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Bifurcation and hysteresis varieties for the thermal-chainbranching model II: positive modal parameter

Published online by Cambridge University Press:  24 October 2008

Ian Stewart  and
Alexander Woodcock
Ian Stewart
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England 218 Tulip Drive, Gaithersburg, Maryland, U.S.A.
Alexander Woodcock
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England 218 Tulip Drive, Gaithersburg, Maryland, U.S.A.
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Extract

When hydrogen and oxygen react in a closed vessel, the reaction either happens slowly or explosively, depending on the initial temperature θ0 and pressure P. In the (θ0, P)-plane the boundary between these behaviours is represented by a curve. On this curve P is triple-valued over θ0 in certain ranges; that is, for certain initial temperatures there are three explosion limits. This phenomenon, known as the explosion peninsula, is among other things a sign that more than one elementary reaction is involved in the oxidation of hydrogen. Other reactions display similar effects.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 331 - 349
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Golubitsky, M. and Schaeffer, D.. A theory for imperfect bifurcation via singularity theory. Comm. Pure Appl. Math. 32 (1979), 21–98.CrossRefGoogle Scholar
[2] Golubitsky, M. and Schaeffer, D.. Imperfect bifurcation in the presence of symmetry. Comm. Math. Phys. 67 (1979), 205–232CrossRefGoogle Scholar
[3]Golubitsky, M. and Schaeffer, D.. Singularities and Groups in Bifurcation Theory, vol. 1. (Springer-Verlag, to appear 1984)Google Scholar
[4] Golubitsky, M., Keyfitz, B. and Schaeffer, D.. A singularity theory analysis of a thermal- chainbranching model for the explosion peninsula. Comm. Pure Appl. Math. 34 (1981), 433–463.CrossRefGoogle Scholar
[5] Gray, B. F.. Theory of branching reactions with chain interaction. Trans. Faraday Soc. 66 (1970), 1118–1126CrossRefGoogle Scholar
[6] Gray, B. F. and Yang, C. H.. On the unification of the thermal and chain theories of explosion limits. J. Chem. Phys. 69 (1965), 2747.CrossRefGoogle Scholar
[7] StewartI, N. I, N.. Bifurcation and hysteresis varieties for the thermal-chainbranching model with a negative modal parameter. Math. Proc. Cambridge Philos. Soc. 90 (1981), 127–139.CrossRefGoogle Scholar
[8] Stewart, I. N.. Applications of catastrophe theory to the physical sciences. Physica D (1981), 245–305CrossRefGoogle Scholar
[9] Stewart, I. N.. Catastrophe Theory in physics. Rep. Progr. Phys. 45 (1982), 185–221.CrossRefGoogle Scholar