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Bifurcation, Pattern Formation and Chaos in Combustion

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Dynamical Issues in Combustion Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 35))

Abstract

Problems in gaseous combustion and in gasless condensed phase combustion are studied both analytically and numerically. In gaseous combustion we consider the problem of a flame stabilized on a line source of fuel. We find both stationary and pulsating axisymmetric solutions as well as stationary and pulsating cellular solutions. The pulsating cellular solutions take the form of either traveling waves or standing waves. Transitions between these patterns occur as parameters related to the curvature of the flame front and the Lewis number are varied. In gasless condensed phase combustion both planar and nonplanar problems are studied. For planar condensed phase combustion we consider two models: (i) accounts for melting and (ii) does not. Both models are shown to exhibit a transition from uniformly to pulsating propagating combustion when a parameter related to the activation energy is increased. Upon further increasing this parameter both models undergo a transition to chaos: (i) by intermittency and (ii) by a period doubling sequence. In nonplanar condensed phase combustion the nonlinear development of a branch of standing wave solutions is studied and is shown to lead to relaxation oscillations and subsequently to a transition to quasi-periodicity.

Supported by N.S.F. grant DMS 87-01543 and D.O.E. grant DEFG02-87ER25027.

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Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois, 60208-3125, USA

    Alvin Bayliss & Bernard J. Matkowsky

Authors
  1. Alvin Bayliss
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  2. Bernard J. Matkowsky
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The University of Utah, Salt Lake City, UT, 84112, USA

    Paul C. Fife

  2. Escuela de Ingenieros Aeronauticos, Ciudad Universitaria, 28040, Madrid, Spain

    Amable Liñán

  3. Department of AMES, University of California, San Diego, La Jolla, CA, 92093, USA

    Forman Williams

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© 1991 Springer Science+Business Media New York

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Bayliss, A., Matkowsky, B.J. (1991). Bifurcation, Pattern Formation and Chaos in Combustion. In: Fife, P.C., Liñán, A., Williams, F. (eds) Dynamical Issues in Combustion Theory. The IMA Volumes in Mathematics and its Applications, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0947-8_1

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  • DOI: https://doi.org/10.1007/978-1-4612-0947-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6957-1

  • Online ISBN: 978-1-4612-0947-8

  • eBook Packages: Springer Book Archive

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