Download e-book for iPad: Advances in Nuclear Science and Technology by V. Protopopescu (auth.), Jeffery Lewins, Martin Becker

By V. Protopopescu (auth.), Jeffery Lewins, Martin Becker (eds.)

ISBN-10: 1461337577

ISBN-13: 9781461337577

ISBN-10: 1461337593

ISBN-13: 9781461337591

Dur earlier quantity 14 used to be dedicated to an exposition of the themes of sensitivity research and uncertainty thought with its improvement and alertness in nuclear reactor physics on the middle of the dialogue. during this quantity, we go back to our accepted structure as a range of themes of present curiosity, authored through these operating within the box. those subject matters diversity from the theoretical underpinnings of the (linear) Boltzmann delivery equation to a resume of our ex­ pectations in what nonetheless could be considered twenty-first century expertise, the world's fusion reactor application. within the first article of this quantity, we have now Protopop­ escu's research of the constitution of the Boltzmann equation and its suggestions for strength and space-dependent difficulties of an eigenvalue nature. There lengthy has been a curious "folk historical past" influence during this sector~ Wigner and Weinberg may possibly de­ scribe it as "what was once usually identified was once more often than not untrue". This account of the Boltzmann equation without doubt will express rigorous foundation for our expectancies of convinced suggestions may be well-founded on research. Ely Gelbard's evaluate of the equipment of picking out diffusion-type parameters in advanced geometries the place basic diffusion concept will be welcome has required simply as a lot rigor to figure out how such modeling may be made actual, even if to a extra instant and functional objective. the 2 articles may be visible as fascinating contrasts, elements of a similar underlying challenge exhibiting it appears diversified points of a similar relevant core.

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64. , "Time and Space Eigenvalues of the Boltzmann Equation ," in I AEA S yrnp os i um Pulsed Neutron Research, Vienna, 1965, Volurne I, Page 219. 65. , Journal of Nuclear Energy 20, Page 649, 1966. 66. Egelstaff, P. , Journal of Nuclear 204, 1967. 67. Reed, C. , Henry, C. N. and Usner, A. A Nuclear Science and Engineering 30, Page 367, 1967. 68. Lee, R. R. and Daitch, P. , Nuclear Science and Engineering 28, Page 247, 1967. 69. Ritchie, A. I. M. and Rainbow, M. , Nuclear Science and Engineering 38, Page 306,1967; Ritchie, A.

Transport Theory and Stat. Physies Page 135, 1975. 3. Weinberg, A. M. and Wigner, E. , The Physiea1 Theory of Neutron Chain Reaetors, University of Chieago Press, Chieago, 1958. 4. Sjöstrand, N. , "Deeay Constants for Pu1sed Monoenergetie Neutron Systems with Anisotropie Seattering," Preprint CTH-RF-28, 1975. 5. , Sjöstrand, N. , Journal of Nue1ear Seienee and TeehPage 256, 1975. no1ogy~, 6. Hino, T. , Journal of Nuc1ear Seienee and Teehno1ogy 12, Page 388, 1975. 7. Sjöstrand, N. , Journal of Nue1ear Seienee and Teehno1ogy ~, Page 81, 1976.

Ko ko~o x ReA 0 -1 )( -k -k Figure 10. o ~ 0 o The Spectrum of the Reduced Operator in the Model a; a = 0 The eigenva1ues are given by the dispersion equation .!. k a arctan H1 k1!. :! 8) 1eading to (1-~ )k~ ± k~ /(1-~o)2 - 4~2tan2k.!. -1 + o a a 0 The eigenva1ues can be comp1ex. Indeed, for a persion 1aw reads (also, see Figure 11): 1 a kW 2 tan a k = Ik I .!. 2 1,2, ••. L 2kJ!. 10 ) 31 EIGENVALUE PROBLEMS FOR THE BOLTZMANN OPERATOR For k=l, a=8 and . t h e equat~on TI '4 ~ equal to the solution between 0 and 1 of 0 5 TI 5 TI~o 5 TI~o = 2 arctan 16 - 2 arctan ~ - arctan - 4 - = 0 r (it does existl), w obtain A = -3/5; that is, a true eigenvalue beyond A = - 2' in a model which in this case, displays approach to equilibrium (toward the constant mode, corresponding to A 0) • o As before, one must be careful when considering the equivalent integral equations in the strip {A I - 1 < Re A< -cd and in the half plane {AI Re A< -l}.

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Advances in Nuclear Science and Technology by V. Protopopescu (auth.), Jeffery Lewins, Martin Becker (eds.)


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