Three problems are investigated in the context of quantum collective dynamics. First, we examine the optomechanics of a Bose-Einstein condensate trapped in an optical ring cavity and coupled to counter-propagating light fields. Virtual dipole transitions cause the light to recoil elastically from the condensate and to excite its atoms into momentum side modes. These momentum side modes produce collective density oscillations. We contrast the situation to a condensate trapped in a Fabry-Perot cavity, where only symmetric ("cosine") side modes are excited. In the ring cavity case, antisymmetric ("sine") modes can be excited also. We explore the mean field limit and find that even when the counter-propagating light fields are symmetrically pumped, there are parameter regions where spontaneous symmetry breaking occurs and the sine mode becomes occupied. In addition, quantum fluctuations are taken into account and shown to be particularly significant for parameter values near bifurcations of the mean field dynamics. The next system studied is a hybrid composed of a high quality micromechanical membrane coupled magnetically to a spinor condensate. This coupling entangles the membrane and the condensate and can produce position superposition states of the membrane. Successive spin measurements of the condensate can put the membrane into an increasingly complicated state. It is possible in principle to produce nonclassical states of the membrane. We also examine a model of weaker, nonprojective measurements of the condensate's spin using phase contrast imaging. We find an upper limit on how quickly such measurements can be made without severely disrupting the unitary dynamics. The third situation analyzed is the string breaking mechanism in ultrahigh energy collisions. When quark-antiquark pairs are produced in a collision, they are believed to be linked by a tube of chromoelectric field flux, the color string. The energy of the string grows linearly with quark separation. This energy is converted into real particles by the Schwinger mechanism. Screening of the color fields by new particles breaks the string. By quantizing excitations of the string using the conjugate coordinates of field strength and string cross-section, we recover the observed exponential spectrum of outgoing particles.

We present a stacked weak-lensing analysis of 27 richness selected galaxy clusters at 0.40 <= z <= 0.62 in the COnstrain Dark Energy with X-ray galaxy clusters (CODEX) survey. The fields were observed in five bands with the Canada-France-Hawaii Telescope (CFHT). We measure the stacked surface mass density profile with a 14 sigma significance in the radial range 0.1 < R Mpc h(-1) < 2.5. The profile is well described by the halo model, with the main halo term following a Navarro-Frenk-White profile (NFW) profile and including the off-centring effect. We select the background sample using a conservative colour-magnitude method to reduce the potential systematic errors and contamination by cluster member galaxies. We perform a Bayesian analysis for the stacked profile and constrain the best-fitting NFW parameters M-200c = 6.6(- 0.8)(+1.0) x 10(14) h(-1)M(circle dot) and c(200c) = 3.7(+0.7) (-0.6). The off-centring effect was modelled based on previous observational results found for redMaPPer Sloan Digital Sky Survey clusters. Our constraints on M(200)c and c(200)c allow us to investigate the consistency with numerical predictions and select a concentration-mass relation to describe the high richness CODEX sample. Comparing our best-fitting values forM(200c) and c(200c) with other observational surveys at different redshifts, we find no evidence for evolution in the concentration-mass relation, though it could be mitigated by particular selection functions. Similar to previous studies investigating the X-ray luminosity-mass relation, our data suggest a lower evolution than expected from self-similarity.

We present cosmological constraints from the Dark Energy Survey (DES) using a combined analysis of angular clustering of red galaxies and their cross-correlation with weak gravitational lensing of background galaxies. We use a 139 deg(2) contiguous patch of DES data from the Science Verification (SV) period of observations. Using large-scale measurements, we constrain the matter density of the Universe as Omega(m) = 0.31 +/- 0.09 and the clustering amplitude of the matter power spectrum as sigma(8) = 0.74 +/- 0.13 after marginalizing over seven nuisance parameters and three additional cosmological parameters. This translates into S-8 = sigma(8)(Omega(m)/0.3)(0.16) = 0.74 +/- 0.12 for our fiducial lens redshift bin at 0.35 < z < 0.5, while S-8 = 0.78 +/- 0.09 using two bins over the range 0.2 < z < 0.5. We study the robustness of the results under changes in the data vectors, modelling and systematics treatment, including photometric redshift and shear calibration uncertainties, and find consistency in the derived cosmological parameters. We show that our results are consistent with previous cosmological analyses from DES and other data sets and conclude with a joint analysis of DES angular clustering and galaxy-galaxy lensing with Planck Cosmic Microwave Background data, baryon accoustic oscillations and Supernova Type Ia measurements.

Cosmic voids are usually identified in spectroscopic galaxy surveys, where 3D information about the large-scale structure of the Universe is available. Although an increasing amount of photometric data is being produced, its potential for void studies is limited since photometric redshifts induce line-of-sight position errors of >= 50 Mpc h(-1)which can render many voids undetectable. We present a new void finder designed for photometric surveys, validate it using simulations, and apply it to the high-quality photo-z redMaGiC galaxy sample of the DES Science Verification data. The algorithm works by projecting galaxies into 2D slices and finding voids in the smoothed 2D galaxy density field of the slice. Fixing the line-of-sight size of the slices to be at least twice the photo-z scatter, the number of voids found in simulated spectroscopic and photometric galaxy catalogues is within 20 per cent for all transverse void sizes, and indistinguishable for the largest voids (R-v >= 70 Mpc h(-1)). The positions, radii, and projected galaxy profiles of photometric voids also accurately match the spectroscopic void sample. Applying the algorithm to the DES-SV data in the redshift range 0.2 < z < 0.8, we identify 87 voids with comoving radii spanning the range 18-120 Mpc h(-1), and carry out a stacked weak lensing measurement. With a significance of 4.4 sigma, the lensing measurement confirms that the voids are truly underdense in the matter field and hence not a product of Poisson noise, tracer density effects or systematics in the data. It also demonstrates, for the first time in real data, the viability of void lensing studies in photometric surveys.

Polyconvexity is a standard assumption on hyperelastic stored energy densities which, together with some growth conditions, ensures the weak lower semicontinuity of the respective energy functional. The present work first reviews known results about gradient polyconvexity, introduced by Benešová, Kružík and Schlömerkemper in 2017. It is an alternative property to polyconvexity, better-suited e.g. for the modelling of shape-memory alloys. The principal result of this thesis is the extension of an elastic material model with gradient polyconvex energy functional to an elastoplastic body and proving the existence of an energetic solution to an associated rate- independent evolution problem, proceeding from previous work of Mielke, Francfort and Mainik. 1

O objetivo deste trabalho foi determinar a massa do aglomerado de galáxias RXC J1504-0248, localizado em z = 0.215, através da análise de lentes fracas, e comparar os resultados com aqueles obtidos em trabalhos anteriores através da análise de raios-X. Imagens do aglomerado foram obtidos nas bandas r\', g\' e i\' com o detector GMOS do telescópio Gemini Sul. A partir dessas imagens, contruímos um catálogo de objetos no campo usando o software Sextractor (SE) (Bertin e Arnouts, 1996). Este software também foi utilizado para classificá-los como galáxias ou estrelas. Foram identificadas 172 galáxias neste campo, que também foram detectadas no Data Release 7 do Sloan Digital Sky Survey (SDSS). Estas galáxias foram então usadas para obter uma calibração fotométrica das imagens, comparando as magnitudes instrumentais e do SDSS nas mesmas bandas. Após a calibração fotométrica, e através da comparação com imagens do CFHTLS obtidas em cores semelhantes, as galáxias foram classificadas como membros de cluster, foreground ou background, a partir de sua posição nos diagramas cor-cor e cor-magnitude. A reconstrução da massa do aglomerado através da análise de lentes gravitacionais foi realizada em duas etapas. Na primeira, foi utilizado o software IM2SHAPE, desenvolvido por Bridle et al. (1998), que modela os objetos, adicionando até três gaussianas, cada uma definida por seis parâmetros: as coordenadas do centro do objeto, x0 e y0, a elipticidade e, o ângulo de posição , o produto dos semi-eixos maior e menor ab, e a amplitude A. Inicialmente, o programa foi executado apenas para as estrelas do campo, com o objetivo de se obter uma estimativa da distribuição da PSF. A estimativa foi então utilizado como entrada para a análise das galáxias. Na segunda etapa, para estimar a massa do aglomerado foi utilizado o programa LENSENT, desenvolvido por Marshall et al. (2002), cujos parâmetros de entrada são a elipticidade das galáxias de fundo e seus erros. Na técnica de lentes gravitacionais fracas, a dependência radial da deformação das galáxias de fundo permite determinar o perfil de massa do aglomerado. Para estimar a massa, ajustamos um perfil de uma Esfera Isotérmica Singular (SIS, na sigla em inglês), e determinamos o valor da massa dentro de um raio de 3Mpc, 1.3 ± 0.6 x 10¹ Msol. O resultado é consistente com o obtido por Bohringer et al., 2005, 1.7 x 10¹ Msol, através da análise em raios-X. Comparando o mapa de distribuição de luminosidade e da emissão de raios-X concluímos que eles são muito semelhantes à distribuição superficial de massa, resultado que indica equilíbrio. / In this work we studied the galaxy cluster RXC J1504-0248, at z=0.215, from images in the bands r\', g\' and i\' obtained with Gemini South telescope. The photometric calibration was performed by comparison with field objects identified in the Sloan Digital Sky Survey (SDSS). From the analysis of color-color and color-magnitude diagrams, galaxies in the field were then divided into cluster members, background and foreground objects. We determined the PSF using the IM2SHAPE program \\cite{Bridle98}. These results enabled us to obtain the cluster projected mass distribution through a weak lensing analysis performed with the LENSENT program \\cite{Marshall02}. We also shown that the cluster luminosity distribution and the X-ray emission are consistent with the mass map. Using a SIS model, we estimated the mass of the cluster, obtaining 1.3 x 10¹ Msun, consistent with the mass obtained in a previous X-ray analysis, 1.7 x 10¹ Msun, by \\cite{Bohringer05}.

Galaxy clusters are the most massive collapsed structures in the Universe and their properties offer a crucial insight into the formation of structure. High quality observational data is forthcoming with ongoing and upcoming surveys, but simulations are needed to provide robust theoretical predictions for comparison, as well mock data for testing observational techniques. Numerical simulations are now able to accurately model a range of astrophysical processes. This is highlighted in the BAHAMAS and MACSIS simulations, which have successfully reproduced the observed scaling relations of galaxy clusters. We use these simulations to quantify the impact baryons have on the mass distribution within galaxy clusters, as well as the bias in X-ray and weak lensing mass estimates. It is shown that baryons have only a minor affect on the spins, shape and density profiles of galaxy clusters and they have no significant impact on the bias in weak lensing mass estimates. When using spectroscopic temperatures and densities, the X-ray hydrostatic mass bias decreases as a function of mass, leading to a bias of ~40% for clusters with M_500 > 10^15 solar masses. In the penultimate chapter, we use the EAGLE and C-EAGLE simulations to construct more realistic mock cluster observations. The EAGLE simulations have been shown to successfully reproduce the properties of field galaxies and they are complemented by the C-EAGLE project, which extends this work to the cluster scale. We use these simulations to construct a cluster lightcone that accounts for the impact of uncorrelated large scale structure on cluster observables, including weak lensing mass estimates, the Sunyaev-Zel'dovich parameter and X-ray luminosity.

Dans cette thèse, nous nous intéressons à deux approximations hyperboliques des équations de Navier-Stokes incompressibles en dimensions 2 et 3 d'espace. Dans un premier temps, on considère une perturbation hyperbolique de l'équation de la chaleur, introduite par Cattaneo en 1949, pour remédier au paradoxe de la propagation instantanée de cette équation. En 2004, Brenier, Natalini et Puel remarquent que la même perturbation, qui consiste à rajouter ε∂tt à l'équation, intervient en relaxant les équations d'Euler. En dimension 2, les auteurs montrent que, pour des sonnées régulières et sous certaines hypothèses de petitesse, la solution globale de la perturbation converge vers l'unique solution globale de (NS). En 2007, Paicu et Raugel améliorent les résultats de [BNP] en étendant la théorie à la dimension 3 et en prenant des données beaucoup moins régulières. Nous avons obtenu des résultats de convergence, avec données de régularité quasi-critique, qui complètent et prolongent ceux de [BNP] et [PR]. La seconde approximation que l'on considère est un nouveau modèle hyperbolique à vitesse de propagation finie. Ce modèle est obtenu en pénalisant la contrainte d'incompressibilité dans la perturbation de Cattaneo. Nous démontrons que les résultats d'existence globale et de convergence du précédent modèle sont encore vérifiés pour celui-ci. / In this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one.

Les amas de galaxies sont des outils cosmologiques et astrophysiques essentiels, car ce sont les objets les plus grands et les plus massifs gravitationnellement liées dans l'Univers. L'étude de leur fonction de masse, de leur fonction de corrélation et des relations d'échelle entre leur masse et différentes observables nous permettent de tester les prévisions des modèles cosmologique et les scenarii de formation des structures. Ils sont aussi d'intéressants laboratoires pour l'étude de la formation et de l'évolution des galaxies, et de leur interactions avec le milieu qui les entourent, dans d’environnements denses. Pour y parvenir, estimer précisément leur masse revêt une importance fondamentale. J’ai étudié la précision de la richesse optique calculée par l’algorithme de détection d’amas RedGOLD (Licitra et al. 2016) en tant que mass proxy, en utilisant des mesures de lentilles gravitationnelles (weak lensing) et des observations en rayon X. J’ai mesuré les masses cumulées d’un échantillon de 1323 amas de galaxies dans le CFHTLS et NGVS à 0.2<z<0.5, dans l’intervalle de richesse 10-70. J'ai testé différents modèles prenant en compte les erreurs sur la position du centre de l'amas, les effets de lentille non faible (non-weak shear), le "two-halo term", la contribution de la galaxie centrale brillante et la dispersion intrinsèque de la relation masse-richesse. J'ai montré que la correction de la position du centre est nécessaire pour éviter un biais dans la mesure de la masse, alors que l'ajout de la galaxie centrale n'affecte pas les résultats. J'ai calculer les coefficients de la relation masse-richesse et ceux de la relation d'échelle entre masses issues du weak lensing et celle estimées à partir d'observations dans les rayons X. Mes résultats sont en accord avec les simulations et les précédents travaux publiés. / Galaxy clusters are essential cosmological and astrophysical tools, since they represent the largest and most massive gravitationally bound structures in the Universe. Through the study of their mass function, of their correlation function, and of the scaling relations between their mass and different observables, we can probe the predictions of cosmological models and structure formation scenarios. They are also interesting laboratories that allow us to study galaxy formation and evolution, and their interactions with the intra-cluster medium, in dense environments. For all of these goals, an accurate estimate of cluster masses is of fundamental importance. I studied the accuracy of the optical richness obtained by the RedGOLD cluster detection algorithm (Licitra et al. 2016) as a mass proxy, using weak lensing and X-ray mass measurements. I measured stacked weak lensing cluster masses for a sample of 1323 galaxy clusters in the CFHTLS W1 and in the NGVS at 0.2<z<0.5, in the optical richness range 10-70. I tested different weak lensing mass models that account for miscentering, non-weak shear, the two-halo term, the contribution of the Brightest Cluster Galaxy, and the intrinsic scatter in the mass-richness relation. I found that the miscentering correction is necessary to avoid a bias in the measured halo masses, while the inclusion of the BCG mass does not affect the results. I calculated the coefficients of the mass-richness relation, and of the scaling relations between the lensing mass and X-ray mass proxies. My results are consistent with simulations and previous works in the literature.

<p>The main aim of this study is to investigate which structural ideas that lies behind the European Union’s marine operation Atalanta that has been put into motion to counteract piracy and robbery outside the coast of Somalia. In order to do this, we have with the use of the theory of weak states, intervention as well as sovereignty, investigated EU’s document in the question with the use of the idea centered analytical method. The questions that has guided this study, lies both on an empirical and theoretical level. On the basis of a theoretical perspective we have investigatet how the principle of sovereignty and thoughts on intervention affects the international community’s handling of the potential problems in weak states. On the empirical level we investigated which conceptions and structural ideas that can explain EU’s strategy in the set up and execution of operation Atalanta.</p><p>The study sowed that the humanitarian ideal is the most prominent idea behind this operation. It also showed that there is a realistic view behind the operation. This view means that one always ought to win something on every operation one executes. Further more, we noticed that the principle of sovereignty ever since the Cold War had to stand back in favor of humanitarian interventions. This can be explained by the fact that human rights has become a stronger ideal. However, the question regarding when it is right and who has he right to intervene is still an object of discussion on both a theoretical level and from case to case.</p><p> </p><p><strong>Key words: </strong>intervention, weak states, sovereignty, Somlia, Atalanta, EU<strong> </strong></p>