Steady State Dynamics of Nonlinear Nuclear Reactor Systems

  • A. Hernández-Machado
  • J. Casademunt


The effects of the nonlinearities in the steady state dynamics of nuclear reactor models have not been considered until recently1,2. The nonlinear terms appear, for example, in the Langevin equation for the number of neutrons, due to an adiabatic elimination of the fast variables (delayed neutrons, fuel temperature, refrigerator temperature, etc.) The reduction in the number of variables gives a more tractable problem in the sense that the validity of the approximations that one uses are more easily known, but the price that is paid is the nonlinearity of the equations. Then, the usual procedure is the linearization of the resulting equations around the deterministic steady state. The validity of this approximation has been considered by many authors3–6. All of these studies agree that the linearization is a good approximation far from the instability points, but it breaks down near them.


Correlation Function Langevin Equation Continue Fraction Expansion Instability Point Steady State Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dutré, W.L. and Debosscher, A.F.; Nucl. Sci. Engn. 62, 355 (1977).Google Scholar
  2. 2.
    Hernández-Machado, A., Rodriguez, M.A. and San Miguel, M.; Ann. Nucl. Energy. 12, 471 (1985).CrossRefGoogle Scholar
  3. 3.
    Williams, M.M.R., “Random Processes in Nuclear Reactors”, Pergamon Press, Oxford (1974).Google Scholar
  4. 4.
    Kishida, K., Kanemoto, S. and Sekiya, T.; J. Nucl. Sci. Tech. 13(1), 19 (1976).CrossRefGoogle Scholar
  5. 5.
    Sako, O., Taniguchi, A. and Kuroda, Y.; Ann. Nucl. Energy 9., 325 (1982).CrossRefGoogle Scholar
  6. 6.
    Rodriguez, M., “Análisis de fluctuaciones en reactores nucleares: modelos no lineales y no markovianos”. Tesis Doctoral. Universidad de Santander (1983).Google Scholar
  7. 7.
    Zwanzig, R., “Lectures in Theoretical Physics” Eds. W. Brittin and L. Dunham, vol.3 (Wiley and Sons, New York, 1961).Google Scholar
  8. 8.
    Casademunt, J. and Hernández-Machado, A., preprint 1988.Google Scholar
  9. 9.a)
    a) Nadler, W. and Schulten, K.; J. Chem. Phys..82, 151 (1985).ADSCrossRefGoogle Scholar
  10. 9.b)
    b) Nadler, W. and Schulten, K.; Z. Physik B59, 53 (1985).ADSGoogle Scholar
  11. 10.
    Brenig, L. and Banai, N.; Physica 5D, 208 (1982).MathSciNetADSGoogle Scholar
  12. 11.
    Graham, R. and Schenzle, A.; Phys. Rev. A25, 1731 (1982).MathSciNetADSGoogle Scholar
  13. 12.
    Fujisaka, H. and Grossman, S.; Z. Physik B43, 69 (1981).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • A. Hernández-Machado
    • 1
  • J. Casademunt
    • 1
  1. 1.Dept. E.C.M., Facultat de FísicaUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations