Dynamics of Carrollian Scalar Fields

Adopting an intrinsic Carrollian viewpoint, we show that the generic Carrollian scalar field action is a combination of electric and magnetic actions, found in the literature by taking the Carrollian limit of the relativistic scalar field. This leads to non-trivial dynamics: even a single particle with non-vanishing energy can move in Carrollian physics.Comment: V2, Refs added and minor modification

From Asymptotic Symmetries to the Corner Proposal

These notes are a transcript of lectures gave by the author in the XVIII Modave summer school in mathematical physics. The introduction is devoted to a detailed review of the literature on asymptotic symmetries, flat holography, and the corner proposal. It covers much more material than needed, for it is meant as a lamppost to help the reader in navigating the vast existing literature. The notes then consist of three main parts. The first is devoted to Noether's theorems and their underlying framework, the covariant phase space formalism, with special focus on gauge theories. The surface-charges algebra is shown to projectively represent the asymptotic symmetry algebra. Issues arising in the gravitational case, such as conservation, finiteness, and integrability, are addressed. In the second part, we introduce the geometric concept of corners, and show the existence of a universal asymptotic symmetry group at corners. A careful treatment of corner embeddings provides a resolution to the issue of integrability, by extending the phase space. In the last part we bridge asymptotic symmetries and corners by formulating the corner proposal. In essence, the latter focuses on the central question of extracting from classical gravity universal results that are expected to hold in the quantum realm. After reviewing the coadjoint orbit method and Atiyah Lie algebroids, we apply these concepts to the corner proposal. Exercises are solved in the notes, to elucidate the arguments exposed.Comment: Lecture notes (XVIII Modave summer school in mathematical physics), V

La voie hydrodynamique vers l’holographie plate

In this thesis we discuss the limit of vanishing cosmological constant (flat limit) of the fluid/gravity correspondence, which is a macroscopic realization of the AdS/CFT. The holographic dictionary is usually implemented in a gauge(Fefferman-Graham), which does not admit a flat limit. In the hydrodynamic formulation of the boundary theory, we introduce a gauge, dubbed derivative expansion, where such a limit turns out to be smooth. In the boundary we show that this corresponds to a Carrollian limit, i.e. a limit where the speed of light vanishes. We present Carrollian hydrodynamics, together with its dual Galilean counterpart. Then, for 4 and 3 bulk dimensions, we exhibit a resummed line element, which provides an asymptotically flat bulk solution of Einsteinequations starting only from boundary (i.e. null infinity) conformal Carrollian hydrodynamic data. In 4 dimensions we exploit specific integrability conditions, which restrict the achievable class of solutions in the bulk. In 3 dimensions every boundary fluid configuration leads to an exact solution of Einstein’s equations. Bañados solutions are a subset of the solutions reached in this way. They are rigorously identified with their surface charges and the corresponding algebra. We emphasize the choice of hydrodynamic frame, often sidesteppedin holography. Finally, we focus on the formulation of AdS/CFT to encompass Weyl symmetry. This symmetry is a key ingredient of fluid/gravity but it is not naturally encoded in the usual formulation of holography. We introduce an appropriate gauge for realizing it, and analyze its far-reaching consequences.L’objet de cette thèse est l’étude de la correspondance fluide/gravité, réalisation macroscopique de la dualité AdS/CFT, à la limite où la constante cosmologique tend vers zéro (limite plate). La jauge de Fefferman-Graham, habituellement utilisée dans le dictionnaire holographique, est singulière à la limite plate. Ici, en passant par la formulation hydrodynamique de la théorie dubord, nous construisons une jauge, appelée jauge du développement en série dérivatif, où cette limite est bien définie. Sur la géométrie du bord, elle correspond en fait à faire tendre vers zéro la vitesse de la lumière, situation connue comme limite carrollienne. Un fluide relativiste admet une telle lim-ite, qui donne lieu à l’hydrodynamique carrollienne, étudiée ici en dimension arbitraire, parallèlement à son homologue galiléen. Ensuite, nous montrons spécifiquement en dimensions 4 et 3 du bulk qu’il est possible de construire des solutions asymptotiquement plates des équations d’Einstein partant de systèmes hydrodynamiques conformes carrolliens du bord, qui est ici l’hypersurface degenre lumière à l’infini. En 4 dimensions nous introduisons des conditions d’intégrabilité permettant de resommer la série dérivative sous formefermée. En 3 dimensions toute configuration fluide du bord aboutit à une solution exacte des équations d’Einstein. Les solutions de Bañados sont un sous-ensemble des solutions obtenues et identifiées au moyen de leurs charges de surface. Nous accordons une attention particulière au rôle du repère hydrodynamique, trop souvent ignoré en holographie. Pour terminer, nous nous concentrons sur la formulation de la AdS/CFT dans laquelle la symétrie de Weyl est explicite. Quoique cette symétrie soit un ingrédient incontournable de la correspondance fluide/gravité, elle n’est pas codée dans la formulation habituelle de l’holographie. Nous introduisons une nouvelle jauge et analysonsses conséquences

Gelatinous zooplankton diversity, distribution and seasonality in the northern Barents Sea and Arctic Ocean

Gelatinous zooplankton, here referring to the phylum Cnidaria and Ctenophora and the class Appendicularia are important components of marine ecosystems due to their very diverse diets, life cycles and seasonal dynamics. In the Barents Sea, several studies reviewed the gelatinous zooplankton diversity, yet few studies documented the diversity and distribution patterns between the advected Atlantic Waters (AW) and Polar waters (PW) and no study reviewed the gelatinous zooplankton seasonality over a full year. The aim of this master thesis is to (1) investigate diversity and distribution patterns between the different water masses and regions of the northern Barents Sea and (2) investigate the gelatinous zooplankton seasonality over a whole year in the northern Barents Sea. For this purpose, during the Nansen Legacy project four seasonal surveys covered the full seasonal cycle of the Barents Sea marginal ice zone and collected both biological and physical data, including gelatinous zooplankton. Overall, 31 gelatinous zooplankton taxa were identified. Fritillaria borealis, Oikopleura sp. and Aeginopsis laurentii were the most abundant taxa and AW and PW influenced areas had different seasonal dynamics and composition, which were significantly influenced by the primary production, the zooplankton biomass, the inflow of AW and the latitudes. Keywords: Gelatinous zooplankton, Barents Sea, Seasonality, Distribution, Atlantic Waters, Polar Waters, Nansen Legac

Carroll geodesics

Using effective field theory methods, we derive the Carrollian analog of the geodesic action. We find that it contains both `electric' and `magnetic' contributions that are in general coupled to each other. The equations of motion descending from this action are the Carrollian pendant of geodesics, allowing surprisingly rich dynamics. As an example, we derive Carrollian geodesics on a Carroll-Schwarzschild background and discover an effective potential similar to the one appearing in geodesics on Schwarzschild backgrounds. However, the Newton term in the potential turns out to depend on the Carroll particle's energy. As a consequence, there is only one circular orbit localized at the Carroll extremal surface, and this orbit is unstable. For large impact parameters, the deflection angle is half the value of the general relativistic light-bending result. For impact parameters slightly bigger than the Schwarzschild radius, orbits wind around the Carroll extremal surface. For small impact parameters, geodesics get reflected by the Carroll black hole, which acts as a perfect mirror.Comment: 7pp, 2figs, v2: added ref

Fluid-gravity correspondence and causal first-order relativistic viscous hydrodynamics

The fluid-gravity correspondence is a duality between anti-de Sitter Einstein gravity and a relativistic fluid living at the conformal boundary. We show that one can accommodate the causal first-order viscous hydrodynamics recently developed by Bemfica, Disconzi, Noronha, and Kovtun in this framework, by requiring a set of natural conditions for the geometric data at the horizon. The latter hosts an induced Carrollian fluid, whose equations of motion are shown to be tightly tied to the ones describing the fluid at the boundary. Functional expressions for the transport coefficients are found --with those associated to viscosity and heat flux uniquely determined--, satisfying a set of known causality requirements for the underlying equations of motion.Comment: V

Lie Algebroids and the Geometry of Off-shell BRST

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated bundles. This turns out to be a simple but elegant change, mathematically involving a quotient that removes spurious structure. The payoff is that the entire geometric structure involves only vector bundles over space-time, and we emphasize that familiar concepts such as BRST are built into the geometry, rather than appearing as adjunct structure. Thus the formulation of gauge theories in terms of Lie algebroids provides a fully off-shell account of the BRST complex. We expect that this formulation will have appealing impacts on the geometric understanding of quantization and anomalies, as well as entanglement in gauge theories. The formalism covers all gauge theories, and we discuss Yang-Mills theories with matter as well as gravitational theories explicitly.Comment: 41 pages, Latex, v

Micro-Scale Catalytic Reactor for Syngas Production

This paper presents both experimental and modeling investigations of a catalytic wall fuel processor consisting of coupled methane reforming and methane combustion sections. The reacting systems are both catalytic and the latter generates the heat required for the occurrence of the former. The catalytic wall reactor was examined for light-off behavior and for steady-state product distribution. On one hand, the analysis of the reaction products distribution after catalyst ignition indicated that in both combustion and reforming sections catalysts undergo to a relatively long transient (about 40 min) before reaching steady state conditions. On the other hand, a much longer reactor thermal transient was observed and the two transient behaviors appear independent of each other. Analysis of the reactor operating under real conditions (nonadiabatic) showed that a 3D model is needed to accurately predict the reactor performance because a 2D model, although much more convenient, cannot allow for the whole heat loss thereby yielding unreliable results