The work done in this thesis includes an exploration of both the conformal field theory techniques and holographic techniques of the Gauge/Gravity duality. From the field theory, we have analyzed the analytical aspects of the Conformal Bootstrap program to gain handle on at least a part of the CFT spectrum. The program applies equally to the strongly coupled as well as the weakly coupled theories. We have considered both the regimes of interest in this thesis. In the strongly coupled sector, as we have shown that it is possible to extract information about the anomalous dimensions, of a particular subset of large spin operators in the spectrum, as a function of the spin and twist of these operators. The holographic analog of the anomalous dimensions from CFT are the binding energies of generalized free fields in the bulk, which has also been analyzed in this thesis. On the contrary, in the weakly coupled sector, the same idea can be used to calculate the anomalous dimensions of operators, with any spin and dimension in an expansion. We have considered a simple set of scalar operators, whose anomalous dimensions are reproduced correctly up to O( 2). In another holographic calculation, we have analyzed generic higher derivative theories of gravity, which corresponds to boundary theories with in finite colors but finite `t Hooft coupling. Certain universal aspects of these theories, such as anomalies and correlation functions are also calculated. The three point functions for these higher derivative theories will serve as a building block for considering four point functions for finitely coupled boundary CFTs. In the conclusion, we have pointed out the directions of interest which could be locating the bulk duals of large N finitely coupled theories, or that of an intermediate theory with both finite `t Hooft coupling as well as finite gauge group, with a speculative string theory dual.

Negative energy densities are an abundant and necessary feature of quantum field theory (QFT) and may lead to surprising measurable effects. Some of these stand in contrast to classical physics, so that the accumulation of negative energy, also in quantum field theory, must be subject to some constraints. One class of such constraints is commonly referred to as quantum energy inequalities (QEI). These are lower bounds on the averaged stress-energy tensor which have been established quite generically in quantum field theory, however, mostly excluding models with self-interaction. A rich but mathematically tractable class of interacting models are those subject to integrability. In this thesis, we give an overview of the construction of integrable models via the inverse scattering approach, extending previous results on the char- acterization of local observables to models with more than one particle species and inner degrees of freedom. We apply these results to the stress-energy tensor, leading to a characterization of the stress-energy tensor at one-particle level. In models with simple interaction, where the S-matrix is independent of the particles’ momenta, this suffices to con- struct the full stress-energy tensor and provide a state-independent QEI. In models with generic interaction, we obtain QEIs at the one-particle level and find that they substantially constrain the choice of reasonable stress-energy tensors, in some cases fixing it uniquely.:Acknowledgements 4 Contents 5 1 Introduction 7 2 Constructive aspects of integrable quantum field theories 13 2.1 General notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Particle spectrum and one-particle space . . . . . . . . . . . . . . . . 15 2.3 The scattering function . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Full state space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Asymptotic completeness; closing the circle . . . . . . . . . . . . . . . 29 2.6 Connection to algebraic quantum field theory . . . . . . . . . . . . . 33 3 Locality and the form factor series 37 3.1 Locality and the form factor series . . . . . . . . . . . . . . . . . . . 38 3.2 Local commutativity theorem for one- and two-particle form factors . 44 3.3 Transformation properties of the form factors . . . . . . . . . . . . . 58 3.3.1 Form factors of invariant operators and derivatives . . . . . . 62 4 Structure of form factors and the minimal solution 64 4.1 Classification of two-particle form factors . . . . . . . . . . . . . . . . 64 4.2 Existence of the minimal solutions and asymptotic growth . . . . . . 68 4.3 Computing a characteristic function . . . . . . . . . . . . . . . . . . . 74 5 The stress-energy tensor 77 5.1 The stress-energy tensor from first principles . . . . . . . . . . . . . . 77 5.2 The stress-energy tensor at one-particle level . . . . . . . . . . . . . . 83 5.3 Characterization at one-particle level . . . . . . . . . . . . . . . . . . 88 6 State-independent QEI for constant scattering functions 94 6.1 Candidate for the stress-energy tensor . . . . . . . . . . . . . . . . . 94 6.2 A generic estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Derivation of the QEI . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.4 Discussion of the QEI . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.5 Supplementary computations . . . . . . . . . . . . . . . . . . . . . . 108 7 QEIs at one-particle level for generic scattering functions 110 7.1 Derivation of the QEI at one-particle level . . . . . . . . . . . . . . . 111 7.2 Extending the scope of the QEI result . . . . . . . . . . . . . . . . . 117 7.3 A general recipe to obtain QEIs at one-particle level . . . . . . . . . 119 8 Examples 123 8.1 Models with one scalar particle type without bound states . . . . . . 123 8.2 Generalized Bullough-Dodd model . . . . . . . . . . . . . . . . . . . 125 8.3 Federbush model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.4 O(n)-nonlinear sigma model . . . . . . . . . . . . . . . . . . . . . . . 130 9 Conclusion, discussion, and outlook 134 A Constructive aspects of integrable quantum field theory 137 A.1 Representation theory of the Poincaré group in 1+1d . . . . . . . . . 137 A.2 Discrete symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 A.3 S-function and ZF operators in a basis . . . . . . . . . . . . . . . . . 143 A.4 Improper rapidity eigenstates . . . . . . . . . . . . . . . . . . . . . . 145 A.5 Bound states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.6 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 B Literature survey: Form factor conventions 158 C Stress-energy tensor 159 C.1 Stress-energy tensors for the free scalar field . . . . . . . . . . . . . . 159 C.2 A weaker notion for the density property . . . . . . . . . . . . . . . . 163 C.3 Stress-energy tensor at one-particle level generating the boosts . . . . 164 Bibliography 166

Le Golfe de Californie (GOC) est un exemple de rift très oblique, au stade d'accrétion depuis 3,6 Ma au sud. La déformation continentale débute au Miocène dans un contexte arrière-arc, en relation avec la subduction de la plaque Pacifique sous la Plaque Nord-Américaine. L'objectif de cette thèse est de déterminer I'histoire de la déformation à I'origine de la rupture continentale ainsi que les phénomènes post-rupture. Cette étude utilise des données tectoniques, sismologiques et géomorphologiques sur la marge Ouest du GOC en Basse Californie du Sud. Elles sont calées temporellement par des datations d'isotopes radiogéniques et cosmogéniques. Une histoire polyphasée de la déformation, essentiellement post-magmatique, est proposée en termes d'évolution des directions des failles et de déformations relativement à la cinématique des plaques. Je démontre dans cette zone que la déformation qui conduit à l'amincissement et à l'étirement lithosphérique est d'abord fortement oblique et devient transtensive et moins oblique relativement à la cinématique à partir de 7-8 Ma. La marge étudiée est intégrée de manière cohérente à I'ensemble des domaines déformés associés à la formation du GOC. On montre notamment que les marges du GOC sont diachrones et qu'elles se forment par migration vers I'Ouest de la déformation vers la zone de subduction, qui devient inactive vers 12 Ma. La dynamique post-breakup du GOC est interprétée en termes de mobilisation par fluage de la croûte inférieure en relation avec un évènement thermique lié à la rupture du slab. En conclusion, l'évolution du GOC ne peut s'expliquer par les modèles simples de rifting oblique et de formation de marges passives. / The Gulf of California (GOC) is an example of highly-oblique rift. Oceanic accretion started 3.6 Ma ago at its southern end. The earliest continental extension started during the Miocene, in a back-arc setting, in connection with the subduction of the Pacific plate (PAC) beneath North America (NAM). ln this study, I reconstitute the strain evolution along the proximal Baja California margin. For this, I used original tectonic and seismological data which I collected in Baja California Sur (BCS). Those data were time-constrained with absolute dating (radiogenic and cosmogenic isotopes). I outline that the main stretching and thinning of the Late Miocene-Pliocene Baja California margin was highly oblique regarding NAM-PAC kinematic vector, turning less oblique. By integrating the studied margin in the evolution of the GOC, it is proposed that the final break-up mechanism occurred within a broad semi-ductile right-lateral central shear-zone. lt is shown that the two GOC passive margins didn't form at the same time, crustal strain migrating westward during the Miocene in response to a probable retreat of the dying slab. The active post-breakup deformation in the proximal BCS is best interpreted in connection with an outward flow of the lower crust in a trend compatible with the margin shaping inherited from the major GOC-normal to GOC-oblique Miocene crustal deformation. This ductile flow would be enhanced by the heat input from the slab rupture. To conclude, the GOC evolution as an oblique rift system adjusts with no existing analogical or numerical model of strain field evolution of oblique rifting, a probable consequence to the complex dynamics in back-arc settings.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24896号 / 工博第5176号 / 新制||工||1988(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)准教授 PIPATPONGSA Thirapong, 教授 肥後 陽介, 教授 岸田 潔, 教授 安原 英明 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The present work combines experimental and numerical analyses to improve current understanding of turbulence in stably stratified flows. An extensive literature review is presented on the mechanisms governing turbulence under stratified conditions, with a special focus on the Richardson number parameter, as it is often adopted as a switch to turn turbulence modelling on/off. Anisotropization of turbulence is investigated, as it is found to be an important mechanism for turbulence survival at any Richardson number, but usually overlooked in turbulence parameterizations. For this purpose, an experimental dataset previously collected over an Alpine glacier is used, with a focus on the anisotropy of the Reynolds stress tensor, as the scientific community has recently shown improvements in the description of the atmospheric surface layer by taking this aspect into account. Different sources leading stresses to deviate from the isotropic limit are explored, as well as energy exchanges across scales and between kinetic and potential reservoirs, in order to identify the main processes that should be included in turbulence parameterizations to properly represent anisotropic turbulence under stable conditions. High-resolution numerical simulations are then performed with the Weather Research and Forecasting (WRF) model to evaluate different PBL parameterizations in reproducing specific stable atmospheric conditions developing over complex terrain, and their influence on the local circulation. For this purpose, two wintertime case studies in a basin-like area of an Alpine valley are investigated. Both are fair-weather episodes with weak synoptic forcing and well-developed diurnal local circulations, differing by the thermal stratification in the basin. In particular, the influence of thermal stratification on the outbreak of a valley-exit wind coming from a tributary valley is investigated, and the influence of such type of flows on turbulence anisotropy in stably stratified conditions is discussed for future investigations.

Όταν ηλεκρομαγνητική (ΗΜ) ακτινοβολία, προερχόμενη από κάποια πηγή, προσπίπτει σε σύνολο από σωμάτια τότε λαμβάνουν χώρα δύο φαινόμενα. Πρώτον, ασκούνται δυνάμεις στα σωμάτια οι οποίες οφείλονται αποκλειστικά στην σκέδαση της ΗΜ ακτινοβολίας της πηγής από αυτά. Οι δυνάμεις αυτές ονομάζονται Optical Trapping Forces. Δεύτερον, τα ίδια τα σωμάτια σκεδάζοντας την ΗΜ ακτινοβολία της πηγής, λειτουργούν και αυτά ως πηγές ακτινοβολίας. Έτσι ασκούν δυνάμεις το ένα στο άλλο. Οι δυνάμεις αυτές ονομάζονται Optical Binding Forces. H παράλληλη δράση των δύο αυτών ειδών δυνάμεων έχει ως αποτέλεσμα την δημιουργία ευσταθών δομών από τα σωμάτια. Προκειμένου την θεωρητική πρόβλεψη των δομών που αναπτύσσονται, χρειαζόμαστε έναν ταχύτατο αλγόριθμο υπολογισμού των δυνάμεων. Ο πιο ταχύς αλγόριθμος θα είναι το αποτέλεσμα της εύρεσης ενός αναλυτικού τύπου υπολογισμού των δυνάμεων. Η κατασκευή και η παρουσίαση του αναλυτικού τύπου αυτού είναι και το περιεχόμενο της εργασίας που ακολουθεί. / When the electromagnetic radiation, originating from a source, meets an ensemble of particles, there are two phenomena which take place. First, there are forces acting on these particles due exclusively to the scattering of the electromagnetic radiation from the particles. These are the so-called “Optical Trapping Forces”. Second, particles themselves act as sources of radiation since they scatter the radiation, and they exert forces one to another. These are the so-called “Optical Binding Forces”. The coexistence of these two different forces results in the creation of stable structures where the particles are self-organized. To achieve the theoretical prediction of these structures, we need a very efficient algorithm to calculate the forces. The fastest possible and thus more efficient algorithm originates from the analytical formula of the forces. The construction and the solution of the forces analytical formula is the content of this research work.

La caractérisation de la source d’un séisme se fait à partir de l’analyse des mesures des déplacements transitoires et statiques du sol, et dépend de la quantité et de la qualité de ces mesures. Nous avons travaillé sur la détermination des mécanismes au foyer des séismes modérés de Tadjena (Mw 5.0, 2006), Béni-Ilmane (Mw 5.5, 2010), Hammam Melouane (Mw 5.0, 2013), Bordj-Ménaïel (Mw 4.1, 2014), Alger (Mw 5.7, 2014) et M’ziraa (Mw 5.1, 2016). Pour cela, nous avons inversés les formes d’ondes en champ proche et régional des stations large bandes et accélérométriques du réseau sismologique algérien (ADSN). Nous avons déterminé la distribution spatio-temporelle du glissement cosismique du séisme de Boumerdes-Zemmouri (Mw 6.8, 2003) en inversant conjointement l’ensemble des données disponibles, sismologiques (télésismiques, accélérometriques) et géodésiques (GPS, InSAR, soulèvement côtier). Nous avons travaillé sur la relation qui peut exister entre le séisme de Boumerdes-Zemmouri et les séismes de Hammam Melouane, Bordj Ménaïel et Alger (Mw 5.7, 2014) en termes de transfert de contrainte (CFF). Nous avons calculé le champ de contrainte dans différentes régions de l’Algérie par inversion des mécanismes aux foyers disponibles dans chaque région. / Studies of the earthquake source are based on observations of seismic and static ground motions, which depend on the quality and the density of measurements. In this thesis, we present studies of the determination of the focal mechanism of the Tadjena (Mw 5.0, 2006), Béni-Ilmane (Mw 5.5, 2010), Hammam Melouane (Mw 5.0, 2013), Bordj-Ménaïel (Mw 4.1, 2014), Alger (Mw 5.7, 2014) and M’ziraa (Mw 5.1, 2016) earthquakes, by modeling waveforms in the near and regional field with broadband and strong motion stations of the Algerian Digital Seismic Netwok (ADSN). In addition, we determined the coseismic slip distribution of the Boumerdes-Zemmouri earthquake (Mw 6.8, 2003) by inverting a most comprehensive set of data (teleseismic, strong motion, GPS, InSAR, coastal uplift). We calculated the Coulomb Failure Function between the Boumerdes-Zemmouri earthquake (source fault) and the Hammam Melouane, Bordj Ménaïel and Algiers (Mw 5.7, 2014) events (receiver faults). We computed the stress tensor in different regions of Algeria obtained from the inversion of the available focal mechanisms.

The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.

Dans cette thèse nous développons des estimations d'erreur a posteriori par équilibrage de flux pour la poro-mécanique et la poro-plasticité.En se basant sur ces estimations, nous proposons des algorithmes adaptatifs pour la résolution numérique de problèmes en mécanique des sols.Le premier chapitre traite des problèmes en poro-élasticité linéaire.Nous obtenons une borne garantie sur l'erreur en utilisant des reconstructions équilibrées et $H({rm div})$-conformes de la vitesse de Darcy et du tenseur de contraintes mécaniques.Nous appliquons cette estimation dans un algorithme adaptif pour équilibrer les composantes de l'erreur provenant de la discrétisation en espace et en temps pour des simulations en deux dimensions.La contribution principale du chapitre porte sur la reconstruction symétrique du tenseur de contraintes.Dans le deuxième chapitre nous proposons une deuxième technique de reconstruction du tenseur de contraintes dans le cadre de l'élasticité nonlinéaire.En imposant la symétrie faiblement, cette technique améliore les temps de calcul et facilite l'implémentation.Nous démontrons l'éfficacité locale et globale des estimateurs obtenus avec cette reconstruction pour une grande classe de lois en hyperélasticité.En ajoutant un estimateur de l'erreur de linéarisation, nous introduisons des critères d'arrêt adaptatifs pour le solveur de linéarisation.Le troisième chapitre est consacré à l'application industrielle des résultats obtenus. Nous appliquons un algorithme adaptatif à des problèmes poro-mécaniques en trois dimensions avec des lois de comportement mécanique élasto-plastiques. / In this Ph.D. thesis we develop equilibrated flux a posteriori error estimates for poro-mechanical and poro-plasticity problems.Based on these estimations we propose adaptive algorithms for the numerical solution of problems in soil mechanics.The first chapter deals with linear poro-elasticity problems.Using equilibrated $H({rm div})$-conforming flux reconstructions of the Darcy velocity and the mechanical stress tensor, we obtain a guaranteed upper bound on the error.We apply this estimate in an adaptive algorithm balancing the space and time discretisation error components in simulations in two space dimensions.The main contribution of this chapter is the symmetric reconstruction of the stress tensor.In the second chapter we propose another reconstruction technique for the stress tensor, while considering nonlinear elasticity problems.By imposing the symmetry of the tensor only weakly, we reduce computation time and simplify the implementation.We prove that the estimate obtained using this stress reconstuction is locally and globally efficient for a wide range of hyperelasticity problems.We add a linearization error estimator, enabling us to introduce adaptive stopping criteria for the linearization solver.The third chapter adresses the industrial application of the obtained results.We apply an adaptive algorithm to three-dimensional poro-mechanical problems involving elasto-plastic mechanical behavior laws.