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By Lewins J. (Ed)

Considering its initiation in 1962, this sequence has provided authoritative experiences of crucial advancements in nuclear technology and engineering, from either theoretical and utilized views. furthermore, many unique contributions are integrated.

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Konno Institute of Information Sciences and Electronics University of Tsukuba Tsukuba, Ibaraki 305, Japan 1. INTRODUCTION The Boltzmann equation for low-density gases has supplied various useful concepts for statistical mechanics of transport and relaxation phenomenon; Bogoliubov (1946) and Kirkwood (1946, 1947). Ehrenfest (1911) pointed out the importance of the coarse-graining in µ space. Twenty years ago, Tokuyama and Mori (1976) proposed a statistical mechanical theory and derived the Boltzmann equation without the use of any assumption like Bogoliubov’s functional postulate and Kirkwood’s time smoothing and the product assumption for the spatially coarse-grained particle density in µ space (1) where c = N/Ω , Ω being the volume of the system, pi(t) and ri(t) are the momentum and the position of the i-th particle at time t, respectively.

The break frequency wb is approximated by |s_ | which shifts toward higher frequency region as the reactor power increases. 5. Reactor-power dependence of neutronic variance The variance of neutron fluctuation σ NN becomes (71) where . This means that when k 0 > 1, C2 > 0; the stable steady state is realized under the constant reactivity insertion. The variance diverges as C2 → +O. Namely, C2 = 0 is the just critical point of the reactor. The divergence of variance known in linear theory is suppressed by the nonlinear negative feedback.

128) with (133) Note that when h' = 0, the phase motion is independent of the amplitude without the mean field approximation. Direct numerical simulation supports the validity of these approximations. The relevance of the nonlinear term h'|A | 2 A* is not easily determined only from the phase distribution. Consider next the amplitude pdf. , the cosine term cos2φ is replaced by 〈 cos 2φ〉, oversimplifies the coupling between the amplitude and the phase. Mean field theory is not appropriate to provide the amplitude pdf (129).

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