Numerical Methods for Neutron Transport Calculations of Nuclear Reactors

The objective of this thesis, which in clearly inspired by an industrial framework, is to try and narrow the gap between theoretical neutron modelling and application in the context of nuclear reactor design. This thesis is divided into three main chapters, preceded by a general overview. This structure reflects the three main topics which were chosen for this research project. The first topic develops the Spectral Element Method (SEM) approach and its use in conjunction with transport approximations. As it is documented in the specialized numerical analysis handbooks and in previous works by the author, the method has an excellent convergence rate which outperforms most classical schemes, but it has also some important drawbacks which sometimes seem to discourage its use for linear transport problems applied to nontrivial benchmarks. In order to elaborate the methodology of the specific problems encountered in reactor physics, three aspects are addressed looking for improvements. The first topic analyzed is related to the convergence order, whose value is less straightforward to define a priori by means of functional analysis than other numerical schemes. The adjective “spectral” refers in fact to the maximum order claimed, exponential with respect to the average size of the mesh. A comprehensive set of convergence tests is carried out applying SEM to a few transport models and with the aid of manufactured solutions, thus isolating the numerical effects from the deviations which are due only to modelling approximations. The hypothesis of grid conformity is also relaxed, replacing the classical Galerkin variational formulation with the Discontinuous Galerkin theory, characterized by a more flexible treatment of the mesh interfaces; this scheme allows local grid refinement and opens the way, in perspective, to mesh adaption. Finally, a simple and sufficiently flexible technique to deform the boundaries of each mesh is introduced and applied, in order to adapt the grid to curved geometries. In this way, the advantages of SEM can be applied to a vast class of common problems like lattice calculations. Moreover, thanks to a change of the basis functions used in SEM, it is possible to obtain elements with three sides (straight or deformed), that are a typical war horse of the Finite Element approach. The second topic is essentially devoted to the most “industrial” part of the thesis, developed entirely during the stay of the author in the AREVA NP headquarters in Paris. In AREVA, and in all other nuclear engineering enterprises, neutron diffusion is still the preferred neutronic model for full-core studies. Better approximations are reserved for library preparation, fuel studies and code validation, none of these being typically too much time or budget-constrained. Today needs start to require a certain level of improvement also in full-core analyses, trying to fitly model localized dis-homogeneities and reduce the penalizing engineering margins which are taken as provisions. On the other hand, a change in the model does not mean only an effort to write a new code, but has huge follow-ups due to the validation processes required by the authorities. Second-order transport may support the foreseen methodology update because it can be implemented re-using diffusion routines as the computational engine. The AN method, a second-order approximation of the transport equation, has been introduced in some studies, and its effect is discussed. Moreover, some effort has been reserved to the introduction of linear anisotropy in the model. The last topic deals with ray effects; they are a known issue of the discrete ordinate approach (SN methods) which is responsible for a reduction in the accuracy of the solution, especially in penetration problems with low scattering, like several shielding calculations performed for operator safety concerns. Ray effects are here characterized from a formal point of view in both static and time dependent situations. Then, quantitative indicators are defined to help with the interpretation of the SN results. Based on these studies, some mitigation measures are proposed and their efficacy is discussed

Integrating Shape-from-Shading & Stereopsis

This thesis is concerned with inferring scene shape by combining two specifictechniques: shape-from-shading and stereopsis. Shape-from-shading calculates shape using the lighting equation, which takes surface orientation and lighting information to irradiance. As irradiance and lighting information are provided this is the problem of inverting a many to one function to get surface orientation. Surface orientation may be integrated to get depth. Stereopsismatches pixels between two images taken from different locations of the same scene - this is the correspondence problem. Depth can then be calculated using camera calibration information, via triangulation. These methods both fail for certain inputs; the advantage of combining them is that where one fails the other may continue to work. Notably, shape-from-shading requires a smoothly shaded surface, without texture, whilst stereopsis requires texture - each works where the other does not. The first work of this thesis tackles the problem directly. A novel modular solution is proposed to combine both methods; combining is itself done using Gaussian belief propagation. This modular approach highlights missing and weak modules; the rest of the thesis is then concerned with providing a new module and an improved module. The improved module is given in the second research chapter and consists of a new shape-from-shading algorithm. It again uses belief propagation, but this time with directional statistics to represent surface orientation. Message passing is performed using a novel method; it is analytical, which makes this algorithm particularly fast. In the final research chapter a new module is provided, to estimate the light source direction. Without such a modulethe user of the system has to provide it; this is tedious and error prone, andimpedes automation. It is a probabilistic method that uniquely estimates the light source direction using a stereo pair as input

Mapping of Ice and Gas on 1000 AU Scales

Many of the molecules in interstellar space are in the solid state, in so-called interstellar ices. The research in this thesis is focused around two key astronomical questions; How is ice distributed in star forming regions? How is ice affected by - or affecting - star formation processes? I provide answers to these questions through the analysis of submillimeter and near-infrared observations. The observations analysed in this thesis consist of (partially published) archival data acquired mainly with the AKARI and Herschel space telescopes, and the ground-based ESO/VLT. To facilitate the reduction and analysis of some of this data two major software packages (ARF2 and Omnifit) were created with the Python programming language The operation of both packages is fully documented in the thesis appendix. The study of methanol ice prevalence in star-forming regions found that methanol ice can be found towards many more lines of sight than previously reported, and that its abundance relative to water ice can vary between a few to ~40%. I also confirm that methanol very likely exists mixed in a water-rich ice component, a result consistent with our current understanding of methanol ice formation. Proof was found of high-temperature chemistry forming water in the warm postshock gas of YSOs. In this same region it was found that up to 99% of the methanol is being destroyed as it is sputtered from the surfaces of dust grains into the gas phase. A novel analysis technique of slitless AKARI near-infrared spectroscopy yields an unprecedented number of water ice column density estimates towards background star lines of sight covering 12 separate 10' x 10' fields of view in as many molecular clouds. A moderate correlation is found between water ice column density and dust optical depth at 250 microns, with the correlation potentially varying from cloud to cloud

Mathematical linguistics

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ESARDA 37th Annual Meeting Proceedings

The 37th ESARDA symposium on Safeguards and Nuclear Non-Proliferation was held in Manchester, United Kingdom from 19-21 May, 2015. The Symposium has been preceded by meetings of the ESARDA Working Groups on 18 May 2015. The event has once again been an opportunity for research organisations, safeguards authorities and nuclear plant operators to exchange information on new aspects of international safeguards and non-proliferation, as well as recent developments in nuclear safeguards and non-proliferation related research activities and their implications for the safeguards community. The Proceedings contains the papers (118) submitted according to deadlines.JRC.E.8-Nuclear securit