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Fluctuations associated with power and detector readings in a nuclear reactor, commonly known as reactor noise, are of great importance in nuclear science and engineering. Two different types of no...

Detector dead time, caused by both physical components in the detection system and the electronic data acquisition, may have a dramatic effect on the regulation system and in-pile experiments. For example, when conducting the Feynman-α experiments in a marginally sub-critical configuration, the dead time effect is known to bias the variance to mean ratio. Analytic computations of the influence of the dead time on the detection count distribution are hard. Therefore, conducting Feynman-α experiments, or other noise experiments, in the presence of a noticeable dead time effect, is challenging. In the present study, we develop the stochastic differential equations approach to stochastic transport, by providing a model for the detection count in a sub-critical configuration under a non-paralyzing detector dead time. The analysis is based on tools from renewal processes and on a nonlinear filter for detection losses. After constructing the full model, a second order approximation is provided and solved, suggesting a novel first order correction to the Feynman-Y function. The proposed correction is compared with experimental results and past known results, showing improvement and high accuracy.

Most basic models for the power (or equivalently, the neutron population) in a nuclear core consider the power as a function of time (with an energetic and spatial distribution) and lead to deterministic description of the reactor kinetics. While these models are of common use and are undoubtedly the main analytic tool in understanding the reactor kinetics, the true nature of the power in a reactor core is stochastic and should be considered as a stochastic process in time. The stochastic fluctuations of the power around the mean field (which is given by the deterministic models) are referred to as “reactor noise”, and understanding them is a basic topic in nuclear science and engineering. Traditionally, most models for reactor noise consider a sub-critical core, reaching steady state after exposure to an external source. The focus on a sub-critical setting is driven by two main factors. First, from a practical point of view, measuring the power fluctuations in a sub-critical core (known as “noise experiments”) has proven to be a very efficient tool for estimating the static and kinetic parameters of the core. Second, once we assume a critical setting, the current models become statistically unstable, while the mean field solution has a stationary solution, the variance tends to $$\infty $$ linearly in time. The instability of the stochastic models is a known problem, and it has been conjectured in the past that this (some what strange) increase in the variance—that is not observed in physical systems—can be restrained by power feedback. However, this conjecture was never proven. The outline of the present study is to present a stochastic analysis to the point reactor kinetics model, proving that once the reactivity has a negative feedback, it not only forces a specific steady-state solution (in terms of the mean field equation), but also prevents the variance to “explode”, and the variance is bounded in time.

Reactor noise, caused both by the probabilistic nature of the fission chains and external reactivity noises, is one of the basic topics in nuclear science and engineering, both in theory and practice. Classical approaches to modeling this noise and neutron count distribution in the detection system rely on the stochastic transport equation for the probability generating function and on transfer function response to random perturbations. In recent years, a third modeling approach has been proposed, relying on Ito stochastic differential equations , which enjoys the tractability that the first aforementioned approach has, and at the same time accounts for fluctuations, by modeling noise in terms of Brownian motion. This paper develops the latter approach to incorporate the stochasticity in the detection process to the model equations. The resulting neutron count distributions are explicitly computable. As an application of our approach we present a straightforward derivation of the well-known Feynman-Y formula. We then propose an alternative to the traditional sampling scheme of this formula, based on mean absolute deviation , known from the statistics literature to be more robust than the mean square deviation estimator. The study focuses on a single energy point model and neglects the effect of the delayed neutrons. Extensions of the approach to multiple energy levels and the incorporation of delayed neutrons are discussed, as well as further applications of the approach and its advantages over existing diffusion scale approximations.

Dead time losses in neutron detection, caused by both the detector and the electronics dead time, is a highly nonlinear effect, known to create high biasing in physical experiments as the power grows over a certain threshold. Analytic modeling of the dead time losses is a highly complicated task due to the different nature of the dead time in the different components of the monitoring system (paralyzing vs. non-paralyzing), and the stochastic nature of the fission chains. The most basic analytic models for a paralyzing dead time correction assume a non-correlated source, resulting in an exponential model for the dead time correction. While this model is often used and very useful for correcting the average count rate in low count rates, it is totally impractical in noise experiments and the so-called Feynman-α experiments. In the present study, a new technique is introduced for dead time corrections, based on backward extrapolation of the losses, created by imposing increasing artificial dead time...

Noise experiments, and the Feynman- α method in particular, are considered a standard in-pile experiment, often used in zero power reactors in a sub critical configuration to estimate the reactivity level. In the Feynman- α method, the variance to mean ratio of event triggered neutron count is fitted on the so called Feynman-Y function, resulting with an experimental estimation of the α decay mode. In a recent study, analytic formulas for the expected statistical uncertainty in the Feynman- α method were derived, using the backward stochastic transport equation. The outline of the present study is to experimentally validate these analytic formulas. The formulas were implemented on 4 different signals, obtained from the MINERVE reactor at CEA Cadarache. For each of the four measurements, the signal was truncated in increasing measurement lengths (ranging from 1 to 60 min), in order to observe the functional behavior of the statistical error through time. Then, the measured statistical error was compared with the analytic estimation. Results indicate a very high correspondence between the expected statistical error and the measured one.

Dead time losses in neutron detection, caused by both the detector and the electronics dead time, is a highly nonlinear effect, known to create high biasing in physical experiments as the power grows over a certain threshold, up to total saturation of the detector system. Analytic modeling of the dead time losses is a highly complicated task due to the different nature of the dead time in the different components of the monitoring system (e.g., paralyzing vs. non paralyzing), and the stochastic nature of the fission chains. In the present study, a new technique is introduced for dead time corrections on the sampled Count Per Second (CPS), based on backward extrapolation of the losses, created by increasingly growing artificially imposed dead time on the data, back to zero. The method has been implemented on actual neutron noise measurements carried out in the MINERVE zero power reactor, demonstrating high accuracy (of 1–2%) in restoring the corrected count rate.

Power spectral density (PSD) methods are well-known and widely used for the analysis of neutron noise experiments and obtaining the reactor's integral kinetic parameters, i.e., the effective delayed neutron fraction βeff and the prompt neutron generation time Λ . Many uncertainties are usually associated with PSD methods, e.g., statistical fluctuations in the neutron flux, power drifts, uncertainties in the Diven factor, the integral fission rate, and in the reactivity value. However, the uncertainty associated with the numerical parameters used in the power spectrum calculation procedure is hardly discussed in the literature and generally overlooked. The aim of this paper is to study the uncertainties in the kinetic parameters of a reactor core, obtained by PSD methods, which are associated with the numerical parameters of the method. A comprehensive estimation of the kinetic parameters, including all other uncertainties, is not pursued. In this paper, PSD methods are implemented to analyze critical and subcritical configurations of the MINERVE zero power reactor in order to measure its integral kinetic parameters β eff and Λ . Both cross and auto power spectral densities are calculated and the kinetic parameters are obtained via Lorentzian curve fitting over the calculated PSD. The sensitivity of the obtained kinetic parameters to the choice of numerical parameters used for spectrum calculations is studied and found to be significant with respect to other uncertainties. A novel methodology is proposed for analyzing the kinetic parameters' sensitivity to the PSD calculations and for quantifying the associated uncertainties.

We give necessary and sufficient conditions for both the existence of minimal factorization of a rational function of N complex variables and the cascade representation of a Fornasini–Marchesini linear system. In particular, we generalize the well known result of Bart, Gohberg, Kaashoek and Van Doren on minimal factorization of a rational function of one complex variable.

We further develop the study of Fornasini---Marchesini linear systems with upper triangular state operators, addressing the problem of constructing a triangular Fornasini---Marchesini model equivalent (under a proper definition) to a given system. In particular, we are interested in the problem of determining when such a system can be constructed, without losing the information about the state of the original system.

This paper deals with certain realizations of rational matrix valued functions of N complex variables. In particular, necessary and sufficient for so called triangular realization is provided.

We introduce and study the notion of weak triangularization for a set of N matrices, which is a weaker version of simultaneous triangularization. We prove that for the special case of 2-by-2 matrices, weak triangularization is equivalent to simultaneous triangularization. Mathematics subject classification (2000): 15A15.

We use reproducing kernel Hilbert space methods to solve a Carathéodory–Fejér type interpolation problem with mixed derivatives (corresponding to a so-called lower inclusive set) in the class of Schur multipliers.

We prove a realization theorem for rational functions of several complex variables.

We solve a boundary interpolation problem in the reproducing kernel Hilbert space of functions analytic in the unit ball of CN with reproducing kernel 1/(1−∑1Nzkwk*). We introduce the notion of Brune factor (or Blaschke–Potapov factor of the third kind) in this setting.

A minimal model for mechanical motion of the left ventricle is proposed. The model assumes the left ventricle to be a harmonic oscillator with two distinct phases, simulating the systolic and diastolic phases, at which both the amplitude and the elastic constant of the oscillator are different. Taking into account the pressure within the left ventricle, the model shows qualitative agreement with functional parameters of the left ventricle. The model allows for a natural explanation of heart failure with preserved systolic left ventricular function, also termed diastolic heart failure. Specifically, the rise in left ventricular filling pressures following increased left-ventricular wall stiffness is attributed to a mechanism aimed at preserving heart rate and cardiac output., Comment: accepted for publishing in Medical Physics and Engineering

We use the theory of reproducing kernel Hilbert spaces to solve a Caratheodory–Fejer interpolation problem in the class of Schur multipliers of the reproducing kernel Hilbert space of functions analytic in the unit ball of C N with reproducing kernel 1 1−∑ 1 N z k w k * .

Recently Bolotnikov and Rodman characterized finite dimensional backward shift invariant subspaces of the Arveson space. In this note we study finite dimensional backward shift invariant Hilbert spaces contractively included in the Arveson space. To that purpose we redefine in an appropriate way the backward shift operators in terms of power series expansions.

Natural connections between positive semidefinite solutions X of homogeneous algebraic Riccati equations and finite dimensional reproducing kernel de Branges spaces based on a J-inner proper rational square matrix valued functions are known. In this paper analogous connections between the positive semidefinite solutions X of nonhomogeneous algebraic Riccati equations and finite dimensional reproducing kernel Hilbert spaces based on rectangular (J,J∼)-coinner proper rational matrix valued functions Θ(λ) are developed and are then applied to obtain factorization formulas for Θ(λ) in terms of elementary factors. Enroute, formulas for the factors in a version of a theorem of Leech are also obtained.