weeratunga, S. 1984. The stability and structure of flame-bubble. Combust. Sci. Technol., 35, 287–296.
Buckmaster, J., Joulin, G., and Ronney, P. 1990. The structure and stability of nonadiabatic flame balls. Combust. Flame, 79, 381–392.
Buckmaster, J.D. 1979. The quenching of two-dimensional premixed flames. Acta Astronaut., 6, 741–769.
Buckmaster, J.D., and Ludford, G.S.S. 1988. The effect of structure on stability of detonations. I. Role of the induction zone. Proc. Comb. Inst., 21, 1669–1676.
Burke, S.P., and Schumann, T.E.W. 1928. Diffusion flames. Ind. Eng. Chem., 20(10), 998–1004.
Burrows, A. 2013. Perspectives on core-collapse supernova theory. Rev. Mod. Phys., 85, 245–261.
Bychkov, V. 1999. Analytical scalings for flame interaction with sound waves. Phys. Fluids, 11(10), 3168–3173.
Bychkov, V., Golberg, S., and Liberman, M. 1994. Self-consistent model of the Rayleigh– Taylor instability in ablatively accelerated laser plasma. Phys. Plasmas, 1, 2976–2986.
Bychkov, V., Modestov, M., and Law, C.K. 2015. Combustion phenomena in modern physics: Inertial confinement fusion. Prog. Energy Combust. Sci., 47, 32–59.
Bychkov, V., Petchenko, A., Akkerman, V., and L.-E., Eriksson. 2005. Theory and modelling of accelerating flames in tubes. Phys. Rev. E, 72(4), 046307.
Callen, H.B. 1985. Thermodynamics. 2nd edn. New York: Wiley.
Cambray, P., and Joulin, G. 1994. Length-scales of wrinkling of weakly-forced unstable premixed flames. Combust. Sci. Technol., 97, 405–428.
Candel, S., Durox, D., Schuller, T., Palies, P., Bourgouin, J.-F., and Moeck, J.P. 2012. Progress and challenges in swirling flame dynamics. C. R. Mécanique, 340, 758–768.
Carnot, S. 1824. Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. Bachelier.
Carslaw, H.S., and Jaeger, J.C. 1959. Conduction of heat in solids. Clarendon Press–Oxford Science Publications.
Chandrasekhar, S. 1967. An introduction to the study of stellar structure. Dover Publications.
Chapman, S., and Cowling, T.G. 1939. The mathematical theory of non-uniform gases. Cambridge University Press.
Chen, Z., and Ju, Y. 2007. Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Combust. Theor. Model., 11(3), 427–453.
Ciccarelli, G., and Dorofeev, S. 2008. Flame acceleration and transition to detonation in ducts. Prog. Energy Combust. Sci., 34, 499–550.
Clanet, C., and Searby, G. 1996. On the ‘tulip flame’ phenomenon. Combust. Flame, 105, 225–238.
Clanet, C., and Searby, G. 1998. First experimental study of the Darrieus–Landau instability. Phys. Rev. Lett., 80(17), 3867–3870.
Clanet, C., Searby, G., and Clavin, P. 1999. Primary acoustic instability of flame propagating in tubes: Cases of spray and premixed gas combustion. J. Fluid Mech., 385, 157–197.
Clavin, P. 1972. Kinetic study on spatially inhomogeneous systems–Preservation of factorization of generalized kinetic-equations. C. R. Acad. Sci. A, 274(13), 1085.
Clavin, P. 1985. Dynamic behaviour of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci., 11, 1–59.
Clavin, P. 1988. Theory of flames. Pages 293–315 of: Guyon, E., Nadal, J.P., and Pomeau, Y. (eds), NATO ASI Series E. Disorder and mixing, vol. 152. Kluwer Academic.
Clavin, P. 1994. Premixed combustion and gasdynamics. Ann. Rev. Fluid Mech., 26, 321–352.
Clavin, P. 2002a. Instabilities and nonlinear patterns of overdriven detonation in gases. Pages 49–97 of: Berestycki, H., and Pomeau, Y. (eds), Nonlinear PDEs in condensed matter and reactive flows. Kluwer Academic.
Clavin, P. 2002b. Self-sustained mean streaming motion in diamond patterns of a gaseous detonation. Int. J. Bifurcation & Chaos, 12(11), 2535–2546.
Clavin, P. 2013. Nonlinear analysis of shock-vortex interaction: Mach stem formation. J. Fluid Mech., 721, 324–339.
Clavin, P., and Almarcha, C. 2005. Ablative Rayleigh–Taylor instability in the limit of an infinitely large density ratio. C. R. Mécanique, 333, 379–388.
Clavin, P, and Denet, B. 2002. Diamond patterns in the cellular front of an overdriven detonation. Phys. Rev. Lett., 88(4), 044502–1–4.
Clavin, P., and Garcia, P. 1983. The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. J. Méc. Théor. Appl., 2(2), 245–263.
Clavin, P., and Graña-Otero, J.C. 2011. Curved and stretched flames: The two Markstein numbers. J. Fluid Mech., 686, 187–217.
Clavin, P., and He, L. 1996a. Acoustic effects in the nonlinear oscillations of planar detonations. Phys. Rev. E, 53(5), 4778–4784.
Clavin, P., and He, L. 1996b. Stability and nonlinear dynamics of one-dimensional overdriven detonations in gases. J. Fluid Mech., 306, 353–378.
Clavin, P., and He, L. 2001. Theory of cellular detonations in gases. Part I: Stability limits at strong overdrive. C. R. Acad. Sci. Paris, 329(IIb), 463–471.
Clavin, P., and Joulin, G. 1983. Premixed flames in large scales and high intensity turbulent flow. J. Phys. Lett., 44, L-1–L-12.
Clavin, P., and Joulin, G. 1989. Flamelet library for turbulent wrinkled flames. Pages 213–240 of: Borghi, R., and Murthy, S.N.B. (eds), Turbulent reactive flows. Lecture Notes in Engineering. New York: Springer.
Clavin, P., and Joulin, G. 1997. High-frequency response of premixed flames to weak stretch and curvature: A variable-density analysis. Combust. Theor. Model., 1, 429–446.
Clavin, P., and Lazimi, D. 1992. Theoretical analysis of oscillatory of homogeneous solid propellant including non-steady gas phase effects. Combust. Sci. Technol., 83, 1–32.
Clavin, P., and Liñan, A. 1984. Theory of gaseous combustion. Pages 291–338 of: Velarde, M.G. (ed), Nonequilibrium cooperative phenomena in physics and related fields. NATO ASI Series B. Physics, vol. 116. Plenum Press.
Clavin, P., and Masse, L. 2004. Instabilities of ablation fronts in inertial fusion: A comparison with flames. Phys. Plasmas, 11, 690–705.
Clavin, P., and Searby, G. 2008. Unsteady response of chain-branching premixed-flames to pressure waves. Combust. Theor. Model., 12(3), 545–567.
Clavin, P., and Siggia, E.D. 1991. Turbulent premixed flames and sound generation. Combust. Sci. Technol., 78, 147–155.
Clavin, P., and Sun, J. 1991. Theory of acoustic instabilities of planar flames propagating in spray or particle-laden gases. Combust. Sci. Technol., 78, 265–288.
Clavin, P., and Williams, F.A. 1979. Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech., 90 part 3, 589–604.
Clavin, P., and Williams, F.A. 1982. Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. J. Fluid Mech., 116, 251–282.
Clavin, P., and Williams, F.A. 2002. Dynamics of planar gaseous detonations near Chapman–Jouguet conditions for small heat release. Combust. Theor. Model., 6, 127–129.
Clavin, P., and Williams, F.A. 2005. Asymptotic spike evolution in Rayleigh–Taylor instability. J. Fluid Mech., 525, 105–113.
Clavin, P., and Williams, F.A. 2009. Multidimensional stability analysis of gaseous detonations near Chapman–Jouguet conditions for small heat release. J. Fluid Mech., 624, 125–150.
Clavin, P., and Williams, F.A. 2012. Analytical studies of the dynamics of gaseous detonations. Philos. Trans. R. Soc. London Ser. A, 370, 597–624.
Clavin, P., He, L., and Williams, F.A. 1997. Multidimensional stability analysis of overdriven gaseous detonations. Phys. Fluids, 9(12), 3764–3785.
Clavin, P., Kim, J.S., and Williams, F.A. 1994. Turbulence-induced noise effects on highfrequency combustion instabilities. Combust. Sci. Technol., 96, 61–84.
Clavin, P., Masse, L., and Roquejoffre, J.-M. 2011. Relaxation to equilibrium in diffusivethermal models with strongly varying diffusion length-scale. Comm. Math. Sci., 9(1), 127–141.
Clavin, P., Masse, L., and Williams, F.A. 2005. Comparison of flame front instabilities with instabilities of ablation fronts in inertial fusion confinement. Combust. Sci. Technol., 177, 979–989.
Clavin, P., Pelcé, P., and He, L. 1990. One-dimensional vibratory instability of planar flames propagating in tubes. J. Fluid Mech., 216, 299–322.
Colgate, S.A., and Johnson, M.H. 1960. Hydrodynamic origin of cosmic rays. Phys. Rev. Lett., 5, 235–238.
Contamine, P. 1999. La guerre au Moyen Âge. 5ème edn. PUF.
Cooperstein, J., and Baron, E.A. 1990. Supernovae: The direct mechanism and the equation of state. Chap. 9, pages 213–266 of: Petschek, A.G. (ed), Supernovae. Springer- Verlag.
Corrsin, S. 1951. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys., 22, 469–473.
Courant, R., and Friedrichs, K.O. 1967. Supersonic flow and shock waves. John Wiley.
Cox, J.P. 1980. Theory of stellar pulsation. Princeton University Press.
Cox, P.A. 1989. The elements, their origin, abundance and distribution. Oxford University Press.
Crank, J. 1986. The mathematics of diffusion. 2nd edn. Clarendon Press–Oxford Science Publications.
Creta, F., Fogla, N., and Matalon, M. 2011. Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability. Combust. Theor. Model., 15(2), 267–298.
Culick, F.E. 1975. Stability of three-dimensional motions in a combustion chamber. Combust. Sci. Technol., 10, 109–124.
Damköhler, G. 1940. Der Einfluss der Turbulenz auf die Flammengeschwindigkeit in gasgemischen. F. Elecktrochem., 601–652.
D'Angelo, Y., Joulin, G., and Boury, G. 2000. On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames. Combust. Theor. Model., 4, 317–338.
Daou, J., Al-Malki, F., and Ronney, P. 2009. Generalized flame balls. Combust. Theor. Model., 13(2), 1–26.
Daou, R., and Clavin, P. 2003. Instability threshold of gaseous detonations. J. Fluid Mech., 482, 181–206.
Darrieus, G. 1938. Propagation d'un front de flamme. Communication presented at La Technique Moderne (1938) and at Congrès de Mécanique Appliquée, Paris (1945).
Dautray, R. 2004. Quelle énergie pour demain. Odile Jacob.
Davis, S.G., Quinard, J., and Searby, G. 2002a. Determination of Markstein numbers in counterflow premixed flames. Combust. Flame, 130, 112–122.
Davis, S.G., Quinard, J., and Searby, G. 2002b. Determination of Markstein numbers in counterflows, methane– and propane–air flames: A computational study. Combust. Flame, 130, 123–136.
de Groot, S.R., and Mazur, P. 1984. Non-equilibrium thermodynamics. Dover.
Denet, B. 2006. Stationary solutions and Neumann boundary conditions in the Sivashinsky equation. Phys. Rev. E, 74, 036303–1–9.
Denet, B., Biamino, L., Lodato, G., Vervisch, L., and Clavin, P. 2015. Model equation for the dynamics of wrinkled shock waves. Comparison with DNS and experiments. Combust. Sci. Technol., 187(1–2), 296–323.
Deshaies, B., and Joulin, G. 1984. On the initiation of a spherical flame kernel. Combust. Sci. Technol., 37, 99–116.
Deshaies, B., and Joulin, G. 1989. Flame-speed sensitivity to temperature changes and the deflagration-to-detonation transition. Combust. Flame, 77, 201–212.
Dimont, G., et al. 2004. A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration. Phys. Fluids, 16(5), 1668–1693.
Dominguez, I., and Khokhlov, A. 2011. Incomplete carbon-oxygen detonation in type Ia supernovae. Astrophys. J., 730, 87–102.
Drazin, P.G., and Reid, W.H. 1982. Hydrodynamic instability. Cambridge University Press.
Duchemin, L., Josserand, C., and Clavin, P. 2005. Asymptotic behavior of the Rayleigh– Taylor instability. Phys. Rev. Lett., 94, 224501.
Durox, D., Baillot, F., Searby, G., and Boyer, L. 1997. On the shape of flames under strong acoustic acceleration: A mean flow controlled by the unsteady flow. J. Fluid Mech., 350, 295–310.
D'yakov, S.P. 1954. The stability of shockwaves: Investigation of the problem of stability of shock waves in arbitrary media. Zh. Eksp. Teor. Fiz., 27, 288.
Dzieminska, E., Fukuda, M., Hayashi, A.K., and Yamada, E. 2012. Fast flame propagation in hydrogen/oxygen mixture. Combust. Sci. Technol., 184, 1608–1615.
Eddington, A. 1926. The internal constitution of stars. Cambridge University Press.
Editorial. 1873. The rapidity of detonation. Nature, 8(208), 534.
Einstein, A. 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. (Leipzig), 17, 549–560.
El-Rabii, H., Joulin, G., and Kazakov, K.A. 2010. Stability analysis of confined V-shaped flames in high velocity streams. Phys. Rev. E, 81, 066312.
Ellis, O.C. deC., 1928. Flame movement in gaseous explosive mixtures. J. Fuel Sci., 7(11), 502–508.
Ellzey, J.L., Henneke, M.R., Picone, J.M., and Oran, E.S. 1995. The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves. Phys. Fluids, 7(1), 172–184.
Erpenbeck, J.J. 1962a. Stability of steady-state equilibrium detonations. Phys. Fluids, 5, 604–614.
Erpenbeck, J.J. 1962b. Stability of step shocks. Phys. Fluids, 5(10), 1181–1187.
Erpenbeck, J.J. 1966. Detonation stability for disturbances of small transverse wavelength. Phys. Fluids, 9, 1293–1306.
Euler, L. 1944. Cinq mémoires sur la nature et la propagation du feu. Association pour la sauvegarde du patrimoine métallurgique du Haut-Marnais.
Faraday, M. 1831. On a peculiar class of acoustical figures and on certain forms assumed by a group of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. London, 121, 299–338.
Farquhar, I.E. 1964. Ergodic theory in statistical mechanics. Monographs in statistical physics, vol. 7. Interscience.
Fermi, E. 1956. Thermodynamics. New York: Dover.
Fernandez-Galisteo, D., Sanchez, A.L., Liñan, A., and Williams, F.A. 2009a. The hydrogen–air burning rate near the lean flammability limit. Combust. Theor. Model., 13(4), 741–761.
Fernandez-Galisteo, D., Sanchez, A.L., Liñan, A., and Williams, F.A. 2009b. One-step reduced kinetics for lean hydrogen–air deflagration. Combust. Flame, 156, 985–996.
Fernández-Tarrazo, E., Vera, M., and Liñán, A. 2006. Liftoff and blowoff of a diffusion flame between parallel streams of fuel and air. Combust. Flame, 144(1–2), 261–276.
Ferro, M. 2001. Histoire de France. Odile Jacob.
Ferzigzer, J.H., and Kaper, H.G. 1972. Mathematical theory of transport processes in gases. North-Holland.
Fickett, W., and Davis, W.C. 1979. Detonation. University of California Press.
Fickett, W., and Wood, W.W. 1966. Flow calculations for pulsating one-dimensional detonations. Phys. Fluids, 9, 903–916.
Filyand, L., Sivashinsky, G.I., and Frankel, M.L. 1994. On self-acceleration of outward propagating wrinkled flames. Physica D, 72, 110–118.
Fisher, R.A. 1937. The wave of advance of advantageous genes. Annals of Eugenics, 7, 355–369.
Forster, D. 1975. Hydrodynamic fluctuations, broken symmetry, and correlation functions. Benjamin Cummings.
Fowles, G.R. 1981. Stimulated and spontaneous emission of acoustic waves from shock fronts. Phys. Fluids, 24(2), 220–227.
Frankel, M.L. 1990. An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows. Phys. Fluids, A 2(10), 1897–1883.
Frankel, M.L., and Sivashinsky, G.I. 1983. On the effects due to thermal expansion and Lewis number in spherical flame propagation. Combust. Sci. Technol., 31, 131–138.
Frankel, M.L., and Sivashinsky, G.I. 1984. On quenching of curved fronts. Combust. Sci. Technol., 40, 257.
Frisch, U. 1995. Turbulence. Cambridge University Press.
Frisch, U., and Morf, R. 1981. Intermittency in nonlinear dynamics and singularities at complex times. Phys. Rev. A, 23(5), 2673–2705.
Gamezo, V.N., Poludnenko, A.Y., and Oran, E.S. 2011. One-dimensional evolution of fast flames. Pages 24–29 of: Proceedings of 23rd ICDERS.
Garcia, P., Nicoli, C., and Clavin, P. 1984. Soret and dilution effects on premixed flames. Combust. Sci. Technol., 42, 87–109.
Garcia-Schäfer, J.E., and Liñan, A. 2001. Longitudinal acoustic instabilities in slender solid propellant rockets: Linear analysis. J. Fluid Mech., 437, 229–254.
Goldreich, P., and Weber, S.V. 1980. Homologously collapsing stellar cores. Astrophys. J., 238, 991–997.
Goncharov, V., Betti, R., McCrory, R., Sorotokin, P., and Verdon, C. 1996. Self-consistent stability analysis of ablation fronts with large Froude number. Phys. Plasmas, 3, 1402–14.
Gostintsev, Yu.A., Istratov, A.G., and Shulenin, Yu.V. 1988. Self-similar propagation of a free turbulent flame in mixed gas mixtures. Combust. Expl. Shock Waves, 24(5), 563–569.
Graña-Otero, J.C. 2009. Nonlinear dynamics of unsteady premixed planar flames. Ph.D. thesis, Universidad Politécnica de Madrid, ETSIA.
Groff, E.G. 1982. The cellular nature of confined spherical propane–air flames. Combust. Flame, 48, 51–62.
Guichard, L., Vervisch, L., and Domingo, P. 1995. Two-dimensional weak shock-vortex interaction in a mixing zone. AIAA J., 33(10), 1797–1802.
Guilly, V., Khasainov, B., Presles, H.-N., and Desbordes, D. 2006. Numerical simulation of detonation with double cellular structure. C. R. Acad. Sci. Paris, 334(11), 679–685.
Gurbatov, S.N., Saichev, A.I., and Shandarin, S.F. 2012. Large scale structure of the universe. The Zeldovich approximation and the adhesion model. Sov. Phys.–Uspeki, 55(3), 223–249.
He, L. 2000. Critical conditions for spherical flame initiation in mixtures with high Lewis numbers. Combust. Theor. Model., 4, 159–172.
He, L., and Clavin, P. 1992. Critical conditions for detonation initiation in cold gaseous mixtures by nonuniform hot pockets of reactive gases. Proc. Comb. Inst., 24, 1861–1867.
He, L., and Clavin, P. 1993a. Premixed hydrogen–oxygen flames. Part 1. Combust. Flame, 93, 391–407.
He, L., and Clavin, P. 1993b. Premixed hydrogen–oxygen flames. Part 2: Quasi-isobaric ignition and flammability limits. Combust. Flame, 93, 408–420.
He, L., and Clavin, P. 1994a. On the direct initiation of gaseous detonations by an energy source. J. Fluid Mech., 277, 227–248.
He, L., and Clavin, P. 1994b. Theoretical and numerical analysis of the photochemical initiation of detonation in hydrogen–oxygen mixtures. Proc. Comb. Inst., 25, 45–51.
He, L., and Law, C.K. 1996. Geometrical effects on detonation initiation by a nonuniform hot pocket of reactive gas. Phys. Fluids, 8(1), 248–257.
He, L., and Lee, J.H. 1995. On the dynamic limit of one-dimensional detonations. Phys. Fluids, 7, 1151–1158.
Hewson, J.C., and Williams, F.A. 1999. Rate–ratio asymptotic analysis of methane–air diffusion-flame structure for prediction of oxides of nitrogen. Combust. Flame, 117, 441–476.
Higgins, B. 1802. On the sound produced by a current of hydrogen gas passing through a tube. A Journal of Natural Philosophy, Chemistry and the Arts, 1, 129–131.
Higuera, F.J. 2009. Aerodynamics of a slender axisymmetric Bunsen flame with large gas expansion. Combust. Flame, 156, 1063–1067.
Higuera, F.J. 2010. Effects of fresh gas velocity and thermal expansion on the structure of a Bunsen flame tip. Combust. Flame, 157(8), 1586–1593.
Hinze, J.O. 1975. Turbulence. McGraw-Hill.
Huang, K. 1987. Statistical mechanics. 2nd edn. New York: Wiley.
Hugoniot, P.H. 1889. Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits. Journal de l'École Polytechnique, 58(1), 1–125.
Istratov, A.G., and Librovich, V.B. 1969. On the stability of gasdynamic discontinuities associated with chemical reaction; the case of spherical flame. Acta Astronaut., 14, 453–457.
Ivanov, M.F., Kiverin, A.D., and Liberman, M.A. 2011. Hydrogen–oxygen flame acceleration and transition to detonation in channels with no-slip walls for a detailed chemical reaction model. Phys. Rev. E, 83, 056313.
Ivanov, M.F., Kiverin, A.D., Yakovenko, I.S., and Liberman, M.A. 2013. Hydrogen–oxygen flame acceleration and deflagration-to-detonation transition in three-dimensional rectangular channel with no-slip walls. J. Hydrogen Energy, 38, 16427–16440.
Janka, H.T. 2012. Explosion mechanism of core-collapse supernovae. Annu. Rev. Nucl. Part. Sci., 62, 407–451.
Janka, H.-T., Langanke, K., Marek, A., Martnez-Pinedo, G., and Müller, B. 2007. Theory of core-collapse supernovae. Phys. Rep., 442, 38–74.
Jomaas, G., Law, C.K., and Bechtold, J.K. 2007. On the transition to cellularity in expanding spherical flames. J. Fluid Mech., 583, 1–26.
Joubert, F., Desbordes, D., and Presles, H.-N. 2008. Detonation cellular structure in NO2/N2O4-fuel gaseous mixtures. Combust. Flame, 152, 482–495.
Joulin, G. 1985. Point-source initiation of lean spherical flames of light reactants: An asymptotic theory. Combust. Sci. Technol., 43, 99–113.
Joulin, G. 1987. Preferential diffusion and the initiation of lean flames of light fuels.SIAM. J. Appl. Math., 47(5), 998–1016.
Joulin, G. 1989. On the hydrodynamic stability of curved premixed flames. J. Phys.–Paris., 50, 1069–1082.
Joulin, G. 1994a. Nonlinear hydrodynamic instability of expanding flames: Intrinsic dynamics. Phys. Rev. E, 50(3), 2030–2047.
Joulin, G. 1994b. On the response of premixed flames to time-dependent stretch and curvature. Combust. Sci. Technol., 97, 219–229.
Joulin, G., and Cambray, P. 1992. On a tentative approximate evolution equation for markedly wrinkled premixed flames. Combust. Sci. Technol., 81, 243–256.
Joulin, G., and Clavin, P. 1976. Analyse asymptotique des conditions d'extinction des flammes laminaires. Acta Astronaut., 3, 223–240.
Joulin, G., and Clavin, P. 1979. Linear stability analysis of nonadiabatic flames: Diffusional-thermal model. Combust. Flame, 35, 139–153.
Joulin, G., and Vidal, P. 1998. An introduction to the instability of flames, shocks, and detonations. Pages 493–675 of: Godrèche, G., and Manneville, P. (eds), Hydrodynamics and nonlinear instabilities. Cambridge University Press.
Joulin, G., El-Rabii, H., and Kazakov, K.A. 2008. On-shell description of unsteady flames. J. Fluid Mech., 608, 217–242.
Kagan, L., Gordon, P., and Sivashinsky, G. 2015. An asymptotic study of the transition from slow to fast burning in narrow channels. Proc. Comb. Inst., 35, 913–920.
Kagan, L., and Sivashinsky, G. 2000. Flame propagation and extinction in large-scale vortical flows. Combust. Flame, 120(1–2), 222–232.
Kagan, L., and Sivashinsky, G. 2003. The transition from deflagration to detonation in thin channels. Combust. Flame, 134, 389–397.
Kagan, L., and Sivashinsky, G. 2014. Modeling of deflagration-to-detonation transition with ignition-temperature. In: Roy, G. S., and Frolov, S.M. (eds), Transient combustion and detonation phenomena. Moscow: Torus Press.
Kagan, L., Gordon, P., and Sivashinsky, G. 2015. An asymptotic study of the transition from slow to fast burning in narrow channels. Proc. Comb. Inst., 35, 913–920.
Kagan, L.K., and Sivashinsky, G. 2008. Autoignition due to hydraulic resistance and deflagration-to-detonation transition. Combust. Flame, 154, 186–190.
Kampe, T. 1986. Acoustic emission by vortex motion. J. Fluid Mech., 173, 643.
Kapila, A.K., Schwendeman, D.W., Quirk, J.J., and Hawa, T. 2002. Mechanism of detonation formation due to a temperature gradient. Combust. Theor. Model., 6, 553–594.
Kapitza, P.L. 1951. Dynamic stability of a pendulum when its point of suspension vibrates. Sov. Phys. – JETP, 21(in Russian).
Karlin, V., and Sivashinsky, G. 2006. The rate of expansion of spherical flames. Combust. Theor. Model., 10(4), 625–637.
Karlovitz, B., Denniston, J.R., Knapschaeffer, D.H., and Wells, F.E. 1953. Studies in turbulent flames. Proc. Comb. Inst., 4, 613.
Kaskan, W.E. 1953. An investigation of vibrating flames. Proc. Comb. Inst., 4, 575–591.
Kazakov, K.A. 2005. On-shell description of stationary flames. Phys. Rev. Lett., 17, 032107.
Kazakov, K.A. 2012. Analytical study in the mechanism of flame movement in horizontal tubes. Phys. Fluids, 24, 022108.
Kazakov, K.A. 2013. Analytical study in the mechanism of flame movement in horizontal tubes. II. Flame acceleration in smooth open tubes. Phys. Fluids, 25, 082107.
Kazakov, K.A. 2015. Mechanism of partial flame propagation and extinction in a strong gravitational field. Phys. Rev. Lett., 115, 264051.
Kelley, A.P., Jomaas, G., and Law, C.K. 2009. Critical radius for sustained propagation of spark-ignited spherical flames. Combust. Flame, 156, 1006–1013.
Keshet, U., and Balberg, S. 2012. Critical conditions for core-collapse supernovae. Phys. Rev. Lett., 108, 251101.
Kessler, D.A., Gamezo, V.N., and Oran, E.S. 2010. Simulations of flame acceleration and deflagration-to-detonation transitions in methane–air systems. Combust. Flame, 157, 2063–2077.
Khokhlov, A.M. 1993. Stability of detonations in supernovae. Astrophys. J., 419, 200–206.
Kippenhahn, R., and Weigert, A. 1994. Stellar structure and evolution. 3rd edn. Springer-Verlag.
Kolmogorov, A.N., Petrovskii, I.G., and Piskunov, N.S. 1937. A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Bjul. Moskovskovo Gos. Univ, 1(7), 1–72.
Konnov, A.A. 2009. Implementation of the NCN pathway of prompt-NO formation in the detailed reaction mechanism. Combust. Flame, 156, 2093–2105.
Kontorovich, V.M. 1957. Concerning the stability of shock waves. Zh. Eksp. Teor. Fiz., 33, 1525.
Korobeinikov, P.V. 1971. Gas dynamics of explosions. Ann. Rev. Fluid Mech., 3, 317–346.
Kull, H.J. 1989. Incompressible description of Rayleigh–Taylor instabilities in laserablated plasmas. Phys. Fluids, B1, 170–82.
Kull, H.J. 1991. Theory of the Rayleigh–Taylor instability. Phys. Rep., 206(5), 197–325.
Kuo, K.K. 2005. Principles of combustion. 2nd edn. Hoboken, N.J.: John Wiley and Sons.
Kuramoto, Y. 1978. Diffusion-induced chaos in reaction systems. Prog. Theor. Phys. Supp., 64, 346–367.
Kuramoto, Y., and Tsuzuki, T. 1976. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Prog. Theor. Phys., 55(2), 356–369.
Kurdyumov, V., Sanchez, A.L., and Liñan, A. 2003. Heat propagation from a concentrated external heat source in gas. J. Fluid Mech., 491, 379–410.
Kuznetsov, M., Alekseev, V., Matsukov, I., and Dorofeev, S. 2005. DTT in a smooth tube filled with hydrogen–oxygen mixture. Shock Waves, 14(3), 205–215.
Kuznetsov, M., Liberman, M., and Matsukov, I. 2010. Experimental study of the preheated zone formation and deflagration to detonation transition. Combust. Sci. Technol., 182, 1628–1644.
Kwon, O.C., Abid, M., Liu, J.B., Ronney, P.D., Struk, P.M., and Weiland, K.J. 2004. Structure of Flame Balls at Low Lewis Number (SOFBALL) Experiment. Paper No. 2004–0289 of: 42nd AIAA Aerospace Sciences Meeting, Reno.
Landau, L. 1944. On the theory of slow combustion. Acta Phys. Chim., 19, 77–85.
Landau, L., and Lifchitz, E. 1967. Mécanique quantique. Mir.
Landau, L., and Lifchitz, E.M. 1982. Statistical physics. Part I. 3rd edn. Oxford: Pergamon Press.
Landau, L., and Lifchitz, E.M. 1986. Fluid mechanics. 1st edn. Pergamon.
Landau, L.D., and Lifshitz, E.M. 1976. Mechanics. Butterworth-Heinemann.
Lapworth, K.C. 1959. An experimental investigation of the stability of planar shock waves. J. Fluid Mech., 6, 469–480.
Larsson, J., and Lele, S.K. 2009. Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids, 21, 126101.
Lavrentiev, M., and Chabat, B. 1980. Effets hydrodynamiques et modèles mathématiques. Editions MIR.
Law, C.K. 2006. Combustion physics. Cambridge University Press.
Law, C.K., Ishizuka, S., and Cho, P. 1982. On the opening of premixed Bunsen flame tips. Combust. Sci. Technol., 28, 89–96.
Layzer, D. 1955. On the instability of superposed fluids in a gravitational field. Astrophys. J., 122, 1–12.
Lee, J.H. 1977. Initiation of gaseous detonation. Ann. Rev. Phys. Chem., 28, 75–104.
Lee, J.H. 1984. Dynamic parameters of gaseous detonations. Ann. Rev. Fluid Mech., 16, 311–336.
Lee, J.H., and Higgins, A.J. 1999. Comments on criteria of direct initiation of detonation. Proc. R. Soc. London Ser. A, 357, 3503–3521.
Lee, J.H., Knystautas, R., and Yoshikawa, N. 1978. Photochemical initiation of gaseous detonations. Acta Astronaut., 5, 971–982.
Lee, J.H.s. 2008. The detonation phenomenon. Cambridge University Press.
Lee, J.H.s., and Berman, M. 1997. Hydrogen combustion and its application to nuclear reactor safety. Advances in Heat Transfer, 29, 59–126.
Lee, J.H.s., and Moen, I.O. 1980. The mechanism of transition from deflagration to detonation in vapor cloud explosions. Prog. Energy Combust. Sci., 6, 359–389.
Lee, Y.C., and Chen, H.H. 1982. Nonlinear dynamical models of plasmas turbulence. Phys. Scripta, T2, 41–47.
Lehr, H.F. 1972. Experiments on shock-induced combustion. Acta Astronaut., 17, 589–597.
Lenglet-Dufresnoy, N. 1742. Histoire de la philosophie hermétique. Coustelier, Quai des Augustins.
Lewis, B., and von Elbe, G. 1961. Combustion flames and explosions of gases. Academic Press.
Libby, P.A., and Bray, K.N.C. 1981. Countergradient diffusion in premixed turbulent flames. AIAA J., 19, 205–213.
Libby, P.A., and Williams, F.A. 1982. Structure of laminar flamelets in premixed turbulent flames. Combust. Flame, 44(1–3), 287–303.
Libby, P.A., and Williams, F.A. 1987. Premixed laminar flames with general rates of strain. Combust. Sci. Technol., 54(1–6), 237–273.
Libby, P.A., Liñan, A., and Williams, F.A. 1983. Strained premixed laminar flames with nonunity Lewis numbers. Combust. Sci. Technol., 34, 257–291.
Liberman, M.A., Sivashinsky, G.I., Valiev, D.M., and Eriksson, L.-E. 2006. Numerical simulation of deflagration-to-detonation transition: The role of hydrodynamic instability. Int. J. Transp. Phenomena, 8, 253–277.
Lide, David R. (ed). 2014–2015. CRC handbook of chemistry and physics. 75th edn. CRC Press.
Lifshitz, E.M., and Pitaevskii, L.P. 1999. Physical kinetics. Butterworth Heinemann.
Lighthill, M.J. 1952. On sound generated aerodynamically. 1. General theory. Proc. R. Soc. London Ser. A, A221, 564–587.
Lighthill, M.J. 1954. On sound generated aerodynamically. 2. Turbulence as source of sound. Proc. R. Soc. London Ser. A, 222, 1–32.
Liñan, A. 1971. A theoretical analysis of premixed flame propagation with an isothermal chain reaction. AFOSR Contract No. E00AR68-0031 1. INTA Madrid.
Liñan, A. 1974. The asymptotic structure of counterflow diffusion flames for large activation energies. Acta Astronaut., 1(7–8), 1007–1039.
Liñan, A., and Clavin, P. 1987. Premixed flames with nonbranching chain reactions (structure and dynamics). Combust. Flame, 70, 137–159.
Liñan, A., Kurdyumov, V., and Sanchez, A.L. 2012a. Initiation of reactive blast waves by external energy sources. C. R. Mécanique, 340, 829–844.
Liñan, A., Kurdyumov, V., and Sanchez, A.L. 2012b. Initiation of reactive blast waves by external energy sources. In: Vazquez-Cendon, E., et al. (eds), Numerical methods of hyperbolic equations, vol. 61–74. Taylor and Francis.
Lindl, J.D. 1998. Inertial confinement fusion. Springer.
Lodato, G., and Vervisch, L. 2014. DNS of shock-vortex interaction using spectral difference high-order methods. Private communication.
Longair, M. 2003. Theoretical concepts in physics. Cambridge University Press.
Majda, A., and Rosales, R. 1983. A theory for spontaneous Mach stem formation in reacting fronts, I: The basic perturbation analysis. SIAM J. Appl. Math., 43(6), 1310–1334.
Mallard, E.E., and Le Chatelier, H. 1883. Recherches expérimentales et théoriques sur la combustion des mélanges gazeux explosifs. Annales des Mines, Paris, Series 8(4), 296–378.
Manneville, P. 2014. On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular. J. Mech. B/Fluids, 49(SI), 345–362.
Marble, F.E. 1985. Growth of a diffusion flame in the field of a vortex. Pages 395–413 of: Recent advances in the aerospace sciences. New York: Plenum Press.
Marble, F.E., and Candel, S. 1977. Acoustic disturbances from gas non-uniformities convected through a nozzle. J. Sound Vib., 55(2), 225–243.
Markstein, G.H. 1953. Instability phenomena in combustion waves. Proc. Comb. Inst., 4, 44–59.
Markstein, G.H. 1956. A shock-tube study of flame front pressure wave interaction. Proc. Comb. Inst., 6, 387–398.
Markstein, G.H. 1957. Flow disturbances induced near a slightly wavy contact surface, or flame front, traversed by a shock wave. J. Aero. Sci., 24, 238–239.
Markstein, G.H. 1964. Nonsteady flame propagation. New York: Pergamon.
Matalon, M. 2007. Intrinsic flame instabilities in premixed and nonpremixed combustion. Ann. Rev. Fluid Mech., 39, 163–191.
Matalon, M., and Creta, F. 2012. The turbulent flame speed of wrinkled premixed flames. C. R. Mécanique, 340, 845–858.
Matalon, M., and Matkowsky, B.J. 1982. Flames as gas dynamic discontinuities. J. Fluid Mech., 124, 239–259.
McComb, W.D. 1990. The physics of fluid turbulence. Clarendon Press–Oxford Science Publications.
McQuarrie, D.A. 1973. Statistical mechanics. Harper and Row.
McQuarrie, D.A. 2003. Mathematical methods for scientists and engineers. University Science Books.
Mendoza, E. (ed). 1977. Reflections on the motive power of fire by Sadi Carnot and other papers. Gloucester, Mass.: Peter Smith.
Mery, Y., Hakim, L., Scouflaire, P., Vingert, L., Ducruix, S., and Candel, S. 2013. Experimental investigation of cryogenic flame dynamics under transverse acoustic modulations. C. R. Mécanique, 341, 100–109.
Merzhanov, A.G., and Khaikin, B.I. 1988. Theory of combustion in homogeneous media. Prog. Energy Combust. Sci., 14(1), 1–98.
Meunier, P., and Villermaux, E. 2010. The diffusive strip method for scalar mixing in two dimensions. J. Fluid Mech., 662, 134–172.
Mevel, R., Davidenko, D., Austin, J.M., Pintgen, F., and Shepherd, J.E. 2014. Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen–oxygen–diluent mixtures. J. Hydrogen Energy, 39, 6044–6060.
Meyer, J.M., Urtiew, P.A., and Oppenheim, A.K. 1970. On the inadequacy of gas dynamic processes for triggering the transition to detonations. Combust. Flame, 14(1), 13–20.
Michelson, D.M., and Sivashinsky, G.I. 1977. Nonlinear analysis of hydrodynamic instability in laminar flames – II. Numerical experiments. Acta Astronaut., 4, 1207–1221.
Monin, A.S., and Yaglom, A.M. 1971. Statistical fluid mechanics. Vols. 1 and 2. MIT Press.
Morse, P.M., and Ingard, K.U. 1986. Theoretical acoustics. Princeton University Press.
Müller, I. 2007. A history of thermodynamics. Springer.
Murray, J.D. 1993. Mathematical biology. Biomathematics, vol. 19. Springer.
Nicoli, C., and Pelcé, P. 1989. One-dimensional model for the Rijke tube. J. Fluid Mech., 202, 83–96.
Nicoli, C., Clavin, P., and Liñan, A. 1990. Travelling waves in the cool flame regime. Pages 317–334 of: Gray, P., Nicolis, G., Barras, F., Borkmans, P., and Scott, S.K. (eds), Spatial inhomogeneities and transient behavior in chemical kinetics. Manchester University Press.
NIST (ed). NIST-JANAF Thermochemical tables. http://kinetics.nist.gov/janaf/.
Noiray, N., and Schuermans, B. 2013a. Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Int. J. NonLin. Mech., 50, 152–163.
Noiray, N., and Schuermans, B. 2013b. On the dynamic nature of azimuthal thermoacoustic modes in annular gas turbine combustion chambers. Proc. R. Soc. London Ser. A, 469, 20120535.
Onsager, L. 1949. Statistical hydrodynamics. Nuovo Cimento, 6, 279–287.
Oppenheim, A.K., and Soloukhin, R.I. 1973. Experiments in gasdynamics of explosions. Ann. Rev. Fluid Mech., 5, 31–58.
Oran, E.S., and Gamezo, V. N. 2007. Origins of the deflagration-to-transition detonation in gas-phase combustion. Combust. Flame, 148, 4–47.
Oran, E.S., Gamezo, V.N., and Zipf, R.K. 2015. Large-scale experiments and absolute detonability of methane–air mixtures. Combust. Sci. Technol., 187, 324–341.
Ostriker, J.P. (ed). 1992. Selected works of Ya.B. Zeldovich. Vol. 1, p. 193. Princeton University Press.
Palm-Leis, A., and Strehlow, R.A. 1969. On the propagation of the turbulent flames. Combust. Flame, 13, 111–129.
Pathria, P.K. 1972. Statistical mechanics. Pergamon Press.
Pelcé, P. 2004. New visions on form and growth. Oxford University Press.
Pelcé, P., and Clavin, P. 1982. Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech., 124, 219–237.
Pelcé, P., and Clavin, P. 1987. The stability of curved fronts. Europhys. Lett., 3, 907–913.
Pelcé, P., and Rochwerger, D. 1992. Vibratory instability of cellular flames propagating in tubes. J. Fluid Mech., 239, 293–307.
Peters, N. 1986. Laminar flamelet concepts in turbulent combustion. Proc. Comb. Inst., 21, 1231–1250.
Peters, N. 1997. Kinetic foundation of thermal flame theory. Prog. Astronaut. Aeronaut., 173, 73–91.
Peters, N. 2000. Turbulent combustion. Benjamin Cummings.
Peters, N., and Rogg, B. (eds). 1993. Reduced kinetic mechanisms for applications in combustion systems. Springer-Verlag.
Peters, N., and Williams, F.A. 1987. The asymptotic structure of stoichiometric methane air flames. Combust. Flame, 68(2), 185–207.
Peters, N., and Williams, F.A. 1988. Premixed combustion in a vortex. Proc. Comb. Inst., 22, 495–503.
Phillips, A.C. 1994. The physics of stars. John Wiley and Sons.
Piriz, A.R. 2001. Hydrodynamic instability of ablation fronts in inertial confinement fusion. Phys. Plasmas, 8, 997–1002.
Piriz, A.R., Sanchez, A.L., and Ibanez, L.F. 1997. Rayleigh–Taylor instability of the steady ablation fronts: The discontinuity model revisited. Phys. Plasmas, 4, 1117–1126.
Pocheau, A. 1994. Scale invariance in turbulent combustion. Phys. Rev. E, 49, 1109–1122.
Pocheau, A. 2000. Scale covariance and geometry in turbulent combustion. Pages 187– 204 of: Chaté, H., Chomaz, J.M., and Villermaux, E. (eds), Chaos and turbulence. Series B, vol. 373. NATO ASI.
Pocheau, A., and Harambat, F. 2008. Front propagation in a laminar cellular flow: Shapes, velocities, and least time criterion. Phys. Rev. E, 77(3), 036304.
Pocheau, A., and Queiros-Condé, D. 1996a. Scale covariance of the wrinkling law of turbulent propagating interfaces. Phys. Rev. Lett., 76(18), 3352–3355.
Pocheau, A., and Queiros-Condé, D. 1996b. Transition from Euclidean to fractal forms within a scale-covariant process: A turbulent combustion study. Europhys. Lett., 35, 439–444.
Poincaré, H. 1908. Conférences sur la télégraphie sans fil. Revue d'électricité, 387.
Poinsot, T., and Veynante, D. 2005. Theoretical and numerical combustion. Edwards.
Poinsot, T., Candel, S., and Trouvé, A. 1996. Application of direct numerical simulation to premixed turbulent combustion. Prog. Energy Combust. Sci., 21, 531–576.
Poisson, S.D. 1808. Mémoire sur la théorie du son. Journal de l'École Polytechnique, 14(7), 319–392.
Pomeau, Y. 1986. Front motion, metastability and subcritical bifurcation in hydrodynamics. Physica D, 23, 3–11.
Pomeau, Y. 2014. The transition to turbulence in parallel flow: A personal view. C. R. Acad. Sci. A, 343(3), 210–218.
Pope, S.B. 2000. Turbulent flows. Cambridge University Press.
Presles, H.N., Desbordes, D., and Bauer, P. 1987. An optical method for the study of the detonation front structure in gaseous explosive mixtures. Combust. Flame, 70, 207–213.
Prigogine, I. 1967. Thermodynamics of irreversible processes. 3rd edn. Interscience.
Prigogine, I., and Kondepudi, D. 1999. Thermodynamique. Des moteurs thermiques aux structures dissipatives. Odile Jacob.
Radulescu, M.I., Sharpe, G., Law, C.K., and Lee, J.H.s. 2007. The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech., 580, 31–81.
Rahibe, M., Aubry, N., Sivahinsky, G.I., and Lima, R. 1995. Formation of wrinkles in outwardly propagating flames. Phys. Rev. E, 52(4), 3675–3686.
Rankine, W.J.M. 1870. On the thermodynamic theory of waves of finite longitudinal disturbance. Philos. Trans. R. Soc. London, 160, 277–288.
Rauschenbakh, B.V. 1961. Vibrational combustion. Moscow: Fizmatgiz, Mir.
Rayleigh, J.W.S. 1910. Aerial plane waves of finite amplitude. Proc. R. Soc. London, 84, 247–284.
Rayleigh, J.W.S. 1945. The theory of sound. Vols. 1 and 2. New York: Dover.
Reif, F. 1965. Fundamentals of statistical and thermal physics. McGraw-Hill.
Ribner, S.S. 1985. Cylindrical sound wave generated by shock–vortex interaction. AIAA J., 23(11), 1708–1715.
Richtmyer, R.D. 1960. Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math., 13, 297–319.
Riemann, B. 1860. Über die fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. Abhandl. Ges. Wiss. Göttingen, 8, 43–65. (English translation Int. J. Fusion Energy 2, 1–23, 1980).
Rijke, P.L. 1859. On the vibration of the air in a tube open at both ends. Phil. Mag., 17, 419–422.
Ronney, P.D. 1985. Effects of gravity on laminar premixed gas combustion. II: Ignition and extinction phenomena. Combust. Flame, 62, 121–133.
Ronney, P.D. 1990. Near-limit flame structures at low Lewis number. Combust. Flame, 82, 1–14.
Ronney, P.D., and Wachman, H.Y. 1985. Effect of gravity on laminar premixed gas combustion. I: Flammability limits and burning velocities. Combust. Flame, 62, 107–119.
Ronney, P.D., Wu, M.S., Pearlman, H.G., and Weiland, K.J. 1998. Experimental study of flame balls in space: Preliminary results from STS-83. AIAA J., 36, 1361–1368.
Salamandra, G.D., Bazhenova, T.V., and Naboko, I.M. 1958. Formation of detonation wave during combustion of gas in combustion tube. Proc. Comb. Inst., 7, 851–855.
Sanchez, A.L., and Williams, F.A. 2014. Recent advances in understanding of flammability characteristics of hydrogen. Prog. Energy Combust. Sci., 41, 1–55.
Sanchez, A.L., Carretero, M., Clavin, P., and Williams, F.A. 2001. One-dimensional overdriven detonations with branched-chain kinetics. Phys. Fluids, 13(3), 776–792.
Sanz, J. 1994. Self-consistent analytical model of the Rayleigh–Taylor instability in inertial confinement fusion. Phys. Rev. Lett., 73, 2700–2703.
Sanz, J. 1996. Self-consistent analytical model of the Rayleigh–Taylor instability in inertial confinement fusion. Phys. Rev. E, 53, 4026–45.
Sanz, J., Liñan, A., Rodriguez, M., and Sanmartin, J.R. 1981. Quasi-steady expansion of plasma ablated from laser-irradiated pellets. Phys. Fluids, 24(11), 2098–2106.
Sanz, J., Masse, L., and Clavin, P. 2006. The linear Darrieus–Landau and Rayleigh–Taylor instabilities in inertial confinement fusion revisited. Phys. Plasmas, 13, 102702.
Saxena, P., and Williams, F.A. 2006. Testing a small detailed chemical-kinetic mechanism for the combustion of hydrogen and carbon monoxide. Combust. Flame, 145, 316–323.
Searby, G. 1992. Acoustic instability in premixed flames. Combust. Sci. Technol., 81, 221–231.
Searby, G., and Clavin, P. 1986. Weakly turbulent wrinkled flames in premixed gases. Combust. Sci. Technol., 46, 167–193.
Searby, G., and Quinard, J. 1990. Direct and indirect measurements of Markstein numbers of premixed flames. Combust. Flame, 82(3-4), 298–311.
Searby, G., and Rochwerger, D. 1991. A parametric acoustic instability in premixed flames. J. Fluid Mech., 231, 529–543.
Searby, G., Sabathier, F., Clavin, P., and Boyer, L. 1983. Hydrodynamical coupling between the motion of a flame front and the upstream gas flow. Phys. Rev. Lett., 51(16), 1450–1453.
Searby, G., Truffaut, J.M., and Joulin, G. 2001. Comparison of experiments and a nonlinear model for spatially developing flame instability. Phys. Fluids, 13, 3270–3276.
Sedov, L.I. 1959. Similarity and dimensional methods in mechanics. Academic Press.
Seshadri, K., and Peters, N. 1990. The inner structure of methane–air flames. Combust. Flame, 81, 96–118.
Seshadri, K., Peters, N., and Williams, F.A. 1994. Asymptotic analyses of stoichiometric and lean hydrogen–air flames. Combust. Flame, 96, 407–427.
Shandarin, S.F., and Zeldovich, Ya.B. 1989. The large-scale structure of the universe. Rev. Mod. Phys., 61(2), 185–222.
Shchelkin, K.I., and Troshin, Ya.K. 1965. Gasdynamics of combustion. Baltimore, Md.: Mono Book Corp.
Shepherd, J.E. 2009. Detonation in gases. Proc. Comb. Inst., 32, 83–98.
Shy, S.S., Ronney, P.D., Buckley, S.G., and Yakhot, V. 1992. Experimental simulation of premixed turbulent combustion using aqueous autocatalytic reactions. Proc. Comb. Inst., 24, 543–551.
Sivashinsky, G.I. 1977a. Diffusional-thermal theory of cellular flames. Combust. Sci. Technol., 15, 137–146.
Sivashinsky, G.I. 1977b. Nonlinear analysis of hydrodynamic instability in laminar flames – I. Derivation of basic equations. Acta Astronaut., 4, 1177–1206.
Sivashinsky, G.I. 2002. Some developments in premixed combustion modeling. Proc. Comb. Inst., 29, 1737–1761.
Sivashinsky, G.I., and Clavin, P. 1987. On the nonlinear theory of hydrodynamic instability in flames. J. Phys., 48, 193–198.
Smith, G.P., Golden, D.M., Frenklach, M., Moriarty, N.W., Eiteneer, B., Goldenberg, M., Bowman, C.T., Hanson, R.K., Song, S. Jr., Gardiner, W.C., Lissianski, V.V., and Qin, Z. 2000. GRI-Mech 3.0. www.me.berkeley.edu/grimech/.
Spitzer, L.J. 1962. Physics of fully ionized plasmas. 2nd edn. New York:Wiley Interscience.
Stoker, J.J. 1989. Differential geometry. Wiley-Interscience.
Strahle, W.C. 1985. A more modern theory of combustion noise. Pages 103–114 of: Casci, C., and Bruno, C. (eds), Recent advances in the aerospace sciences. New York: Plenum Press.
Strehlow, R.A. 1979. Fundamentals of combustion. New York: Kreiger.
Swesty, F.D., Lattimer, J.M., and Myra, E.S. 1994. The role of the equation of state in the prompt phase of type II supernovae. Astrophys. J., 425, 195–204.
Takabe, H., Montierth, L., and Morse, R.L. 1983. Self-consistent eigenvalue analysis of the Rayleigh–Taylor instability in an ablating plasma. Phys. Fluids, 26, 2299–2307.
Takabe, H., Mima, K, Monthierth, L., and Morse, R.L. 1985. Self-consistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma plasma. Phys. Fluids, 28, 3676–82.
Taylor, B.D., Kessler, D.A., Gamezo, V.N., and Oran, E.S. 2013. Numerical simulations of hydrogen detonations with chemical kinetics. Proc. Comb. Inst., 34, 2009–2016.
Taylor, G.I. 1950a. The dynamics of the combustion products behind plane and spherical detonation fronts in explosives. Proc. R. Soc. London Ser. A, 200, 235–247.
Taylor, G.I. 1950b. The formation of a blast wave by a very intense explosion. Part I. Proc. R. Soc. London Ser. A, 201(1065), 159–174.
Taylor, G.I. 1950c. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. London, A 201, 192–196.
Thual, O., Frisch, U., and Henon, M. 1985. Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts. J. Phys., 46(9), 1485–1494.
Truelove, J.K., and McKee, C.F. 1999. Evolution of nonradiative supernova remnants. Astrophys. J., 120, 299–326.
Truffaut, J.M. 1998. Etude expérimentale de l'origine du bruit émis par les flammes de chalumeaux. University thesis, Université d'Aix-Marseille I.
Truffaut, J.M., and Searby, G. 1999. Experimental study of the Darrieus–Landau instability on an inverted-‘V’ flame and measurement of the Markstein number. Combust. Sci. Technol., 149, 35–52.
Turing, A.M. 1952. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London, B 237, 37–72.
Turns, S.R. 2000. An introduction to combustion. 2nd edn. McGraw-Hill.
Uhlenbeck, G.E., and Ford, G.W. 1963. Lectures in statistical mechanics, Lectures in applied mathematics. Providence, R.I.: American Mathematical Society.
Urtiew, P.A., and Oppenheim, A.K. 1966. Experimental observations of the transition to detonation in an explosive gas. Proc. R. Soc. London Ser. A, 295, 13–28.
Vagelopoulos, C.M., and Egolfopoulos, F.N. 1998. Direct experimental determination of laminar flame speeds. Proc. Comb. Inst., 27, 513–519.
Valiev, D., Bychkov, V., Akkerman, V., Eriksson, L.-E., and Markelund, M. 2008. Heating of the fuel mixture due to viscous stress ahead of accelerating flames in deflagrationto- detonation transition. Phys. Lett. A, 372, 4850–4857.
Valiev, D.M., Bychkov, V., Akkerman, V., and Eriksson, L.-E. 2009. Different stages of flame acceleration from slow burning to Chapman–Jouguet deflagration. Phys. Rev. E, 80, 036317.
Valiev, D.M., Bychkov, V., Akkerman, V., Eriksson, L.-E., and Law, C.K. 2013. Quasisteady stages in the process of premixed flame acceleration in narrow channels. Phys. Fluids, 25, 096101–16.
Van Maaren, A., Thung, D.S., and de Goey, L.P.H. 1994. Measurement of flame temperature and adiabatic burning velocity of methane/air mixtures. Combust. Sci. Technol., 96(4–6), 327–344.
Van-Mooren, K., and George, A.R. 1975. On the stability of plane shock. J. Fluid Mech., 68(1), 97–108.
Vaynblat, D., and Matalon, M. 2000. Stability of pole solutions for planar propagating flames. SIAM J. Appl. Math., 60(2), 703–728.
Vieille, P. 1900. Structure des détonations. C. R. Acad. Sci. Paris, 131, 413.
Villermaux, E. 2012. Mixing by porous media. C. R. Mécanique, 340, 933–943.
Villermaux, E., Innocenti, C., and Duplat, J. 2001. Short circuits in the Corrsin–Obukhov cascade. Phys. Fluids, 13(1), 284–289.
Vladimirova, N., Constantin, P., Kiselev, A., Ruchayskiy, O., and Ryzhik, L. 2003. Flame enhancement and quenching in fluid flows. Combust. Theor. Model., 7(3), 487–508.
von Hahnemann, H., and Ehret, L. 1943. Uber den Einfluss starker Schallwellen auf eine stationär brennende Gasflamme. Zeitschrift für Technische Physik, 24, 228–242.
Wheeler, J.C. 2012. Astrophysical explosions: From solar flares to cosmic gamma-ray bursts. Philos. Trans. R. Soc. London Ser. A, 370, 774–799.
Whitham, G.B. 1957. A new approach to problem of shock dynamics. Part I: Twodimensional problem. J. Fluid Mech., 2(2), 145–171.
Whitham, G.B. 1974. Linear and nonlinear waves. John Wiley.
Williams, F.A. 1985. Combustion theory. 2nd edn. Menlo Park, Calif. Benjamin- Cummings.
Woosley, S., and Janka, H.T. 2005. Type II supernova. https://arxiv.org/abs/astro-ph/0601261, 1–11.
Woosley, S.E., Heger, A., and Weaver, T.A. 2002. The evolution and explosion of massive stars. Rev. Mod. Phys., 74, 1015–1071.
Wouchuk, J.G., Huete Ruiz de Lira, C., and Velikovich, A.L. 2009. Analytical linear theory of planar shock wave with isotropic turbulent flow field. Phys. Rev. E, 79(066315).
Wu, F., Saha, A., Chaudhuri, S., and Law, C.K. 2014. Facilitated ignition in turbulence through differential diffusion. Phys. Rev. Lett., 113, 024503.
Wu, M., and Wang, C. 2011. Reaction propagation modes in millimeter-scale tubes for ethylene/oxygen mixtures. Proc. Comb. Inst., 33, 2287–2293.
Wu, M., Burke, M.P., Son, S.F., and Yetter, R.A. 2007. Flame acceleration and the transition to detonation of stoichiometric ethylene/oxygen in microscale tubes. Proc. Comb. Inst., 31, 2429–2436.
Yahil, A. 1983. Self-similar stellar collapse. Astrophys. J., 265, 1047–1055.
Yanez, J., Kuznetsov, M., and Grune, J. 2015. Flame instability of lean hydrogen–air mixtures in a smooth open-ended vertical channel. Combust. Flame, 162, 2830–2839.
Yang, V., and Anderson, W. 1995. Liquid rocket engine combustion instability. Progress in Astronautics and Aeronautics, vol. 169. Washington, D.C. AIAA.
Yungster, S., and Radhakrishnan, K. 2004. Pulsating one-dimensional detonations in hydrogen–air mixtures. Combust. Theor. Model., 8, 745–770.
Yvon, J. 1966. Les corrélations et l'entropie. Dunod.
Zeldovich, Ya.B. 1941. The theory of the limit of propagation of a slow flame. Zh. Eksp. Teor. Fiz., 11(1), 159–169.
Zeldovich, Ya.B. 1961. Chain reactions in hot flames – an approximate theory for flame velocity. Kinetika i Katalis, 2, 305–313.
Zeldovich, Ya.B. 1980. Regime classification of an exothermic reaction with nonuniform initial conditions. Combust. Flame, 39, 211–214.
Zeldovich, Ya.B., and Frank-Kamenetskii, D.A. 1938. A theory of thermal flame propagation. Acta Phys. Chim., 9, 341–350.
Zeldovich, Ya.B., and Kompaneets, A.S. 1960. Theory of detonation. Academic Press.
Zeldovich, Ya.B., and Novikov, I.D. 1971. Stars and relativity. Dover.
Zeldovich, Ya.B., and Raizer, Yu.P. 1966. Physics of shock waves and high-temperature hydrodynamic phenomena I. Academic Press.
Zeldovich, Ya.B., and Raizer, Yu.P. 1967. Physics of shock waves and high-temperature hydrodynamic phenomena II. Academic Press.
Zeldovich, Ya.B., Kogarko, S.M., and Simonov, N. 1956. An experimental investigation of spherical detonation of gases. Sov. Phys. Tech. Phys., 1, 1689–1713.
Zeldovich, Ya.B., Librovich, V.B., Makhviladze, G.M., and Sivashinsky, G.I. 1970. On the development of detonations in a non-uniformly preheated gases. Acta Astronaut., 15, 313.
Zeldovich, Ya.B., Istratov, A.G., Kidin, N.I., and Librovich, V.B. 1980. Flame propagation in tubes. Combust. Sci. Technol., 24, 1–13.
Zeldovich, Ya.B., Barenblatt, G.I., Librovich, V.B., and Makhviladze, G.M. 1985. The mathematical theory of combustion and explosions. New York: Plenum.

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