La croissance de la phase vésiculée, moteur de l'éruption, est contrôlée par les processus de diffusion qui permettent la migration des gaz (et notamment des gaz rares) dans les bulles. On utilise la haute volatilité des gaz rares comme traceur géochimique de l'évolution d'une phase gazeuse sans interaction chimique. Ainsi, documenter précisément les mécanismes de diffusion des différents gaz rares (He, Ne, Ar) lors de l'éruption (c'est-à-dire en fonction de la chute de température et de pression du système), permet de quantifier les phénomènes de fractionnement de la phase gazeuse. La compréhension des processus de fractionnements cinétiques, permet dès lors de prédire le temps nécessaire pour atteindre une certaine quantité de gaz rares dans une bulle (située au sein d'un système magmatique), lors de l'éjection des laves. Pour cela, la compréhension de l'influence de la température et de la structure du réseau silicaté sur les coefficients de diffusion est nécessaire. Cependant, la compréhension physique des processus de diffusion ainsi que l'évolution des coefficients de diffusion en fonction de la température, n'est pas suffisante pour dériver des temps caractéristiques d'une éruption volcanique de type Plinian. La complexité symptomatique de tels systèmes, nécessite une résolution numérique des équations de diffusion prenant en compte la dépendance des coefficients de diffusion à la température. Plusieurs verres synthétiques et naturels de composition basaltique ont été fabriqués dans le but de déterminer la vitesse de diffusion des gaz rares. Les données de diffusivités expérimentales mesurées sur ces systèmes, depuis l'état vitreux de basse température (T = 423 K) jusqu'à des températures sur-liquidus (T = 1823 K), documentent nos connaissances des processus physiques de diffusion dans ces milieux. Un modèle numérique intègre ces données et permet de suivre en continue la variation des coefficients de diffusion lors de la trempe d'une lave. On a pu ainsi montré : - La relation particulière entre la structure du milieu diffusif et les espèces diffusantes. La quantité de formateurs de réseaux (SiO2) et de modificateurs (CaO - MgO - etc.), joue sur la connectivité des chemins de diffusions de chaque gaz rare, avec un effet antagoniste entre l'ouverture globale du réseau et la connexion des tétraèdres de la structure. - La présence de comportements non-arrheniens des gaz rares proches de la Tg, due à la relaxation du réseau silicate. - L'importance des données expérimentales dans l'étude des mécanismes de dégazage des magmas basaltiques. En effet, les études précédentes utilisent des extrapolations des coefficients de diffusions, mesurés dans le verre pour extrapoler les diffusivités dans le liquide silicaté. Nos données montrent que le fractionnement cinétique des gaz rares pendant le dégazage de lave basaltique, est surestimé par ces extrapolations basées sur les vitesses de diffusions aux basses températures (T << Tg) / Noble gas geochemistry is an important tool for constraining the history of the volatile phase during magmatic eruptions. Degassing processes control the gas flux from liquid to bubble, leading to solubility- or kinetic-control of the fractionation mechanisms. Noble gases have no chemical interactions at magmatic conditions and are therefore well adapted to tracing gas fractionation mechanisms during the evolution of the gas phase. Well constrained diffusion coefficients, and their dependence on temperature, of several noble gases are critical for estimating the timescale of a plinian eruption, for example. During the quench phase of the lava ejected in the plume, atmospheric noble gases will diffuse through the liquid/glass shell surrounding gas bubbles. Diffusion of these atmospheric gases determine the gas content measured in the eruption products, which are therefore a function of the timescale of the eruption, the initial and final temperatures, the glass/liquid shell thickness and the cooling rate of the magma. Therefore, it should be possible to calculate plinian eruption timescales from noble gas fractionation patterns trapped in pumice. However, in order to perform the diffusion calculations, it is first necessary to model the diffusive system: a numerical resolution of the diffusion equations for hollow sphere geometry is required as there are no analytical solutions (for complex thermal histories such as for a plinian ash column). In order to constrain the diffusion mechanisms (He, Ne and Ar) in silicate glasses and liquids, several synthetic basaltic glasses were produced. Diffusion coefficients were measured from low temperatures (423 K) to the Tg (glass transition temperature) of the system (1005 K). These experiments allowed us to investigate the physical processes that limit diffusion in glassy media: He, Ne and Ar diffusion in silicate glasses show non-Arrhenian behavior as the Tg is approached thought to be due to structural relaxation of the silicate network itself. Complementary diffusion experiments (on He and Ar) at super-liquidus conditions (1673 K and 1823 K) provide important information on the temperature dependency of He/Ar fractionation in silicate liquids. These diffusion measurements required that a new experimental protocol was developed in order to investigate noble gas diffusivities in silicate melts. The results show that relative He and Ar diffusion (i.e. DHe/DAr) decreases with temperature, from 165 at temperatures close to the Tg to 3.2 at high (>1823K) temperature. The measured coefficient diffusions are incorporated to a numerical model of the diffusion equations for a hollow sphere geometry that were developed as a MatLab code as part of this thesis work. This enabled us to determine the likely timescales of plinian eruptions from existing noble gas measurements. These results also have important implications for mechanisms of degassing in basaltic magmas: previous work used diffusivities measured on glasses in order to extrapolate to noble gas diffusivities at magmatic temperatures. Our measurements show that kinetic fractionation of noble gases during degassing of basaltic magmas has likely been overstated because noble gas diffusion in the glass cannot be extrapolated to the liquid state

Hydrated polysaccharide systems primarily using xylans along with mutans and alternans were studied using long atomistic simulations over a few microseconds to analyse structure-function relationships and nanoscale interactions with moisture. The influence of various structural and chemical factors such as alignment, nature of glycosidic linkage, effect of moisture / chemical substitutions was explored with a focus on structure-dynamics correlations to aid in the effective functionalisation of biomaterials for the development of a green, circular bioeconomy. The effect of initial geometry in terms of alignment of the xylan chains was observed to affect xylan chain extension and water dynamics significantly. Xylan interaction with moisture studied at high and low moisture contents showed compression along with structural locking, and evolution into segregated water-rich and polymer-rich phases respectively. The effect of chemical heterogeneity in terms of substitutions appeared to improve xylan dispersion in water resulting in faster dynamics for substituted residues with reference to unsubstituted residues along a given polymer chain. In addition, significant correlations between local hydration and polymer dynamics / structure in terms of relaxation times and order parameters was observed across differently substituted hydrated xylan systems, such that the polymer dynamics could be expressed as a local hydration water dependent component and a second partially stochastic component. In addition, the molecular structure of mixed linkage (1,3 and 1,6) as well as 1,3 linked glucans elucidated the effect of the nature of glycosidic linkage on the molecular structure of glucan oligosaccharides. A combination of glucan linkages and the ratio of different conformation states of the hydroxymethyl dihedral angle was observed to yield linear, twisted and extended structures in mutans, or helical coils of varying pitch sizes in alternans. Further modeling of structure-dynamics dependencies in hydrated xylan systems and analysis of the effect of alignment / chemical substitutions at the nanoscale is to be correlated with scattering or related experimental techniques in the future to understand the dynamics of hydrated xylan aggregates in typically aqueous solutions at varying intermediate length / timescales. In addition, the methodologies derived in this work to identify atom-specific, temporally sensitive, structural / dynamical parameters for analysing structural / dynamical variations at the nanoscale can be extended to study other hydrated biopolymeric systems. The role of substitutions, involving its polar nature and interactions with other xylans, can be extended to neutral groups such as arabinose sugars to broaden knowledge in carbohydrate science as well as being analysed further to improve effective functionalisation for tailoring physical properties influencing phenomena like aggregation / dispersion. / Hydrerade polysackaridsystem som primärt använde xylaner, mutaner och alternaner studerades med hjälp av långa atomistiska simuleringar under några mikrosekunder för att analysera struktur-funktionsförhållanden och interaktioner med fukt i nanoskala. Inverkan av olika strukturella och kemiska faktorer såsom placering, karaktären av glykosidbindning, effekten avfukt/kemiska substitutioner undersöktes med fokus på struktur-dynamiska korrelationer för att hjälpa till med en effektiv funktionalisering av biomaterial för utvecklingen av en grön, cirkulär bioekonomi. Effekten av initial geometri i termer av placering av xylan-kedjorna observerades påverka xylan-kedjeförlängningen och vattendynamiken signifikant. Xylaninteraktionen medfukt studerades vid höga och låga fukthalter och visade kompression tillsammans med strukturell låsning och utveckling till segregerade vattenrika och polymerrika faser respektive. Effekten av kemisk heterogenitet i termer av substitutioner verkade förbättra dispersionen av xylan i vatten vilket resulterade i snabbare dynamik för substituerade delar jämfört med osubstituerade delar längs en given polymerkedja. Dessutom observerades signifikanta korrelationer mellan lokal hydratisering och polymerdynamik/struktur i termer av relaxationstider och ordningsparametrar över olika substituerade hydratiserade xylansystem, så att polymerdynamiken kunde uttryckas som en lokal hydreringsvattenberoende komponent och en andra delvis stokastisk komponent. Dessutom klargjorde den molekylära strukturen av blandad koppling (1,3 och 1,6) såväl som 1,3 länkade glukaner effekten av glykosidkopplingens natur på molekylstrukturen hos glukanoligosackarider. En kombination av glukanbindningar och förhållandet mellan olika konformationstillstånd för den hydroximetyldiedriska vinkeln observerades i linjära, vridna och utsträckta strukturer som i mutaner, eller som spiralformade spolar med varierande stigningsstorlekar i alternaner. Ytterligare modellering av struktur-dynamiska beroenden i hydratiserade xylansystem och analys av effekten av inriktning/kemiska substitutioner på nanoskala ska korreleras med spridning av relaterade experimentella tekniker i framtiden för att förstå dynamiken hos hydratiserade xylanaggregat i typiskt vattenhaltiga lösningar vid varierande medellängd /tidsskalor. Dessutom kan de metoder som härrör från detta arbete för att identifiera atomspecifika, tidsmässigt känsliga, strukturella/dynamiska parametrar för analys av strukturella/dynamiska variationer på nanoskala, utvidgas till att studera andra hydratiserade biopolymera system. Substitutionernas roll, som involverar dess polära natur och interaktioner med andra xylaner, kan utvidgas till neutrala grupper som arabinossocker för att bredda kunskapen inom kolhydratvetenskap samt analyseras ytterligare för att förbättra effektiv funktionalisering för att skräddarsy fysiska egenskaper som påverkar fenomen som aggregering / dispersion. / <p>QC 2023-05-22</p>

This thesis, structured in two parts, addresses a series of problems of relevance in the field of Spatial Geodesy. The first part delves into the application of satellite gravity data to enhance our understanding of water transport dynamics. Here, we present two significant contributions. Both are based on satellite gravity data but stem from different mission concepts with distinct objectives: time-variable gravity monitoring and high-resolution, accurate static geoid modelling. First, the fundamental notions about gravity are introduced and a brief summary is made of the different gravity satellite missions throughout history, with emphasis on the GRACE/GRACE-FO and GOCE missions, whose data are the basis of this work. The first application focuses on estimating water transport and geostrophic circulation in the Southern Ocean by leveraging a GOCE geoid and altimetry data. The Volume Transport across the Antartic Circumpolar Current is analyzed and the resulsts are validated validated using the in-situ data collected during the multiple campaigns in the DP. The second application uses time-variable gravity data from the GRACE and GRACE-FO missions to estimate the water cycle in the Mediterranean and Black Sea system, a critical region for regional climate and global ocean circulation. The analysis delves into the analysis of the different components of the hydrological cycle within this region, including the water flow across the Gibraltar Strait, examining their seasonal variations, climatic patterns, and their connection with the North Atlantic Oscillation Index. The second part of the thesis is more focused on data analysis, with the objective of developing mathematical methods to estimate the cross correlation function between two time series that are both unevenly spaced spaced (the sampling is not uniform over time) and observed at unequal time scales (the set of time points for the first series is not identical to the set of time points of the second series). Such time series are frequently encountered in geodetic surveys, especially when combining data from different sources. The estimation of the the cross correlation function for these time series presents unique challenges and requires the adaptation of traditional analysis methods designed for evenly spaced and synchronized time series. The two main contributions in this context are: (i) the study of the asymptotic properties of the Guassian Kernel estimator, that is the recommended estimator for the cross correlation function when the two time series are observed at unequal time scales; (ii) an extension of the stationary bootstrap that allows to construct bootstrap-based confidence intervals for the cross correlation function for unevenly spaced time series not sampled on identical time points.

The physics of ultracold quantum gases has been the subject of a long-lasting and intense research activity, which started almost a century ago with purely theoretical studies and had a fluorishing experimental development after the implementation of laser and evaporative cooling techniques that led to the first realization of a Bose Einstein condensate (BEC) over 25 years ago. In recent years, a great interest in ultracold atoms has developed for their use as platforms for quantum technologies, given the high degree of control and tunability offered by ultracold atom systems. These features make ultracold atoms an ideal test bench for simulating and studying experimentally, in a controlled environment, physical phenomena analogous to those occurring in other, more complicated, or even inaccessible systems, which is the idea at the heart of quantum simulation. In the rapidly developing field of quantum technologies, it is highly important to acquire an in-depth understanding of the state of the quantum many-body system that is used, and of the processes needed to reach the desired state. The preparation of the system in a given target state often involves the crossing of second order phase transitions, bringing the system strongly out-of-equilibrium. A better understanding of the out-of-equilibrium processes occurring in the vicinity of the transition, and of the relaxation dynamics towards the final equilibrium condition, is crucial in order to produce well-controlled quantum states in an efficient way. In this thesis I present the results of the research activity that I performed during my PhD at the BEC1 laboratory of the BEC center, working on ultracold gases of 23Na atoms in an elongated harmonic trap. This work had two main goals: the accurate determination of the equilibrium properties of a Bose gas at finite temperature, by the measurement of its equation of state, and the investigation of the out-of-equilibrium dynamics occurring when a Bose Einstein condensate is prepared by cooling a thermal cloud at a finite rate across the BEC phase transition.To study the equilibrium physics of a trapped atomic cloud, it is crucial to be able to observe its density distribution in situ. This requires a high optical resolution to accurately obtain the density profile of the atomic distribution, from which thermodynamic quantities can then be extracted. In particular, in a partially condensed atomic cloud at finite temperature, it is challenging to resolve well also the boundaries of the BEC, where the condensate fraction rapidly drops in a narrow spatial region. This required an upgrade of the experimental apparatus in order to obtain a high enough resolution. I designed, tested and implemented in the experimental setup new imaging systems for all main directions of view. Particular attention was paid for the vertical imaging system, which was designed to image the condensates in trap with a resolution below 2 μm, with about a factor 4 improvement compared to the previous setup. The implementation of the new imaging systems involved a partial rebuilding of the experimental apparatus used for cooling the atoms. This created the occasion for an optimization of the whole system to obtain more stable working conditions. Concurrently I also realized and included in the experiment an optical setup for the use of a Digital Micromirror Device (DMD) to project time-dependent arbitrary light patterns on the atoms, creating optical potentials that can be controlled at will. The use of this device opens up exciting future scenarios where it will be possible to locally modify the trapping potential and to create well-controlled barriers moving through the atomic cloud. Another challenge in imaging the density distribution in situ is determined by the fact that the maximum optical density (OD) of the BEC, in the trap center, exceeds the low OD of the thermal tails by several orders of magnitude. In order to obtain an accurate image of the whole density profile, we developed a minimally destructive, multi-shot imaging technique, based on the partial transfer of a fraction of atoms to an auxiliary state, which is then probed. Taking multiple images at different extraction fractions, we are able to reconstruct the whole density profile of the atomic cloud avoiding saturation and maintaining a good signal to noise ratio. This technique, together with the improvements in the imaging resolution, has allowed us to accurately obtain the optical density profile of the Bose gas in trap, from which the 3D density profile was then calculated applying an inverse Abel transform, taking advantage of the symmetry of the trap. From images of the same cloud after a time-of-flight expansion, we measured the temperature of the gas. From these quantities we could find the pressure as a function of the density and temperature, determining the canonical equation of state of the weakly interacting Bose gas in equilibrium at finite temperature. These measurements also allowed us to clearly observe the non-monotonic temperature behavior of the chemical potential near the critical point for the phase transition, a feature that characterizes also other superfluid systems, but that had never been observed before in weakly interacting Bose gases. The second part of this thesis work is devoted to the study of the dynamical processes that occur during the formation of the BEC order parameter within a thermal cloud. The cooling at finite rate across the Bose-Einstein condensation transition brings the system in a strongly out-of-equilibrium state, which is worth investigating, together with the subsequent relaxation towards an equilibrium state. This is of interest also in view of achieving a better understanding of second order phase transitions in general, since such phenomena are ubiquitous in nature and relevant also in other platforms for quantum technologies. A milestone result in the study of second order phase transitions is given by the Kibble-Zurek mechanism, which provides a simple model capturing important aspects of the evolution of a system that crosses a second-order phase transition at finite rate. It is based on the principle that in an extended system the symmetry breaking associated with a continuous phase transition can take place only locally. This causes the formation of causally disconnected domains of the order parameter, at the boundaries of which topological defects can form, whose number and size scale with the rate at which the transition is crossed, following a universal power law. It was originally developed in the context of cosmology, but was later successfully tested in a variety of systems, including superfluid helium, superconductors, trapped ions and ultracold atoms. The BEC phase transition represents in this context a paradigmatic test-bench, given the high degree of control at which this second-order phase transition can be crossed by means of cooling ramps at different rates. Already early experiments investigated the formation of the BEC order parameter within a thermal cloud, after quasi-instantaneous temperature quenches or very slow evaporative cooling. In the framework of directly testing the Kibble-Zurek mechanism, further experiments were performed, both in 2D and 3D systems, focusing on the emergence of coherence and on the statistics of the spontaneously generated topological defects as a function of the cooling rate. The Kibble-Zurek mechanism, however, does not fully describe the out-of-equilibrium dynamics of the system at the transition, nor the post-quench interaction mechanisms between domains that lead to coarse-graining. Most theoretical models are based on a direct linear variation of a single control parameter, e.g. the temperature, across the transition. In real experiments, the cooling process is controlled by the tuning of other experimental parameters and a global temperature might not even be well defined, in a thermodynamic sense, during the whole process. Moreover, the temperature variation is usually accompanied by the variation of other quantities, such as the number of atoms and the collisional rate, making it difficult to accurately describe the system and predict the post-quench properties. Recent works included effects going beyond the Kibble-Zurek mechanism, such as the inhomogeneity introduced by the trapping potential, the role of atom number losses, and the saturation of the number of defects for high cooling rates. These works motivate further studies, in particular of the dynamics taking place at early times, close to the crossing of the critical point. The aim of the work presented in this thesis is to further investigate the timescales associated to the formation and evolution of the BEC order parameter and its spatial fluctuations, as a function of the rate at which the transition point is crossed. We performed experiments producing BECs by means of cooling protocols that are commonly used in cold-atom laboratories, involving evaporative cooling in a magnetic trap. We explored a wide range of cooling rates across the transition and found a universal scaling for the growth of the BEC order parameter with the cooling rate and a finite delay in its formation. The latter was already observed in earlier works, but for a much more limited range of cooling rates. The evolution of the fluctuations of the order parameter was also investigated, with an analysis of the timescale of their decay during the relaxation of the system, from an initial strongly out-of-equilibrium condition to a final equilibrium state. This thesis is structured as follows: The first chapter presents the theoretical background, starting with a brief introduction to the concept of Bose Einstein condensation and a presentation of different models describing the thermodynamics of an equilibrium Bose gas. The second part of this chapter then deals with the out-of-equilibrium dynamics that is inevitably involved in the crossing of a second-order phase transition such as the one for Bose-Einstein condensation. The Kibble-Zurek mechanism is briefly reviewed and beyond KZ effects are pointed out, motivating a more detailed investigation of the timescales involved in the BEC formation. In the second chapter, I describe the experimental apparatus that we use to cool and confine the atoms. Particular detail is dedicated to the parts that have been upgraded during my PhD, such as the imaging system. In the third chapter I show our experimental results on the measurement of the equation of state of the weakly interacting uniform Bose gas at finite temperature. In the fourth chapter I present our results on the out-of-equilibrium dynamics in the formation of the condensate order parameter and its spatial fluctuations, as a function of different cooling rates.

No description available.