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Formation of Mach-Stems on Shock Fronts and Cellular Detonations

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Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

The dynamics of shock waves in polytropic gases is addressed. The planar front was known from a long time to be stable but the relaxation mechanism was not understood. The objective of this paper is to clarify this problem. The formation of singularities of the slope of the front after a finite time elapsed from an initial small disturbance is described by an asymptotic analysis for strong shocks in the Newtonian limit. The results shed light into the mechanisms responsible for the pattern formation of cellular detonations.

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Authors and Affiliations

  1. Institut de Recherche sur les Phénomènes Hors Équilibre Aix-Marseille Université et Centre National de la Recherche Scientifique, 146, 49 rue Joliot Curie, 13384, Marseille Cedex 13, France

    P. Clavin

Authors
  1. P. Clavin
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Correspondence to P. Clavin .

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Editors and Affiliations

  1. , Dpt. Quimica-Fisica-I, UCM, Madrid, 28040, Spain

    Ramon G. Rubio

  2. Instituto Pluridisciplinar, UCM, Paseo Juan XXIII 1, Madrid, 28040, Spain

    Yuri S. Ryazantsev

  3. , Dpt. of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, United Kingdom

    Victor M Starov

  4. , Physics Dpt., East China Normal University, Zhongshan Northern Road 3663, Shanghai, 200062, China, People's Republic

    Guo-Xiang Huang

  5. , Faculty of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    Alexander P Chetverikov

  6. , Dpt. di Ingegneria Elettrica Elettronica, Università di Catania, V. le A. Doria 6, Catania, 95125, Italy

    Paolo Arena

  7. , Dept. of Mathematics, Technion, Haifa, 32000, Israel

    Alex A. Nepomnyashchy

  8. , Instituto Cajal, CSIC, Av. Dr. Arce 37, Madrid, 28002, Spain

    Alberto Ferrus

  9. Shirshov Institute of Oceanology, Nakhimovsky prospekt 36, Moscow, 117851, Russia

    Eugene G. Morozov

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Clavin, P. (2013). Formation of Mach-Stems on Shock Fronts and Cellular Detonations. In: Rubio, R., et al. Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34070-3_32

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  • DOI: https://doi.org/10.1007/978-3-642-34070-3_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34069-7

  • Online ISBN: 978-3-642-34070-3

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