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Concept# Uncertainty principle

Summary

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, x, and momentum, p. Such paired-variables are known as complementary variables or canonically conjugate variables.
Introduced first in 1927 by German physicist Werner Heisenberg, the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa. In the published 1927 paper, Heisenberg originally concluded that the uncertainty principle was ΔpΔq ≈ h using the full Planck constant. The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later tha

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This Master thesis focus on a preliminary analysis of the experimental data obtained during the PETALE program in the CROCUS reactor at EPFL. The objective of PETALE is to validate neutron nuclear data for stainless steel and its main elements –namely iron, nickel, and chromium– and to contribute to the reduction of their uncertainties. For this purpose, transmission experiments were performed using activation dosimetry in separate reflectors made of the four materials. The manuscript is separated in three main parts. In the first part, after a presentation of the experimental setup, the measured spectra of the irradiated dosimeters are analysed. The results obtained with the methodology developed at EPFL are compared with those obtained by the collaboration partner CEA. The second part details two supplementary studies. First an experiment was performed and analysed to assess the impact of position uncertainties of core centre dosimeters. It was estimated to be 0.14 % for a position uncertainty of ±5 mm. The second study dealt with the estimation of PETALE’s monitors dead time. A dead time correction model was applied on a stable period experiment, and validated against activation dosimetry experiments. The power underestimation was estimated at 5 % at 80 W. The last part presents a comparison between experimental results and Serpent simulations of PETALE’s experiments using the JEFF-3.3 nuclear data library. In total twenty experiments were modelled and compared with their respective experiment. In this preliminary study, the results show a general agreement in the thermal range. An underestimation of the transparency of nickel and chromium for neutron with an energy of 2 MeV is observed. At higher energies, around 8 MeV, the chromium transparency is strongly overestimated. Finally, only a slight overestimation of the transparency to 2 MeV neutron is observed for iron and stainless steel reflectors. Outlooks are provided for the next steps of the analysis and validation, as well as for prospects on a longer term.

2021The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from measurements smeared by the finite resolution of the particle detectors. Previous unfolding methods use ad hoc discretization and regularization, resulting in confidence intervals that can have significantly lower coverage than their nominal level. Instead of regularizing using a roughness penalty or stopping iterative methods early, we impose physically motivated shape constraints: positivity, monotonicity, and convexity. We quantify the uncertainty by constructing a nonparametric confidence set for the true spectrum, consisting of all those spectra that satisfy the shape constraints and that predict the observations within an appropriately calibrated level of fit. Projecting that set produces simultaneous confidence intervals for all functionals of the spectrum, including averages within bins. The confidence intervals have guaranteed conservative frequentist finite-sample coverage in the important and challenging class of unfolding problems for steeply falling particle spectra. We demonstrate the method using simulations that mimic unfolding the inclusive jet transverse momentum spectrum at the LHC. The shape-constrained intervals provide usefully tight conservative inferences, while the conventional methods suffer from severe undercoverage.

Alexander Aures, Andreas Pautz, Winfried Zwermann

The impact of nuclear data uncertainties is studied for the reactor power and the reactivity during control rod withdrawal transients with reactivity insertions of 0.5$and 0.97$, respectively, for a PWR mini-core model. Multi-group cross sections, the multiplicities of both prompt and delayed neutrons, and fission spectra are varied by the application of the random sampling-based method XSUSA with covariance data of SCALE 6.1 supplemented by JENDL-4.0. The varied multi-group data are used by TRITON/NEWT to generate varied 2-group cross sections, which are then applied in neutron-kinetic/thermal-hydraulic calculations with DYN3D-ATHLET. A significant impact on both the reactivity uncertainty and the power uncertainty is observed. Since the distributional properties of the output time series vary across the problem time, the distribution-free Wilks tolerance limit is applied as a robust uncertainty measure to complex time series patterns. The most contributing nuclide reactions to the power uncertainty are identified via sensitivity analysis. (C) 2019 Elsevier Ltd. All rights reserved.