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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... more
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.
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We use the theory of reproducing kernel Hilbert spaces to solve a Carathéodory–Fejér interpolation problem in the class of Schur multipliers of the reproducing kernel Hilbert space of functions analytic in the unit ball of with... more
We use the theory of reproducing kernel Hilbert spaces to solve a Carathéodory–Fejér interpolation problem in the class of Schur multipliers of the reproducing kernel Hilbert space of functions analytic in the unit ball of with reproducing kernel .
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ABSTRACT Neutron interrogation facilities for mass evaluation of Special Nuclear Materials (SNM) samples are divided into two main categories: passive interrogation, where all neutron detections are due to spontaneous events, and active... more
ABSTRACT Neutron interrogation facilities for mass evaluation of Special Nuclear Materials (SNM) samples are divided into two main categories: passive interrogation, where all neutron detections are due to spontaneous events, and active interrogation, where fissions are induced on the tested material by an external neutron source. While active methods are, in general, faster and more effective, their analysis is much harder to carry out.In the paper, we will introduce a new formalism for analyzing the detection signal generated by a pulsed source active interrogation facility. The analysis is aimed to distinct between fission neutrons from the main neutron source in the system, and the surrounding “neutron noise”.In particular, we derive analytic expressions for the first three central moments of the number of detections in a given time interval, in terms of the different neutron sources.While the method depends on exactly the same physical assumptions as known models, the simplicity of the suggested formalism allows us to take into account the variance of the external neutron source—an effect that was so far neglected.
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ABSTRACT In recent years, the data acquisition in neutron multiplicity measurements is rapidly changing from traditional shift-register electronics into fully digital LIST-mode acquisition machinery, allowing us to digitally record the... more
ABSTRACT In recent years, the data acquisition in neutron multiplicity measurements is rapidly changing from traditional shift-register electronics into fully digital LIST-mode acquisition machinery, allowing us to digitally record the detection time of each neutron. In the present study, we introduce two novel applications to the LIST-mode acquisition in neutron multiplicity counting. In the first application, we estimate the statistical uncertainty of the measurement using bootstrap analysis, and in the second application, we use the LIST mode acquisition to preform dead time corrections using a backward extrapolation technique. The applications were first tested by computer based simulations, and later applied to actual low mass fissile measurements conducted by the Institute of Isotopes in Hungary, showing satisfactory results. The methods presented in this study, while fairly easy to implement and do not require any prior calibration, often provide increased accuracy and higher reliability, when compared to the current methods traditionally used for shift-register multiplicity measurements. (C) 2013 Elsevier B.V. All rights reserved
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Abstract We prove a realization theorem for rational functions of several complex variables.
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Abstract Neutron multiplicity counting (NMC) measurements are often affected by the detection system dead time. Still, dead time losses are often neglected in analytic NMC models, and most of the dead time corrections are done through... more
Abstract Neutron multiplicity counting (NMC) measurements are often affected by the detection system dead time. Still, dead time losses are often neglected in analytic NMC models, and most of the dead time corrections are done through empirical models, experimentally fitted to the measurement system. In the present paper, we introduce a new analytic model for calculating the effect of a system dead time on the outcome of NMC. The model is subjected to two assumptions (in addition to the standard model assumptions in multiplicity counting): The first is that the dead time can be described by a paralyzable model, and the second is that the dead time effect may occur only between neutrons arriving from the same source event. The second assumption is, in fact, a restriction on the source event rate in the system and, in certain cases, may eventually be translated into a restriction on the mass of the measured sample.
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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... more
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.
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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.