Unified Theory of Fluctuations and Parametric Noise

  • M. San Miguel
  • M. A. Rodríguez


Generally speaking a system composed of many particles which are being created and annihilated has an intrinsic stochasticity associate with birth and death processes. Fluctuations associated with this process are usually called internal fluctuations. They, are described by a master equation or probability balance equation1. In the context of stochastic nuclear reactor models the birth and death process is the stochastic fission process with associated emission and absorption probabilities per unit time2. In the limit in which the number of particles N goes to infinity or system size goes to infinity (thermodynamic limit) internal fluctuations become negligeable. In this limit the master equation leads to a deterministic or rate equation. For nuclear reactors this is the point kinetia reactor equation.


Master Equation Noise Source Langevin Equation External Noise Counting Process 
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.-
    N.G. Van Kampen, “Stochastic Processes in Physics and Chemistry”, North-Holland, Amsterdam (1983).Google Scholar
  2. 2.-
    M.M.R. Williams, “Random Processes in Nuclear Reactors”, Pergamon Press, Oxford (1974).Google Scholar
  3. 3.-
    M.A. Rodríguez, M. San Miguel and J.M. Sancho, Ann. nucl. Energy, 10, 263 (1983).CrossRefGoogle Scholar
  4. 4.-
    M.A. Rodriguez, M. San Miguel and J.M. Sancho, Ann. nucl. Energy, 11, 321 (1984).CrossRefGoogle Scholar
  5. 5.-
    M.A. Rodriguez, L. Pesquera, M. San Miguel and J.M. Sancho, J. Stat. Phys. 40, 669 (1985).MathSciNetADSCrossRefGoogle Scholar
  6. 6.-
    K. Saito, Prog. nucl. Energy, 3:157 (1979).ADSCrossRefGoogle Scholar
  7. 7.-
    W. Horsthemke and R. Lefever, “Noise Induced Transitions”, Springer, New York (1983).Google Scholar
  8. 8.-
    J.M. Sancho and M. San Miguel, J. Stat. Phys. 37: 151 (1984).MathSciNetADSCrossRefMATHGoogle Scholar
  9. 9.-
    Z. Ackasu, J. Stat. Phys. 16:33 (1977).ADSCrossRefGoogle Scholar
  10. 10.-
    K. Saito, Ann. nucl. Energy 1:31, 107, 209 (1974).Google Scholar
  11. 11.-
    W. Seifritz, Atomkernenergie 16:29 (1970).Google Scholar
  12. 12.-
    N.G. Van Kampen, Physica 25:3 (1981).Google Scholar
  13. 13.-
    S.A. Wright, R.W. Albrecht and M.F. Edelmann, Ann. nucl. Energy 2:367 (1975).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • M. San Miguel
    • 1
  • M. A. Rodríguez
    • 2
  1. 1.Dpto. de FísicaUniv. de las Islas BalearesPalma de MallorcaSpain
  2. 2.Dpto. de Física ModernaUniv. de CantabriaSantanderSpain

Personalised recommendations