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Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media

  • J. R. Leith
Part of the Institute for Nonlinear Science book series (INLS)

Abstract

Critical slowing down in thermal ignition of energetic media is examined by application of both deterministic and stochastic system models. The framework for analytical description of the thermal ignition problem derives from the generalized concept of critical point exponents. In particular, the time to thermal ignition diverges as the system driving condition approaches its minimum requisite value necessary to induce a sustained exothermic reaction. It is shown here, from both theoretical predictions and laboratory experiments, that there is an evolution of the critical behavior and a broadening of the range of time to ignition for smaller driving conditions and that these are consequences of increased reactant consumption and the inherent stochastic behavior in the approach to thermal ignition.

Keywords

Stochastic Differential Equation Critical Behavior Critical Phenomenon Ignition Time Colored Noise 
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References

  1. [1]
    H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).Google Scholar
  2. [2]
    J. Kestin, A Course in Thermodynamics, vol. 2 (Hemisphere, New York, 1979).Google Scholar
  3. [3]
    H. Thomas, Critical Phenomena, edited by F. Hahne (Springer-Verlag, Berlin, 1983), pp. 141–208.CrossRefGoogle Scholar
  4. [4]
    F.T. Arecchi, Critical Phenomena and Related Topics, edited by C.P. Enz (Springer-Verlag, Berlin, 1979), pp. 357–385.CrossRefGoogle Scholar
  5. [5]
    D.A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics (Plenum Press, New York, 1969).Google Scholar
  6. [6]
    T. Boddington, C.G. Feng, and P. Gray, Proc. R. Soc. London A 385, 289 (1983).ADSCrossRefGoogle Scholar
  7. [7]
    T. Boddington, C.G. Feng, and P. Gray, Proc. R. Soc. London A 391, 269 (1984).ADSCrossRefGoogle Scholar
  8. [8]
    W. Horsthemke, Non-Equilibrium Dynamics in Chemical Systems, edited by C Vidal and A. Pacault (Springer-Verlag, Berlin, 1984), pp. 150–160.CrossRefGoogle Scholar
  9. [9]
    W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984).zbMATHGoogle Scholar
  10. [10]
    C.W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer-Verlag, Berlin, 1985).Google Scholar
  11. [11]
    G.E. Uhlenbeck and L.S. Ornstein, Phys. Rev. 36, 823 (1930).ADSCrossRefGoogle Scholar
  12. [12]
    R.F. Fox, Noise and Chaos in Nonlinear Dynamical Systems, edited by F. Moss, L.A. Lugiato, and W. Schleich (Cambridge University Press, Cambridge, 1990), pp. 207–227.Google Scholar
  13. [13]
    F. Baras, G. Nicolis, M.M. Mansour, and J.W. Turner, J. Stat. Phys. 32, 1 (1983).ADSCrossRefGoogle Scholar
  14. [14]
    G. Blankenship and G.C Papanicolaou, SIAM J. Appl. Math. 34, 437 (1978).MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    K.G. Pierce and J.R. Leith, in Proc. 11th International Pyrotechnics Seminar (IIT Research Institute, Chicago, 1986), pp. 457–470.Google Scholar
  16. [16]
    G. Nicolis, F. Baras, and M.M. Mansour, Non-Equilibrium Dynamics in Chemical Systems, edited by C Vidal and A. Pacault (Springer-Verlag, Berlin, 1984), pp. 184–199.CrossRefGoogle Scholar
  17. [17]
    G. Nicolis and V. Altares, Synergetics and Dynamic Instabilities, edited by G. Caglioti, H. Haken, and L. Lugiato (North-Holland, Amsterdam, 1988), pp. 298–328.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

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  • J. R. Leith

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