By V. Protopopescu (auth.), Jeffery Lewins, Martin Becker (eds.)
Dur prior quantity 14 used to be dedicated to an exposition of the themes of sensitivity research and uncertainty idea with its improvement and alertness in nuclear reactor physics on the middle of the dialogue. during this quantity, we go back to our frequent layout as a range of themes of present curiosity, authored by means of these operating within the box. those themes diversity from the theoretical underpinnings of the (linear) Boltzmann delivery equation to a resume of our ex pectations in what nonetheless could be regarded as twenty-first century know-how, the world's fusion reactor software. within the first article of this quantity, now we have Protopop escu's research of the constitution of the Boltzmann equation and its strategies for strength and space-dependent difficulties of an eigenvalue nature. There lengthy has been a curious "folk background" influence during this region~ Wigner and Weinberg may perhaps de scribe it as "what used to be more often than not identified used to be quite often untrue". This account of the Boltzmann equation definitely will express rigorous foundation for our expectancies of convinced strategies could be well-founded on research. Ely Gelbard's evaluate of the tools of settling on diffusion-type parameters in advanced geometries the place uncomplicated diffusion thought will be welcome has required simply as a lot rigor to figure out how such modeling could be made actual, even if to a extra instant and functional goal. the 2 articles could be obvious as fascinating contrasts, features of an identical underlying challenge exhibiting it seems that diversified elements of an identical significant core.
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Hence, even if D(A,k) = 0 has no solutions on the first physical sheet, the main contribution to the solution seems to arise from a "discrete eigenvalue". A denial of t'i1"eContinuous spectrum, though mathematically non-rigorous, might be useful and reasonable for practical purposes; but one must emphasize once more that it does not concern true eigenvalues (as shown by the exact analysis of the problem) and they do not enter into the exact expression of the solution. The crucial problem is the relationship between the poles of the continued operator (1 - HA(k»-l and the srectrum of the original Boltzmann operator.
Advances in Nuclear Science and Technology by V. Protopopescu (auth.), Jeffery Lewins, Martin Becker (eds.)