Abstract
A reaction is called “explosive” when the amount of a reactant becomes infinite in a finite time. When the intrinsic stochastic character of the reaction is taken into account, the explosion time is a random quantity. We compute its probability distribution, or at least its average and variance, for various kinds of reactions. If a reaction is unstable, so that a reactant can either explode or disappear, one first has to compute the probability for an explosion to occur at all, and then the average explosion time. Finally, the same ideas are applied to more general Markov processes.
Similar content being viewed by others
References
D. R. Cox and H. D. Miller,The Theory of Stochastic Processes (Methuen, London, 1965); D. Kannan,An Introduction to Stochastic Processes (North-Holland, New York, 1979).
A. A. Rigos and J. M. Deutch,J. Chem. Phys. 76:5180 (1982); E. Chandler and J. M. Deutch,J. Chem. Phys. 78:4186 (1983).
D. K. Dacol and H. Rabitz,J. Chem. Phys. 81:4396 (1984).
A. Fernández,J. Chem. Phys. 83:4488 (1985).
F. Baras, G. Nicolis, M. Malek-Mansour, and J. W. Turner,J. Stat. Phys. 32:1 (1983).
M. Frankowicz and G. Nicolis,J. Stat. Phys. 33:595 (1983).
N. G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
Z. Schuss,Theory and Applications of Stochastic Differential Equations (Wiley, New York, 1980).
G. H. Weiss,J. Stat. Phys. 42:3 (1986).
N. G. van Kampen,Prog. Theor. Phys. Suppl. 64:389 (1978).
T. G. Kurtz,J. Appl. Prob. 7:49 (1970);8:344 (1971);J. Chem. Phys. 57:2976 (1972).
C. W. Gardiner,Handbook of Stochastic Methods (Springer, Berlin, 1983).
N. G. van Kampen and I. Oppenheim,J. Math. Phys. 13:842 (1972); C. Knessl, B. J. Matkowsky, Z. Schuss, and C. Tier,J. Stat. Phys. 42:169 (1986).
R. B. Griffiths, C. Y. Wang, and J. S. Langer,Phys. Rev. 149:301 (1966); Z. Schuss and B. J. Matkowski,SIAM J. Appl. Math. 36:604 (1979); B. J. Matkowski, Z. Schuss, and C. Tier,J. Stat. Phys. 35:443 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Kampen, N.G. Intrinsic fluctuations in explosive reactions. J Stat Phys 46, 933–948 (1987). https://doi.org/10.1007/BF01011150
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011150