@article{M2AN_1999__33_4_721_0, author = {Allaire, Gr\'egoire and Bal, Guillaume}, title = {Homogenization of the criticality spectral equation in neutron transport}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {721--746}, publisher = {EDP-Sciences}, volume = {33}, number = {4}, year = {1999}, mrnumber = {1726482}, zbl = {0931.35010}, language = {en}, url = {http://www.numdam.org/item/M2AN_1999__33_4_721_0/} }
TY - JOUR AU - Allaire, Grégoire AU - Bal, Guillaume TI - Homogenization of the criticality spectral equation in neutron transport JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 721 EP - 746 VL - 33 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_1999__33_4_721_0/ LA - en ID - M2AN_1999__33_4_721_0 ER -
%0 Journal Article %A Allaire, Grégoire %A Bal, Guillaume %T Homogenization of the criticality spectral equation in neutron transport %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 721-746 %V 33 %N 4 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_1999__33_4_721_0/ %G en %F M2AN_1999__33_4_721_0
Allaire, Grégoire; Bal, Guillaume. Homogenization of the criticality spectral equation in neutron transport. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 721-746. http://www.numdam.org/item/M2AN_1999__33_4_721_0/
[1] Homogénéisation d'équations cinétiques en milieu perforé. C.R. Acad. Sci. Paris Sér. I 313 (1991) 339-344. | MR | Zbl
and ,[2] Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518. | MR | Zbl
,[3] Homogénéisation d'une équation spectrale de transport neutronique. C.R. Acad. Sci. Paris Sér. I 325 (1997) 1043-1048. | MR | Zbl
and ,[4] Homogenization of a spectral problem for a multigroup neutronic diffusion model. Comput Methods Appl. Mech. Engrg. (to appear). | MR | Zbl
and ,[5] Analyse asymptotique spectrale d'un problème de diffusion neutronique. C.R. Acad. Sci. Paris Sér. I 324 (1997) 939-944. | MR | Zbl
and ,[6] Collectively compact operator approximation theory and applications to integral equations. Prentice-Hall Englewood Cliffs, N.J. (1971). | MR | Zbl
,[7] Couplage d'équations et homogénéisation en transport neutronique. Ph.D. thesis, University of Paris 6, France (1997).
,[8] First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport. SIAM J. Appl. Math, (to appear). | MR | Zbl
,[9] An asymptotic analysis for the homogenization of P.W.R. assemblies - The transport case -. Nuclear Sci. Engng. (submitted).
and ,[10] Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités. Note CEA-R 2278 (1964).
,[11] Boundary layers and homogenization of transport processes. Publ. RIMS Kyoto Univ. (1979) 53-157. | MR | Zbl
, and ,[12]Traité de neutronique. Hermann, Paris (1978).
and ,[13] Spectral approximation of linear operators. Academic Press (1983). | MR | Zbl
,[14] Mathematical analysis and numerical methods for Science and Technology, Vol. 6. Springer Verlag, Berlin (1993). | MR | Zbl
and ,[15] The theory of neutron leakage in reactor lattices, in Handbook of nuclear reactor calculations. Vol II, Y. Ronen Ed. (1968) 409-508.
,[16] Homogenization of transport equations. Preprint No. R98003, University of Paris 6, LAN. | MR | Zbl
and ,[17] Homogenization of transport kinetic equation with oscillating potentials. Proc. Roy. Soc. Edin-burgh Sect. A 126 (1996) 1247-1275. | MR | Zbl
and ,[18] Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76 (1988) 110-125. | MR | Zbl
, , and ,[19]
and (personal communication).[20] Neutron transport and diffusion in inhomogeneous media I. J. Math. Phys. 16 (1975) 1421-1427. | MR
,[21] Neutron transport and diffusion in inhomogeneous media II. Nuclear Sci. Engng. 60 (1976) 357-368.
,[22] Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75-81. | MR
and ,[23] Neutron Drift in Heterogeneous Media. Nuclear Sci. Engng. 65 (1978) 290-302.
and ,[24] Étude mathématique et numérique de l'homogénéisation des assemblages combustibles d'un coeur de réacteur nucléaire. Ph.D. thesis, École Polytechnique, France (1996).
,[25] Les équations de la neutronique. Ph.D. thesis, University of Paris XIII, France (1987).
,[26] A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608-623. | MR | Zbl
,[27] Méthodes mathématiques en neutronique. Collection de la Direction des Etudes et Recherches d'EDF, Eyrolles (1995).
,[28] First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53 (1993) 1636-1668. | MR | Zbl
and ,[29] Study of the corrector of the eigenvalue of a transport operator. SIAM J. Math. Anal. 16 (1985) 151-166. | MR | Zbl
,