Noise-Facilitated Critical Behavior in Thermal Ignition of Energetic Media
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.
KeywordsStochastic Differential Equation Critical Behavior Critical Phenomenon Ignition Time Colored Noise
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- H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).Google Scholar
- J. Kestin, A Course in Thermodynamics, vol. 2 (Hemisphere, New York, 1979).Google Scholar
- D.A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics (Plenum Press, New York, 1969).Google Scholar
- C.W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer-Verlag, Berlin, 1985).Google Scholar
- 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
- K.G. Pierce and J.R. Leith, in Proc. 11th International Pyrotechnics Seminar (IIT Research Institute, Chicago, 1986), pp. 457–470.Google Scholar
- 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