Read e-book online Covariance, Bicovariance of the Stochastic Neutron Field - PDF

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Additional info for Covariance, Bicovariance of the Stochastic Neutron Field -

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And Jg in the frequency domain. 7) w hsq (7, w)=ldv, di2, dv di-2 y Coqc (VI) G’ (? ~) lr w The results above are now used for the calculations of the Oq4t and J,,f quantities. lO) by replacing x(V) with X,(V). lO) . ‘ ,. The o-modes are defined by the transport equation b where, CD,,are the time eigenvalues(decay constantsassociatedwith the time evolution of the eigemnodes). We also define the adjoint functions ’ The pair (ai ; Q,) satisfy the boundary conditions, bellow, on a convex surface (C-3) and the biorthogonality conditions (““IyD) 1 n = Non Smt (C-4) The normalization constant,N,, is given by c Non=(*ii (C-5) 1; Qn) I 37 The eignvalues, CO,,are related to the eigenreactivity, k,,.

L. Munoz-Cobo and F. C. Difilippo, p. 59. 12. Difilippo, F. Sci. , 90, 13-18 (1985). 13. Spencer,R. , Nucl. Sci. , 80,603 (1982). l 31 This page intentionally 32 left blank. ’ APPENDIX 6 A Start from . 21 . 2) into (A. 6) and perform the indicated integrals to get . @A(@1 w,)=(2~)-2vp(vp-1)(vp- 2) (c& 10, (0, + 33 02) 0; (OJ 0; (wz)kA*7) Consider next the term CDB(01@2)=(27r)-~ Tdzl dz2 + 013 02 +-;23 exp {i (WI ~1+~2 0,) ~2)) 7 -m dt (@q'c2, @z>IG’ Wmd) (B-4) p& (1, cmq> = up b, - 1) (cf(2) where we used the reciprocity theorem.

Marsaguerra University of Tennessee H. L. Dodds L. F. Miller B. R. Upadhyaya UT-Battelle L. G. Chiang F. C. Difilippo L. Lea1 J. K. Mattingly D. W. McDonald J. T. Mihalczo R. B. Oberer R. B. Perez V . Protopopescu T. E. Valentine J. D. White M. C. NL Laboratory Records (RC) ?

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Covariance, Bicovariance of the Stochastic Neutron Field -

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