Meccanica

, Volume 8, Issue 4, pp 211–215 | Cite as

Some remarks on neutron transport in homogeneous slabs and spheres

  • Giorgio Busoni
  • Luigi Mangiarotti
Article
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Summary

In this work we are concerned with the stationary neutron transport Boltzmann equation (in its integral form) in plane and spherical symmetry; both the study of the properties of the exact and approximate solution are based on functional analysis. We have taken advantage of the fact that the kernel of the integral equation is even, to semplify the general discussion; among the results, we quote that relating to the continuity of the solution with respect to the optical thickness. Moreover we emphasized that the Ritz method seems the most convenient one for the approximate evaluation of the solution; in this connexion, some observations have been made about the convergence of the approximate solutions to the exact one.

Keywords

Mechanical Engineer Integral Equation Civil Engineer Functional Analysis Approximate Solution 
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.

Sommario

In questo lavoro consideriamo l'equazione stazionaria di Boltzmann (nella forma integrale) in simmetria piana e sferica; l'uso di alcuni metodi dell'analisi funzionale ci consente di studiare sia le proprietà della soluzione esatta che di quella approssimata. La semplice osservazione che il nucleo dell'equazione integrale è pari, ci ha permesso di semplificare la discussione generale; tra i risultati segnaliamo quello riguardante la continuità della soluzione rispetto allo spessore ottico. Inoltre abbiamo sottolineato che il metodo di Ritz ci sembra il più opportuno punto di partenza per il calcolo approssimato della soluzione; in relazione a ciò, vengono fatte alcune osservazioni a proposito della convergenza delle soluzioni approssimate verso quella esatta.

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References

  1. [1]
    M. Abramowitz andI. A. Stegun,Handbook of mathematical tables, Dover Publications, N. York, 1965.Google Scholar
  2. [2]
    T. Asaoka, Y. Nakahara andK. Saito,Multiple collision method for neutron transport problems, J. nuclear Energy, no. 18, 665, 1964.Google Scholar
  3. [3]
    T. Asaoka, The jN method for neutron transport problems in a bare sphere, J. nuclear Energy, no. 22, 99, 1968.Google Scholar
  4. [4]
    B. Davison,Neutron transport theory, Clarendon Press, Oxford, 1958.Google Scholar
  5. [5]
    H. Hembd,The integral transform method for neutron transport problems, Nucl. Sci. Engineering, no. 40, 224, 1970.Google Scholar
  6. [6]
    H. Kschwendt, Application of the jN method to neutron transport in slabs and spheres, Nucl. Sci. Engineering, no. 36, 447, 1969.Google Scholar
  7. [7]
    L. Mangiarotti,Un problema di trasporto di neutroni in due regioni accoppiate, Le Matematiche, no. 25, 15, 1970.Google Scholar
  8. [8]
    F. Premuda,Boundness, continuity, positivity and dominance of the solution of the neutron Boltzmann equation, Meccanica no. 4, 204, 1971.Google Scholar
  9. [9]
    F. Riesz andB. Sz-Nagy,Functional analysis, F. Ungar Publishing Co., N. York, 1965.Google Scholar
  10. [10]
    B. Z. Vulikh,Introduction to functional analysis, Pergamon Press, Oxford, 1963.Google Scholar
  11. [11]
    G. M. Wing,An introduction to transport theory, J. Wiley, N. York, 1962.Google Scholar
  12. [12]
    A. C. Zaanen,Linear analysis, North-Holland Publishing Co., Amsterdam, 1964.Google Scholar

Copyright information

© Tamburini Editore s.p.a. Milano 1973

Authors and Affiliations

  • Giorgio Busoni
    • 1
  • Luigi Mangiarotti
    • 1
  1. 1.Istituto Matematico «U. DINI»Firenze

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