Electrical transport in materials is typically diffusive, due to dominant momentum-relaxing scattering of carriers with the phonons or defects. In ultraclean material systems such as GaAs/AlGaAs or graphene/hBN heterostructures, momentum-relaxing can be suppressed, leading to the onset of non-diffusive transport regimes, where Ohm's law is no longer valid. Within these non-diffusive regimes, the hydrodynamic regime occurs when momentum-conserving electron-electron scattering length scale is smaller than the device length scale (usually at intermediate temperatures). On the other hand, weak electron-electron scattering (at low temperatures) results in ballistic transport, commonly understood using the familiar single-particle framework of injected carriers travelling in straight line trajectories with intermittent reflections off device boundaries. Both the ballistic and hydrodynamic regimes can exhibit a emph{negative} nonlocal resistance, and collective behaviour such as the formation of current vortices. In this work, we study nonlocal current-voltage characteristics in mesoscopic devices fabricated from a GaAs/AlGaAs heterostructure that hosts a two-dimensional electron system in a GaAs quantum well. First, we report a quadratic non-linearity in the nonlocal current-voltage characteristics that manifests in any device where a nonlocal voltage measurement is possible. Using measurements at low temperatures ($sim$ 4 K) across multiple devices and considering various contact configurations for each device, we show that the non-linearity is universal. We apply the non-linearity to rectification and frequency multiplication. We also report on a periodic peaks in the nonlocal voltage vs. magnetic field, in an enclosed mesoscopic geometry in which transverse magnetic focusing (TMF) is typically studied. These peaks occur at weak magnetic fields, are independent of the source-detector separation and are distinct from TMF. Our experimental findings are backed by an extensive set of simulations using in both the semiclassical as well as quantum-coherent transport models. / Master of Science / Current is made up of charged particles such as electrons moving through a material. Typically, current is proportional to the applied voltage and flows from higher to lower potential within the device with the potential decreasing monotonically as we move from the source contact to the drain contact irrespective of the path taken through the device. This is commonly known as Ohm's law, and is followed in most materials we come across. The motion of electrons carrying this current is akin to the motion of balls inside a pinball machine, their momentum randomized by intermittent collisions due to lattice vibrations, defects and impurities present in the material. In ultraclean two-dimensional materials at low-intermediate temperatures (where lattice vibration is weak), these collisions become sparse. Collisions of electrons with other electrons now become important. When electron-electron collisions are frequent, the electrons collectively behave like a fluid, giving rise to so called hydrodynamic transport. On the other hand, when electron-electron collisions are sparse as well, electrons move unhindered in ballistic straight line trajectories until they reflect off the device boundaries. This is known as ballistic transport. Under both these transport regimes, Ohm's law breaks down, leading to interesting physical phenomena such as the formation of current whirlpools. In this work, we study the voltage measured at a point in the device which is distinct from the point where current is injected or extracted. This is commonly known as the nonlocal voltage. We explore the relationship between the nonlocal voltage and the injected current and find it to be significantly different from predictions made by Ohm's law. We use this novel current-voltage relationship to build a rectifier and frequency multiplier - two devices commonly used in high-frequency detection, radar systems and telecommunications. We also report previously unseen periodic oscillations in the nonlocal voltage when the magnetic field perpendicular to the device is varied. Using high-resolution simulations, we show the these oscillations can not be explained by looking at individual electron paths, and arise due to contribution from all electrons that travel through the device.

Les Pertuis Charentais sont un site d’écosystèmes interconnectés où les courants marins jouent un rôle déterminant. Un modèle de marée à haute résolution a été développé au cours de cette thèse pour comprendre et cartographier les traits principaux de la circulation hydrodynamique dans les Pertuis. Deux axes sont ainsi mis en avant dans cette étude. D’abord, un nouveau modèle de marées dans les Pertuis Charentais a été construit et validé à partir de différentes sources : données marégraphiques, données de courantomètres ADCP et images satellitaires. Une nouvelle approche de calibration de modèle de marée a été développée, basée sur la comparaison de la position de la ligne d’eau, frontière entre l’eau et la terre, avec celle prédite par le modèle. Puis dans un second temps, le transport et les agrégations en « bloom » de populations de méduses Rhizostoma, dont les proliférations et les échouages sont à l’origine de problèmes socio-économiques, ont été simulés numériquement. Des observations in situ ont permis de paramétrer le comportement de nage des méduses dans le modèle. Deux types de comportements des méduses, actif et passif ont été simulés. Les courants de marées en présence des forçages-type météorologiques ont été pris en compte. Les résultats indiquent que le comportement individuel de nage des méduses pourrait être une réponse adaptative aux facteurs abiotiques qui menacent la continuité de leur espèce mais que les courants marins restent la cause première de la formation des blooms. / The Pertuis Charentais are an interconnected ecosystems site where ocean currents play a key role. A high resolution tidal model was developed in this thesis in order to understand the main features of the hydrodynamic flows inside the Pertuis. Two topics were put forward in this study. First, a new tide model for the Pertuis Charentais was build up and validated by using different datasets: tide gauge records, measurements of currents by ADCP and satellite images. A new approach to model calibration was developed by comparing the observed position of the waterline, the boundary between land and water, with that predicted by the model. Secondly, the transport and bloom-like aggregation of the Rhizostoma jellyfish populations were simulated numerically. The jellyfish proliferation and stranding are a source of socio-economic problems. Two types of jellyfish behavior, active and passive were simulated. The tidal currents and typical meteorological forcing were taken into account. The results show that the individual behavior of swimming jellyfish is an adaptive response to abiotic factors for jellyfish survival.

Ces travaux ont pour objectif de modéliser les mécanismes de dispersion dans les aquifères. L’hétérogénéité du champ de vitesse et le transfert de masse entre zones immobiles et mobiles sont deux origines possibles du comportement non-Fickéen, jusqu’alors étudiées de façon séparée. Notre hypothèse de départ est que ces deux mécanismes coexistent. Nos travaux comprennent : 1) des expériences de traçage sur colonnes de billes de verre et carottes de grès de Berea, en mode flow-through et push-pull, et 2) des simulations numériques réalisées à partir d’images en microtomographie RX segmentées en trois phases : solide, vide et microporosité. L’analyse du champ de vitesse (Stokes) montre l’importance de la discrétisation spatiale et de la prise en compte de la microporosité. Les résultats des simulations de transport (en utilisant la méthode time domain random walk) permettent de quantifier l’effet combiné de l’hétérogénéité du champ de vitesse et des transferts diffusifs dans la fraction micro-poreuse de la roche sur la dispersion non-Fickéenne, caractérisée à partir des courbes de restitution (BTC). Ces résultats sont cohérents avec les observations expérimentales. Nous concluons que ces deux effets doivent être pris en compte même si leur identification à partir de la forme des BTCs issues des traçages des milieux naturels (souvent caractérisés par de faible valeurs du nombre de Peclet ) reste difficile. Enfin, un modèle moyen macroscopique 1D est proposé dans le cadre d’une approche de type continuous time random walk dans laquelle des distributions spécifiques du temps de transfert des particules sont construites pour chacun des deux mécanismes de transport. / His work aims at modeling hydrodynamic dispersion mechanisms in aquifers. So far both flow field heterogeneity and mobile-immobile mass transfer have been studied separately for explaining the ubiquitously observed non-Fickian behaviors, but we postulate that both mechanisms contribute simultaneously. Our investigations combine laboratory experiments and pore scale numerical modeling. The experimental rig was designed to enable push-pull and flow through tracer tests on glass bead columns and Berea sandstone cores. Modeling consists in solving Stokes flow and solute transport on 3D X-ray microtomography images segmented into three phases: solid, void and microporosity. Transport is modeled using time domain random walk. Statistical analysis of the flow field emphasizes the importance of the mesh resolution and the inclusion of the microporosity. Results from the simulations show that both the flow field heterogeneity and the diffusive transport in the microporous fraction of the rock contribute to the overall non-Fickian transport behavior observed, for instance, on the breakthrough curves (BTC). These results are supported by our experiments. We conclude that, in general, this dual control must be taken into account, even if these different influences can hardly be distinguished from a qualitative appraisal of the BTC shape, specifically for the low values of the Peclet number that occurs in natural conditions. Finally, a 1D up-scaled model is developed in the framework of the continuous time random walk, where the influences of the flow field heterogeneity and mobile-immobile mass transfer are both taken into account using distinct transition time distributions.