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Annali di Matematica Pura ed Applicata

, Volume 140, Issue 1, pp 179–207 | Cite as

On the convergence of the multigroup approximations for multidimensional media

  • H. D. VictoryJr.
Article

Summary

In this paper, we investigate the stability, convergence, and consistency properties of steady-state multigroup models for submultiplying media with spatial dimensions greater than one. We define these concepts in a Banach space whose norm measures the collision density integrated over phase space. Stability and consistency occur under the conditions that the maximum fluctuations in the total cross section, and in the expected number of secondary particles arising from each energy level, tend to zero as the energy mesh becomes finer. A concluding example and discussion deal with pathologies of the multigroup model in situations where these fluctuations do not tend to zero as the norms of the energy partitions. The results in this paper complement the time-dependent results of both Belleni-Morante and Busoni for isotropic slabs and of Yang Mingzhu and Zhu Guangtian for bounded, three-dimensional media. This work directly extends the steady-state results of Paul Nelson, Jr. and H. D. Victory, Jr. for slab media to steady-state transport in multidimensional media.

Keywords

Banach Space Phase Space Total Cross Section Spatial Dimension Secondary Particle 
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.

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Copyright information

© Nicola Zanichelli Editore 1985

Authors and Affiliations

  • H. D. VictoryJr.
    • 1
  1. 1.TexasUSA

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