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Discontinuités dans les équations d’Hamilton-Jacobi-Bellman et dans les lois de conservation scalaires rencontrées dans les modèles de dynamique piétonnière
No full textIn macroscopic pedestrian crowd models, the Hamilton-Jacobi-Bellman equations and scalar conservation lawsare nonlinear partial differential equations that emerge naturally. In this context, the corresponding Hamilton-Jacobi equations admit discontinuities, which makes the viscosity solution approach more challenging. Numerousgeneralizations of the notion of viscosity solution have been proposed in recent years to address the Hamiltoniansdiscontinuities. Similarly, numerous recent studies have adapted the notion of entropy solution for discontinuousscalar conservation laws, motivated, among other applications, by car and pedestrian traffic problems.The first focus of this thesis is to demonstrate a correspondence between entropy solutions and viscosity solutions inthe case where both equations feature discontinuous nonlinearities. More precisely, we generalize the following knownresult to the discontinuous context: if we consider a scalar conservation law with homogeneous flux in dimensionone (SCL) and a well-chosen Hamilton-Jacobi equation (HJ), we can show that the space partial derivative of theviscosity solution of (HJ) is equal to the entropy solution of (SCL).The second objective of this thesis is the study of the Hughes model for pedestrian evacuation which couples a scalarconservation law to an eikonal equation (a typical example of a Hamilton-Jacobi equation). In one dimension, themodel can be seen as a scalar conservation law with a single point of discontinuity that moves over time, coupledto an integral equation. We then investigate the existence of a solution to Hughes’ model using a fixed-pointmethod, illustrating its limitations and versatility. In dimension two, the existence of a solution to the Hughesmodel is a largely open problem. We propose theoretical and numerical tools in order to understand the dynamicsof the solutions to Hughes’ model and to develop elements of its mathematical theory. The discontinuous LWRequation and - in the context of Monge solutions - the eikonal equation with a discontinuous source term arestudied within the framework of a decoupling approach. We use numerical schemes adapted to these equationsto provide a discretization for the Hughes model that we implemented in python as an open-source software. Weconduct numerical experiments with this software in order to propose conjectures regarding both the mathematicalproperties and the qualitative aspects of expected solutions to the Hughes model.Dans le contexte de la modélisation macroscopique des foules de piétons, les équations d’Hamilton-Jacobi-Bellmanet les lois de conservation scalaires sont des équations aux dérivées partielles non linéaires qui apparaissent na-turellement. Dans ce contexte, les équations d’Hamilton-Jacobi correspondantes comportent des discontinuités,ce qui rend l’approche par solution de viscosité délicate. De nombreuses généralisations de la notion de solutionde viscosité ont été proposées ces dernières années afin de traiter les discontinuités des Hamiltoniens. De même,récemment, de nombreux travaux adaptent la notion de solution entropique pour des lois de conservation scalairesà flux discontinu, motivés, entres autres, par des problèmes de traffic routier et piétonnier.Le premier objectif de cette thèse est la mise en évidence d’une “correspondance” entre les solutions entropiqueset les solutions de viscosité dans le cas où les deux équations comportent des discontinuités. Plus précisément, ongénéralise au contexte discontinu le résulat connu suivant: si on considère une loi de conservation scalaire à fluxhomogène en dimension une (SCL) et une équation de Hamilton-Jacobi (HJ) bien choisie, on peut montrer que ladérivée spatiale de la solution de viscosité à (HJ) est égale à la solution entropique de (SCL).Le second objectif de cette thèse est l’étude du modèle de Hughes pour l’évacuation piétonnière qui couple une loi deconservation scalaire à une équation eikonale (exemple-type d’équation d’Hamilton-Jacobi). En une dimension, lemodèle fait apparaı̂tre une loi de conservation à flux discontinu avec un unique point de discontinuité qui se déplaceau cours du temps. On analyse l’existence d’une solution au modèle de Hughes par une méthode de point fixe donton illustre les limitations et la versatilité. En dimension deux, l’existence d’une solution au modèle de Hughes est unproblème largement ouvert. On propose plusieurs outils théoriques et numériques afin de comprendre la dynamiquedes solutions du modèle de Hughes et d’élaborer des éléments de sa théorie mathématique. On analyse, dans le cadred’une approche par découplage, l’équation LWR discontinue et -dans le cadre des solutions de Monge- l’équationeikonale avec terme source discontinu. L’utilisation de schémas numériques adaptés à ces équations fournit unediscrétisation pour le modèle de Hughes implémentée en python sous la forme d’un logiciel libre. L’exploitation desrésultats numériques issus de ce logiciel permet de proposer des conjectures quant aux propriétés mathématiqueset qualitatives des solutions au modèle de Hughes
Exploring Oxygen Dissociation and Adsorption on Hexagonal Boron Nitride: Insight from High-Temperature Molecular Dynamics Simulation
No full textInternational audienceHexagonal boron nitride (h-BN), known for its exceptional thermal and chemical stability, is widely used in high-temperature applications and as an encapsulation layer for other twodimensional materials. This study examines the dissociation mechanisms of O2 molecules on the h-BN surface, focusing on activation energies and minimum energy pathways at different adsorption sites using climbing-image nudged elastic band (CI-NEB) calculations. The results reveal several dissociation pathways with significant variations in activation barriers depending on site and configuration, including one low-barrier route favorable for surface reactions. Reactive molecular dynamics (RMD) simulations with the ReaxFF force field are employed to investigate oxidation behavior in multilayer h-BN at 900 K, 1200 K, and 1500 K. At 900 K, O2 adsorbs without penetrating beneath the surface, while higher temperatures enhance dissociation and promote deeper oxygen incorporation. Charge analysis at elevated temperatures shows stronger chemisorption and electron transfer, forming a more uniform, chemically bonded oxygen layer
Recommended Practices in Laser-Induced Fluorescence (LIF) Diagnostics for Electric Propulsion
No full textInternational audienceLaser-induced fluorescence (LIF) spectroscopy uses Doppler-shifted laser photons to excite a bound electron transition in an atom or ion, with subsequent fluorescence emission detected in order to measure the local velocity distribution function (VDF) and/or particle density. Due to its non-invasive nature, high spatial resolution, and acceptable difficulty of implementation, LIF has become a favored diagnostic for electric propulsion (EP) plasmas, particularly in the study of Hall thrusters. This paper presents recommended best practices for LIF measurements in electric thrusters, drawn from over three decades of implementation heritage in the EP community. Focusing on both single-photon LIF (typically used to measure VDFs) and two-photon LIF (TALIF, typically used to determine densities), the paper covers selection of atomic transitions to target, experimental setups, and interpretation of data
Effects of Spacing Between Stone-Rows on the Chemical and Biological Fertility of Lixisoils in Eastern Burkina Faso
No full textInternational audienceThis study assessed the effects of stone-rows spacing on soil fertility and the potential for a fertility gradient to occur in a farming setting. The study was conducted in a rural area of Sampieri, eastern Burkina Faso, within a Sudano-Sahelian environment on Lixisols with a medium slope of up to 5%. The experimental design included three plots, each with a different stone-rows spacing: 15.5 m (P1), 18.5 m (P2) and 22 m (P3). Soil samples were taken at depths of 0-10 and 10-20 cm, with interval ranging from 0 to 15 m from the rows. Soil organic carbon(C), total nitrogen (N), pH and soil microbiological activity were measured. The study showed that C, N, P and pH levels improved more on plots P2 and P1 than on plot P3. Although differences were noted for microbiology, they were not statistically significant. A correlation was found and most soil fertility parameters. However, no soil fertility gradient was evident as a function of slope when moving away from the first stone-rows line. It can be concluded that the optimal spacing between stone-rows is 18.5 m and that it is difficult to deduce a fertility gradient within this interval. However, further research is needed for validation and confirmation of these findings
Chapitre 1. Les flux migratoires en Europe : que nous révèlent les statistiques ?
No full textInternational audienc
La société, personne morale (identification de la société; exercice de la personnalité morale); Sociétés de personnes (Société en nom collectif; Société en commandite simple)
No full textInternational audienc
An empirical study of vowel reduction and preservation in British English
No full textInternational audienceThis article presents a dictionarybased study of vowel reduction and preservation in British English in initial pretonic position and intertonic position. The different variables which have been claimed to influence those processes are tested on a data set of over 4,500 words using regression analyses. Our results confirm the significant effects of syllable structure, position of the vowel, word frequency and opaque prefixation. They also provide weak evidence for other factors such as vowel features and the existence of a base in which the vowel bears a stress, although no clear effects of word segmentability could be found. We also report new findings, as we find that foreign words reduce less than nonforeign words; we find that [+back] vowels reduce less than [-back] vowels in initial pretonic position; and we find a difference in behaviour for vowels followed by /sC/ clusters between nonderived words and stressshifted derivatives
An Introduction to the Finite Element Method with Application to Static and Dynamic Analysis of Structures
No full textEngineering schoo
Modalizzazioni del dire in francese e in italiano parlato. Il caso dei segnali discorsivi 'disons', 'on va dire' e 'diciamo'
No full textInternational audienc
Observations of carbon radio recombination lines with the NenuFAR telescope: I. Cassiopeia A and Cygnus A
No full textInternational audienceContext. Carbon radio recombination lines (CRRLs) at decametre wavelengths trace the diffuse phase of the interstellar medium (ISM) of the Galaxy. Observations of these lines allow for physical parameters of this phase to be measured.Aims. We observed CRRLs with the recently commissioned New Extension in Nançay Upgrading LOFAR (NenuFAR) telescope towards two of the brightest sources at low-frequency (10–85 MHz): Cassiopeia A and Cygnus A (hereafter, Cas A and Cyg A, respectively). We then measured the density, ne, and temperature, Te, of the electrons in line-of-sight clouds.Methods. We used NenuFAR’s beam-forming mode and integrated several tens of hours on each source. The nominal spectral resolution was 95.4 Hz. We developed a reduction pipeline primarily aimed at removing the radio frequency interference (RFI) contamination and correcting the baselines. We then performed a first fitting of the spectral lines observed in absorption associated with the line-of-sight clouds.Results. Cas A is the brightest source in the sky at low frequencies and represents an appropriate test bench for this new telescope. On this source, we detected 398 Cα lines between the principal quantum numbers n = 426 and n = 826. Cyg A is also a bright source, however, the Cα lines were observed to be fainter. We stacked the signal by groups of a few tens of lines to improve the quality of our fitting process. For both sources, we reached a significantly higher signal-to-noise ratio (S/N) and spectral resolution than the most recent detections by the LOw Frequency ARray (LOFAR). The variation of the spectral line widths with the electronic quantum number provides constraints on the physical properties of the clouds: Te, ne, and the temperature, T0, of the radiation field, the mean turbulent velocity, νt, and the typical size of the cloud.Conclusions. Our final constraints differ from those inferred from LOFAR results, with ∼50% lower Te, ∼35% lower ne, and from 10 to 80% higher νt, on average. The NenuFAR observations sample a larger space volume than LOFAR’s towards the same sources due to the differences in instrumental beam sizes. These discrepancies highlight the sensitivity of low-frequency CRRLs as probes of the diffuse ISM, paving the way towards large area surveys of CRRLs in our Galaxy