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New PDF release: Advances in Nuclear Science and Technology: Volume 26

By Jeffery Lewins, Martin Becker

ISBN-10: 0306461102

ISBN-13: 9780306461101

ISBN-10: 0306470888

ISBN-13: 9780306470882

Considering the fact that its initiation in 1962, this sequence has awarded authoritative experiences of crucial advancements in nuclear technological know-how and engineering, from either theoretical and utilized views. furthermore, many unique contributions are incorporated.

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Additional info for Advances in Nuclear Science and Technology: Volume 26 (Advances in Nuclear Science & Technology)

Example text

This model oversimplifies the practical negative feedback in the form of coupled stochastic differential equations from the fuel and the coolant temperatures and others. But this simplification helps readers to understand clearly the main consequences of nonlinear feedback effects and the crucial differences of the results predicted in power reactors from those in the zero-power reactors. Now let us assume that the additive noise FN (t) and the parametric noise k(t) are independent and Gaussian white with null mean : (44) (45) 2.

96). Availability of nonlinear transformations for nonlinear coupled ODEs is demonstrated in an article (Konno and Sawahata, 1995). 5. Incorporation of noise source Consider the situation that a parametric noise ρ (ξ) is incorporated into the reactivity, viz. ρ0 → ρ0 + ρ(ξ). (111) as (113) where R(ξ) and f(ξ) are slowly varying variables. Following the method of KBM, one can put (114) 38 H. (113) into (116) in noticing that mω 2 0 = 1, we obtain (117) Substituting (113) and (114) into (117), we obtain (118) Averaging the cosine terms in the coefficients of R, R 2 and R 3 over one cycle [0,2π] of oscillation, one obtains (119) where (120) Similarly, application of the above averaging procedure to the equation of the phase, (121) leads to (122) where (123) 6.

M) have Gaussian-white nature. (37). , m) are independent Gaussian white noises with null mean: (39) Consider a power reactor model (Sako, 1980; Williams, 1983), (40) The WZ noise correction terms which must be added to (40) are (41) 28 H. KONNO Figure 1: Classification of bifurcations for nonlinear dynamical systems. NONLINEAR STOCHASTIC DYNAMICS 29 3. NONLINEAR EFFECTS IN THE NORMAL STEADY STATE A. One Component Model with Feedback 1. Model Consider a nonlinear stochastic power reactor model for the neutron density N(t) without precursors with an additive noise FN (t) and a parametric noise ρ (t) : (42) 8 where ρ0 is the reactivity inserted and Λ is the neutron lifetime.

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Advances in Nuclear Science and Technology: Volume 26 (Advances in Nuclear Science & Technology) by Jeffery Lewins, Martin Becker

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