Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-29T18:58:39.945Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  24 October 2008

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.

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
Copyright
Copyright © Cambridge Philosophical Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Golubitsky, M. and Schaeffer, D.. A theory for imperfect bifurcation via singularity theory. Comm. Pure Appl. Math. 32 (1979), 2198.CrossRefGoogle Scholar
[2] Golubitsky, M. and Schaeffer, D.. Imperfect bifurcation in the presence of symmetry. Comm. Math. Phys. 67 (1979), 205232CrossRefGoogle 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), 433463.CrossRefGoogle Scholar
[5] Gray, B. F.. Theory of branching reactions with chain interaction. Trans. Faraday Soc. 66 (1970), 11181126CrossRefGoogle 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), 127139.CrossRefGoogle Scholar
[8] Stewart, I. N.. Applications of catastrophe theory to the physical sciences. Physica D (1981), 245305CrossRefGoogle Scholar
[9] Stewart, I. N.. Catastrophe Theory in physics. Rep. Progr. Phys. 45 (1982), 185221.CrossRefGoogle Scholar