Analytical structure of a generalized direct-interaction approximation
Author:
Jon Lee
Journal:
Quart. Appl. Math. 31 (1973), 155-176
DOI:
https://doi.org/10.1090/qam/99705
MathSciNet review:
QAM99705
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Abstract: As a mathematically tractable example, we have investigated the stochastic dynamic problem of an irreversible second-order chemical reaction. A generalized direct-interaction approximation has been devised to close off the hierarchy of moment equations at the arbitrary moment level, and then the results of such a closure technique have been compared term-by-term with the exact moment solutions. This shows qualitatively how the expansion terms summed up in the direct-interaction approximation are different from the classes of expansion terms present in the exact moment solutions. A quantitative comparison of the covariances indicates that the direct-interaction equations which are closed at the triple moment level represent a meaningful statistical approximation of the lowest order for the second-order reactive problem at hand.
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E. E. O’Brien, Phys. Fluids 9, 1561 (1966)
R. H. Kraichnan, in Dynamics of fluids and plasmas (ed., S. I. Pai) pp. 239–255, Academic Press, New York (1966)
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S. A. Orszag, Dynamics of fluid turbulence, PPLAF-13, Plasma Physics Lab., Princeton University (1966)
J. Lee, J. Stat. Phys. 4, 175 (1972)
E. E. O’Brien, Phys. Fluids 11, 1883 (1968)
J. Lee, Phys. Fluids 9, 1753 (1966)
E. E. O’Brien, Phys. Fluids 9, 1561 (1966)
R. H. Kraichnan, in Dynamics of fluids and plasmas (ed., S. I. Pai) pp. 239–255, Academic Press, New York (1966)
R. H. Kraichnan, J. Math. Phys. 2, 124 (1961)
R. von Mises, Mathematical theory of probability and statistics, p. 403, Academic Press, New York (1964)
S. A. Orszag, Dynamics of fluid turbulence, PPLAF-13, Plasma Physics Lab., Princeton University (1966)
J. Lee, J. Stat. Phys. 4, 175 (1972)
E. E. O’Brien, Phys. Fluids 11, 1883 (1968)
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Article copyright:
© Copyright 1973
American Mathematical Society