Malgré leurs mauvaises performances, les modèles de calcul de flux polluants (MCFP) dans les rejets urbains de temps de pluie (RUTP) continuent à susciter de l’intérêt du fait du fort potentiel qu’ils présentent pour prédire et contrôler ces RUTP. La contribution des sédiments à la pollution des RUTP est aujourd’hui largement reconnue comme prépondérante ; en conséquence, une modélisation idoine des processus en réseau apparait comme un élément clé pour améliorer la qualité de ces modèles. Dans ce contexte, plusieurs éléments ont été révélés par des études récentes menées sur les dépôts de réseaux d’assainissement unitaires, notamment sur « Le Marais » : (1) la présence d’une quantité importante de dépôts grossiers quasi-stationnaires qui modifient les caractéristiques du réseau ainsi que les conditions d'écoulement ; (2) l'identification d’un dépôt organique cohésif sur le Marais, la couche organique, capable d’expliquer la contribution du réseau à la pollution de RUTP et qui se constitue dans les parties amonts des collecteurs principaux. L’objectif de cette thèse est d’examiner l’effet de l’intégration de ces observations dans un MCFP de type semi-distribué, en prenant comme cas d’étude le site expérimental du Marais.Dans la première partie, on a travaillé à la prise en compte des dépôts grossiers dans le modèle hydrodynamique, puis on a évalué l’impact de cet ajout sur les processus de transport solide dans les réseaux. Pour y parvenir, un outil de modélisation capable de gérer l’écoulement sur une bathymétrie complexe était nécessaire. Ainsi, un schéma numérique conservatif de type Godounov a été développé et validé par rapport à certains cas de référence, avant de l’appliquer à l'échelle du réseau du Marais. Les résultats ont démontré un effet significatif de ces dépôts grossiers sur l’hydraulique du réseau, qui ensuite influence la production des particules et, dans une moindre mesure, le processus de transfert.Dans la deuxième partie, des données acquises récemment sur plusieurs sites avec des contributions de dépôts aux RUTP comparables et d’états d’encrassement différents (notamment pour la couche organique) ont été analysées dans le but d’identifier le vrai rôle de cette couche organique vis-à-vis de la production en réseau par temps de pluie. Les résultats ont montré que la couche organique ne représente qu’une source mineure vis-à-vis de la production en réseau. Afin d’identifier la source majeure, le modèle hydraulique développé dans la première partie a été couplé avec le modèle d’érosion de Skipworth et le modèle d’advection simple pour tester différents scenarii de localisation de dépôts. Les résultats de ce banc d’essai sont cohérents avec ce qui précède concernant la contribution de la couche organique ; il en ressort par ailleurs que les localisations les plus vraisemblables de la source prépondérante sont, dans l’ordre, le réseau amont et les collecteurs principaux / Despite their disappointing performance, urban stormwater quality models are still considered to be a potentially efficient decision making tool to control combined sewer overflows (CSOs) and thus are receiving ongoing investments to improve their quality. In this respect, in-sewer sediments are now widely recognized for their preponderant contribution to the pollution of CSOs assigning therefore a particular importance to mastering sewer processes module when refining these models. Recent studies conducted on in-sewer sediments in one of the extensively investigated urban catchments in Paris, Le Marais, highlighted new elements that could be helpful when addressing this module: (1) the existence of quasi-steady sewer grits deforming sewer characteristics and thus suspected to modify sewer flow conditions; (2) the identification of the potentially eroded sediment type during wet weather that is formed at the upstream parts of the Marais main trunks, the organic layer, that showed a cohesive like characteristic during in-situ flushing experiments. A site specific model for the Marais catchment is developed in this thesis adopting a semi-distributed configuration to examine the effect of integrating these field observations in its structure on the simulation of outfall discharges’ quality.In the first part, an evaluation of the impact of considering the sewer grits in the hydrodynamic module on the solid production and transfer processes in sewer system was carried out. To do so, a special modelling tool was necessary in order to handle sewer flow over a complex bathymetry. So, a well-balanced Godunov numerical scheme was developed and verified against some reference test cases before being extended to the Marais sewer scale. Results showed a significant impact of these coarse deposits on the hydraulic parameters. Solid production was demonstrated to be more sensible to this impact than the transfer processes.In the second place, previous findings obtained on combined sewer systems having no organic layer and high sewer contribution along with those obtained on the Marais were deeply investigated to identify the real role of this organic layer in sewer wet weather production. Results showed that this latter is only a minor source for wet weather erosion. To identify the major source, a quality module based on Skipworth erosion formulation and simple advection equation was used to test several scenarios of sewer sediment localization. The benchmark confirmed that the organic layer is not the major source of sewer production and that another source is preponderant and that can be located at the upstream branches as well as along the principal collectors with more probability of the former case

In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated Haar unitary matrices. The eigenvalues of these random matrices form determinantal point processes on the complex plane. We also study the limiting expected empirical distribution of appropriately scaled eigenvalues of those matrices as the size of matrices go to infinity. We give the first example of a random matrix whose eigenvalues form a non-rotation invariant determinantal point process on the plane. The second theme of this thesis is infinite products of random matrices. We study the asymptotic behaviour of singular values and absolute values of eigenvalues of product of i .i .d matrices of fixed size, as the number of matrices in the product in-creases to infinity. In the special case of isotropic random matrices, We derive the asymptotic joint probability density of the singular values and also that of the absolute values of eigenvalues of product of right isotropic random matrices and show them to be equal. As a corollary of these results, we show probability that all the eigenvalues of product of certain i .i .d real random matrices of fixed size converges to one, as the number of matrices in the product increases to infinity.

This thesis deals with systems of interacting particles with very low energy in the limit where the particle-particle scattering is much larger than the range of the interactions. We use a quantum-field-theory approach which allows us to study both few-body and dense-matter systems in a unified framework. This allows to introduce composite fields of two and three particles (when appropriate). The quantum corrections are calculated nonperturbatively with the Functional RenormalisationGroup. We deal with three types of systems. First we study systems with three and four scalar particles. For three-particle systems our framework describes the Efimov effect. During the FRG flow in the scaling limit, the four-particle system has an infinite sequence of (unphysical) four-particle states on top of each Efimov trimer. This is a case of super Efimov behaviour. Three of these four-particle states survive to the physical limit. Two of these three states have been found in exact quantum-mechanical calculations, and have also been observed in gases of ultracold atoms. Next, this thesis studies systems of three and four spin-1/2 particles. In the scaling limit, we find attractive fixed points for the three- and four-particle systems. Out of the scaling limit, we study atom-molecule scattering and molecule-molecule scattering, in particular their scattering length. Finally, we study dense-matter systems of spin-1/2 particles. This calculation includes all the two-, three-, and four-particle interactions. These systems show spontaneous symmetry breaking: the two-particle field has a finite classical value. We find the value of the atom gap in units of the chemical potential.

Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.

Le constat scientifique est sans appel : nous subissons une crise environnementale mondiale et endémique. Par ailleurs, nous ne sommes pas sans savoir que l'essentiel des préjudices environnementaux procède des activités humaines, et notamment de l'exploitation d'activités dangereuses pour l'environnement. Les personnes privées sont donc directement intéressées. Pourtant, l'étude du droit positif révèle clairement que nos mécanismes classiques de responsabilité civile ne répondent pas avec pertinence à la spécificité des préjudices environnementaux, et notamment au besoin de prévention. Notre projet de thèse consiste à dépasser les lacunes et incohérences juridiques actuelles afin de dégager un régime de responsabilité civile adapté. Pour ce faire, il est impératif de s'engager dans un effort de conceptualisation des préjudices environnementaux. En effet, cette approche préalable dévoile sous un jour nouveau les imperfections actuelles et révèle toutes les potentialités du droit de la responsabilité civile. Dans cette perspective, nos travaux tendent à démontrer que la conceptualisation des préjudices environnementaux doit être « unitaire ». Pour être plus précis, cette « conception unitaire des préjudices environnementaux » repose sur deux axes complémentaires. Le premier, dévoile l'unité existante entre les préjudices environnementaux et l'homme. Quant au second, il soutient une acception large des préjudices environnementaux à l'aune des risques environnementaux générés par les activités dangereuses. Cette approche est d'autant plus vertueuse qu'elle encourage et justifie le déploiement du régime de responsabilité civile en la matière. / The scientific conclusion is clear: we are experiencing a global environmental crisis and endemic. Moreover, we are not aware that most of the environmental damage proceeds from human activities, including exploitation activities dangerous to the environment. Private persons are directly concerned. Yet the study of positive law makes clear that our traditional civil liability mechanisms do not respond appropriately to the specificity of environmental damage, including the need for prevention. Our thesis project is to go beyond current legal gaps and inconsistencies in order to identify a suitable system of civil liability. To do this, it is imperative to engage in a process of conceptualization of environmental harm. Indeed, this preliminary approach throws new update existing imperfections and reveals the full potential of the law of civil liability. In this perspective, our work tends to show that the conceptualization of environmental damage must be "unitary". To be more precise, the "unitary concept of environmental damage" is based on two complementary approaches. The first reveals the existing unity between environmental damage and man. As for the second, it supports a broad definition of environmental damage in terms of environmental risks caused by hazardous activities. This approach is all the more virtuous it encourages and justifies the deployment of the system of civil liability in the matter.

Quantum speed limits are lower bounds on the evolution time for quantum systems. In this thesis, we consider closed quantum systems. We investigate how different principal bundles offers a geometrical method for obtaining generalizations of the Mandelstam-Tamm quantum speed limit for mixed states. We look at three different principal bundles from which we derive two already known quantum speed limits, the Uhlmann and Andersson QSLs, and one which is new, the Grassmann QSL. We also investigate the tightness of these quantum speed limits and how they compare with each other.

Over the last decades, both band topology and Anderson transitions, as well as their interplay, have been well understood in the context of time-independent energy-conserved systems. This switches the research focus in this field from theoretical descriptions to experimental designs, realizations, and engineering. In such a background, time-dependent perturbations and coupling between quantum systems and environments become the main concern. Along this route, this dissertation first studies the properties of a Chern insulator, one of the simplest topological systems, under time-periodic disorder. We reveal that in certain cases disorder fully localizes the bulk, but surprisingly has a positive effect on the edge, propagating edge states exist throughout the full spectrum. Along this direction, we further explore disorder effects in a network model constructed by arrays of unitary scattering matrices. Here, we go beyond previous works and show that also the shape of network (lattice symmetries) is important. It will result in a new type of topological phase, known as a higher-order topological phase, in which the topological states of a d-dimensional system have a dimension less than (d − 1). Afterwards, we focus on a network model with gain and loss, which breaks energy conservation. Here, we find the system now exhibits a 'supermetal' behavior that surpasses the conventional ballistic transport for perfect metals. At the end of this dissertation, we perform a study on the non-Hermitian defect in time-periodic systems. Our study shows that a boundary defect, due to its non-Hermiticity, can stop the propagation of chiral edge states, which should otherwise be the most robust manifestations of topology in quantum systems.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22968号 / 理博第4645号 / 新制||理||1668(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 市野 篤史, 教授 池田 保, 教授 加藤 周 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

A common practice for government defense agencies and commercial aeronautical companies is to use dual antennas on test flight air vehicles in order to overcome occlusion issues during high-speed telemetric maneuvers. The dual antennas, though never being masked at the same time, unfortunately lead to a drastic increase in nulls in the signal pattern. The result of this interference pattern can be compared to the effect of fading in a multiple-input multiple-output (MIMO) multi-path scattering environment. Confidence in this comparison leads to the use of unitary space-time MIMO codes to overcome the signal self-interference. The possibility and performance of several of these codes will be examined. Such criteria as training for channel estimation, use of shaped offset quadrature phase shift keying (SOQPSK), hardware facility, and data throughput will be compared for each code. A realistic telemetry channel will be derived to increase accuracy of simulated results and conclusions.

This licentiate thesis consists of one paper about unitary representationtheory of ample groupoids and semigroups together with generalizationsto étale and non-Hausdorff groupoids. In the paper we study algebraically the type I and CCR properties forample Hausdorff groupoids. Clarke and Van Wyk proved that both ofthese properties admit a topological characterization for Hausdorff second countable groupoids in terms of separation properties of their orbitspace and the isotropy groups. Using a Stone type duality between ample groupoids and Boolean inverse semigroups with meets, we exploit thischaracterization to get a purely algebraic statement. We also apply thoseresults to get characterizations of the type I and CCR properties for inverse semigroups using their Boolean inverse completions. The generalization is about characterizing the same properties for both étale and ample non-necessarily Hausdorff groupoids which nonethelesshave Hausdorff unit spaces. In this setup, we first give a direct proofof the topological characterization for the CCR property which doesn't rely on the disintegration theory. The argument cannot be adapted toget an easier proof in the type I case, but we rather explain how to geta proof following the original ideas of Clark and Van Wyk in that case.Finally, we state for both étale and ample groupoids algebraic conditionsequivalent to the CCR and GCR properties on their pseudogroup of openand compact open bisections respectively.