Advances in Nuclear Science and Technology by Lewins J. D. (Ed.), Becker M.

# Advances in Nuclear Science and Technology by Lewins J. D. (Ed.), Becker M. By Lewins J. D. (Ed.), Becker M.

The assurance during this sequence levels from the experimental to the theoretical, delivering whatever for all readers devoted to the secure and necessary improvement of nuclear strength and its linked applied sciences.

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Extra resources for Advances in Nuclear Science and Technology

Example text

10) original transfer functions, and can be identified in principle, since If and then and have ambiguities in magnitude. 2 Nonminimum Phase Systems Suppose that one zero, is inside the unit circle then stable eigenvalues of Eq. 3. Solving the symplectic form, we have a set of 4 eigenvectors: where CONTRACTION OF INFORMATION AND ITS INVERSE PROBLEM 49 Here the first column of Eq. (32) is different from that of Eq. (31), because is not a stable eigenvalue. In this case, we have a particular solution, That is, where Since we have we can calculate K: where From the closed loop transfer function matrix of the numerical innovation model, we have an equivalent 5-block feedback system described by where Using transformation formula (10), we can have the feedback loop transfer function, but we cannot identify the zero-power transfer function, due to the appearance of an additional loop 50 K.

KISHIDA III. 1 The System Size Expansion Method Fluctuations in reactor noise phenomena can be described by a master equation as in statistical physics. Noise phenomena in reactor plants are considered to be macroscopic. For such a macroscopic system a general theory using the system size expansion method was developed by Van Kampen , Kubo et al , Tomita et al  and Kishida et al . Let be a set of d extensive macrovariables, and a stochastic process be described by a master equation where P(X,t) is the probability distribution function of X at time t, and is the transition probability per unit time from X to Taking the Kramers-Moyal expansion of Eq.

2 The Inverse Problem From Eq. 29), three coefficient matrices of innovation model (12), K, and H, are determined as A, B, and C numerically via the method of singular value decomposition of Hankel matrix, of which elements are measurable correlation functions. Then, a data oriented or numerical innovation model is given by where and with a transformation matrix in comparison with Eq. (12). From Eq. (16) a numerical closed loop transfer function model is obtained uniquely as where and the superscript denotes that a quantity is calculated from the numerical innovation model (16).