Changes in climatic regimes and land use have led to increases in wildfire activities around the world. Wildfires are now happening more frequently, at higher altitudes, and higher severities. Adverse impacts of wildfires can last years after the fire has been contained through post-fire geohazards, such as shallow landslides. Post-wildfire shallow landslides are often mobilized by rainfall and due to fire-induced changes in soil and land cover properties and near-surface processes. This study aims to develop a physics-based framework to evaluate the stability of burned hillslopes against rainfall-triggered shallow landslides. A coupled hydromechanical infiltration model is developed by employing a closed-form solution of the Richards equation. The model is integrated into an infinite slope stability analysis to capture the effect of temporal changes in the pressure head profile of an unsaturated vegetated slope on its stability. The proposed model considers the antecedent condition of soil and vegetation cover, the time-varying nature of rainfall intensity, and wildfire-induced changes in soil properties, root reinforcement, transpiration rate, and canopy interception. The efficacy of the proposed framework is illustrated through modeling a case study in the Las Lomas watershed in California, USA. The watershed was a part of a larger area that was burned in the San Gabriel Complex Fire (consisting of two separate fires, the Fish Fire and the Reservoir Fire) in 2016. Three years later, during a heavy rainstorm in January 2019, the affected area, including the Las Lomas watershed, experienced widespread landslides. The proposed framework is then integrated into a geographic information system (GIS) to generate a susceptibility map of post-wildfire rainfall-triggered shallow landslides. The applicability of the proposed framework at a regional scale is tested for the entire area affected by the San Gabriel Complex Fire to model the observed shallow landslides within the boundaries of the Fish Fire and the Reservoir Fire. The findings of this study can be used to warn the community of post-wildfire shallow landslides activities.

Laboratory experiments were conducted to investigate the effect of low relative depth and high Froude number on the dimensionless critical shear stress (Shields parameter). Spherical particles of four different densities and an 8mm diameter were used as movable test material. The relative depth ranged from 2 to 12 and the Froude number ranged from 0.36 to 1.29. The results show that the traditional Shields diagram cannot be used to predict the incipient motion of coarse sediment particles when the relative depth is below 10 and the Froude number is above 0.5, approximately. Experiments using glass balls, whose density is almost identical to that of natural gravel, show that the Shields parameter can be twice as large in shallow flows than in deep flows. The results also show that the Shields parameter is dependent on the density of the particles. Data obtained from other studies support the findings of the present work. These findings can result in significant cost savings for riprap. Additionally, velocity profiles using a laser-Doppler velocimeter (LDV) were taken for the glass ball incipient motion experiments. The purpose of this was to study possible changes in the velocity distribution with decreasing relative depth and increasing Froude number. The results show that the von Karman and integral constants in the law of the wall do not change in the range of relative depths and Froude numbers tested. / Master of Science

Within the "forbidden" range of electron energies between the valence and conduction bands of titanium dioxide, crystal lattice irregularities lead to the formation of electron trapping sites. These sites are known as shallow trap states, where "shallow" refers to the close energy proximity of those features to the bottom of the semiconductor conduction band. For wide bandgap semiconductors like titanium dioxide, shallow electron traps are the principle route for thermal excitation of electrons into the conduction band. The studies described here employ a novel infrared spectroscopic approach to determine the energy of shallow electron traps in titanium dioxide nanoparticles. Mobile electrons within the conduction band of semiconductors are known to absorb infrared radiation. As those electrons absorb the infrared photons, transitions within the continuum of the conduction band produce a broad spectral signal across the entire mid-infrared range. A Mathematical expression based upon Fermi–Dirac statistics was derived to correlate the temperature of the particles to the population of charge carriers, as measured through the infrared absorbance. The primary variable of interest in the Fermi – Dirac expression is the energy difference between the shallow trap states and the conduction band. Fitting data sets consisting of titanium dioxide nanoparticle temperatures and their associated infrared spectra, over a defined frequency range, to the Fermi–Dirac expression is used to determine the shallow electron trap state energy. / Master of Science

Orbit propagation is the backbone of many problems in the space domain, such as uncertainty quantification, trajectory optimization, and guidance, navigation, and control of on orbit vehicles. Many of these techniques can rely on millions of orbit propagations, slowing computation, especially evident on low-powered satellite hardware. Past research has relied on the use of lookup tables or data streaming to enable on orbit solutions. These solutions prove inaccurate or ineffective when communication is interrupted. In this work, we introduce the use of physics-informed neural networks (PINNs) for orbit propagation to achieve fast and accurate on-board solutions, accelerated by GPU hardware solutions now available in satellite hardware. Physics-informed neural networks leverage the governing equations of motion in network training, allowing the network to optimize around the physical constraints of the system. This work leverages the use of unsupervised learning and introduces the concept of fundamental integrals of orbits to train PINNs to solve orbit problems with no knowledge of the true solution. Numerical experiments are conducted for both Earth orbits and cislunar space, being the first time a neural network integrator is implemented on flight-like hardware. The results show that the use of PINNs can decrease solution evaluation time by several order of magnitude while retaining accurate solutions to the perturbed two-body problem and the circular restricted three-body problem for deployment on spaceflight-like hardware. Implementation of these neural networks aim to reduce computational time to allow for real-time evaluation of complex algorithms on-board space vehicles.

This thesis gives an overview of the process that led to the development of a novel semi-implicit fluid-structure interaction model. The thesis is dedicated to the creation of a new numerical model that allows to study ship generated waves and ship manoeuvers in waterways for various vessel characteristics and speeds in different external current situations. A model like this requires a coupling between the fluid and the solid to generate the waves and the hydrodynamic forces on the hull. Since the horizontal dimensions are significantly larger than the vertical dimension, we started by employing the shallow water equations, which are based on the assumption of hydrostatic pressure. The discretization was carried out taking only the nonlinear advective terms explicitly while the pressure terms are discretized implicitly, which makes the CFL condition milder. The price to pay for this semi-implicit discretization is an increase in the algorithm complexity compared to a fully-explicit method, but it is still much simpler than a fully-implicit discretization of the governing equations. Indeed, the mass and momentum equations couple, and finding the unknowns involves solving a system of equations with dimensions equal to the number of cells. The grid supporting the discretization is staggered, overlapping and Cartesian. Since the aimed application domain is inland waterways, it is paramount to allow wetting and drying of the cells. This was achieved by acting on the depth function, the relationship between the free-surface elevation and the water depth in the cell. The main novelty of this research project is the two-way coupling of the PDE system for the water flow with the ODE system for the rigid body motion of the ship. The hull defines the ship region, and its shape can range from a simple box to an STL file of a real 3D ship geometry. Where the hull is in contact with the water, the cells are pressurized. This pressurized group of cells generates waves as it moves, and its motion is influenced by incoming external waves. This result is obtained by imposing an upper bound to the depth function, so that the water depth does not increase when it reaches the hull elevation, while the pressure is allowed to increase. This upper bound increases the nonlinearity of the system, which may have dry cells, wet free-surface cells and pressurized cells. The solution of this system is found by a single nested-Newton iterative solver of Casulli and Zanolli [36], in which with two separate linearizations the system is written in a sparse, symmetric, positive semi-definite form. This particular form allows us to employ a matrix-free conjugate gradient method, and efficiently get the unknown pressure. The integral of the pressure over the hull is applied for the hydrodynamic force and torque acting on the ship. After adding the skin friction and other external forces from the propeller or the rudder, the total force is inserted in the equation of motion of the rigid body. The ODE system is discretized with a second-order Taylor method, and it is solved for the six degrees of freedom (3 coordinates for the position vector of the barycenter and 3 rotation angles), providing the next position and orientation of the ship. The vertical translation of the rigid body is governed by the gravitational force and the restoring force from Archimedes' principle. As the ship oscillates up and down, the gravitational potential energy is partially transferred to the radiated free-surface water waves, damping and eventually stopping the motion. Also, the ship pushes and pulls the water around it, inducing the added mass force. All these elements constitute the ODE that was used for the verification of the vertical degree of freedom. The numerical simulation gave the expected results for the vertical motion. The horizontal translation, important for the manoeuvers, presented a numerical instability unseen in our previous test cases, which is connected to the relative motion between the ship and the grid. In each time step in which the ship enters a new cell, the pressure sharply increases and decreases at the ship bow. An oscillation can build up in time and create an unphysical void below the vessel. We implemented a few ideas to attenuate the oscillations. At the heart of all the following techniques is the reduction of the time derivative of the water depth, especially for those cells transitioning to a pressurized state. All these modifications were effective at controlling the oscillations, each with a different intensity, and simulations with a horizontal motion are much more stable than without these techniques. With the collaboration of the BAW research institute, we worked on the model validation. We used data from two separate experiments to compare the measurements with the numerical results. Specifically, we focused on the ship-generated wave height and the hydrodynamic forces on the hull. The comparison is satisfactory for the wave height. The force and torque prediction is plausible but underestimated compared to the measurements. The model seems to displace the water volume correctly during the ship passage, while the force and torque response might need additional work to be trusted in applications. Even though the hydrostatic assumption is mostly correct in our range of applications, the presence and the motion of a ship could generate strong vertical accelerations of the flow, which may not be negligible. For this reason, we implemented an algorithm that corrects the velocity field, introducing also dispersive effects due to a non-hydrostatic pressure. The correction consists of a higher-order Bousinnesq-type term in the momentum equation and the solution of the resulting system. The non-hydrostatic update has a small influence on the wave generation, while it alters significantly the reaction forces. The subgrid method implementation allowed to benefit from high-resolution bottom descriptions while keeping the grid size coarse. The same subgrid can also be used for a refined definition of the hull, which makes the volume computations more accurate. Furthermore, the subgrid introduces new possible states for the cells, as they can be partially dry or partially pressurized. These intermediate states translate into smoother transitions from one state to the other when the free-surface is close to the bathymetry or to the hull. Concerning the software implementation of the developed scheme, in order to improve the execution performance of the prototype script formulated initially in Matlab, the numerical method was rewritten as a Fortran program. Also, thanks to the domain decomposition technique and the MPI standard, each simulation can run in parallel on multiple CPUs, leveraging the computational power of supercomputers. The coupling of the PDE and ODE system, together with an appropriate redefinition of the depth function, proved to be a valuable method for studying fluid-structure interaction problems. The combination of efficient numerical techniques led to the development of a tool with a potential to be applied in the practice for the simulation of floating objects in wide domains.

Os métodos geofísicos constituem um conjunto de várias ferramentas de investigação, com características específicas e com aplicação, em especial, no estudo de áreas submersas, tendo em vista a inacessibilidade as estes ambientes pelos métodos convencionais. Entretanto, sua aplicação nem sempre traz os resultados esperados e assim, o objetivo principal deste estudo é discutir e avaliar a aplicabilidade dos métodos geofísicos, com ênfase nos métodos sísmicos, em estudos de áreas submersas rasas: plataforma continental interna, áreas costeiras, rios, lagos e reservatórios. O estabelecimento de critérios que auxiliem a escolha do método geofísico mais adequado para a melhor solução ao problema geológico ou geotécnico colocado, visa, entre outros aspectos, contribuir para a mitigação dos problemas, principalmente ambientais, causados pela atividade antrópica concentrada nestes ambientes e ampliar o conhecimento geológico básico, propiciando deste modo intervenções sustentadas nestes complexos ambientes. / Geophysical methods consist of a series of investigation tools with specific features that are critical to the study of water-covered areas, since these environments cannot be reached with conventional methods. However, sometimes these applications fail to provide the expected results. The objective of this study is to discuss and assess the applicability of geophysical methods by focusing on seismic methods in studies conducted in shallow water-covered areas: inner continental shelves, coastal areas, rivers, lakes and reservoirs. Criteria to help to select the most appropriate geophysical method to solve geological or geotechnical issues must be established to minimize problems, particularly environmental problems caused by concentrated anthropic activity, and to expand basic geological knowledge to allow for sustained interventions in these complex environments. This study is based on extensive bibliographic research and on several projects developed by IPT (Institute for Technological Research of São Paulo State) and by IOUSP (Oceanography Institute of the University of São Paulo), in addition to partnerships with private companies and other institutes in Brazil that address this field of knowledge. The focus on shallow waters was driven by the lack of systematic data and the demand for geological and geotechnical knowledge in these areas, due to the concentration, in these sectors, of the main economic activities of our current society: projects to build or reassess port dimensions, installation of moles, ducts, marinas, bridges, tunnels, fishing activities, beach regeneration, mineral prospecting, waterways, dredging, installation of reservoirs for water storage or flood containment, and reservoir silting. In any of these topics, basic geological knowledge of the bottom and subbottom of water-covered areas is essential to ensure the venture’s success. Considering this, geophysical methods, particularly seismic ones, are investigation tools that effectively contribute to generate new information, and are the only set of tools available to quickly and objectively provide enough data to improve the geological understanding of the area under investigation. The result of this study includes a discussion on the feasibility of the methodologies recommended, based on an extensive survey conducted in 2005/2006 on the availability of geophysical equipment in research institutes and private companies in Brazil.

Ce travail s'inscrit dans l'étude mathématique d'écoulements de fluides environnementaux. Nous en abordons deux aspects, à travers deux contextes distincts d'application.En lien avec la simulation des écoulements en milieux poreux, on s'intéresse dans une première partie à la discrétisation d'opérateurs de diffusion anisotropes hétérogènes par des méthodes de volumes finis sur des maillages généraux. Dans le but d'obtenir des solutions approchées qui respectent les bornes physiques des modèles, notre attention se porte sur la conservation du principe du maximum pour les opérateurs elliptiques. Nous présentons des mécanismes généraux permettant de corriger tout schéma volumes finis afin de garantir un principe du maximum discret tout en préservant certaines de ses propriétés principales. On étudie en particulier les propriétés de coercivité et de convergence des schémas corrigés.La deuxième partie est consacrée à la construction de modèles approchés pour la propagation des vagues en eaux peu profondes et sur des topographies irrégulières. A cet effet, nous proposons tout d'abord une adaptation de la démarche d'étude classique à des écoulements bidimensionnels sur des topographies polygonales. Dans un cadre plus général, nous développons ensuite une démarche formelle qui débouche sur des alternatives non locales à quelques modèles classiques (équations de Saint-Venant, équations de Serre, système de Boussinesq). Ces nouveaux modèles contiennent des termes régularisants pour les contributions du fond. / This work investigates two research questions associated with environmental flows and their mathematical modeling.The first part is devoted to the development of finite volume methods for anisotropic and heterogeneous diffusion operators arising in models of porous media flows. To ensure that the approximate solutions lie within physical bounds, we aim at maintaining a discrete analogous of the maximum principle for elliptic operators. Starting from any given cell-centered finite volume scheme, we present a general approach to devise non-linear corrections providing a discrete maximum principle while retaining some main properties of the scheme. In particular, we study the coercivity and convergence properties of the modified schemes.The second part of this work focuses on the derivation of approximate models for shallow water wave propagation over rough topographies. In the particular case of one-dimensional polygonal bottom profiles, we first propose an adaptation of the usual derivation method using complex analysis tools. We then develop a formal approach to account for more general topographies. We propose nonlocal alternatives to some classical models (namely Saint-Venant equations, Serre equations and Boussinesq system). All these alternative models only involve smoothing contributions of the bottom.

Due to the low amount or unfavorable annual distribution of precipitation the exploration, allocation, sustainable exploitation, and protection of replenishable as well as fossile water resources are challanging tasks in semiarid and arid regions. Beside a few natural or artifcial surface water reservoirs the porous underground at the same time is the largest storage and transport medium for water and provides protection against evaporation and to a certain degree against surcficial introduction of contaminants. This situation is characteristic for the Near East and thus for the selected investigation areas, that are located in Israel and the West Bank, and that are subject of the conducted partail studies that are presented. The work focuses on three main subjects. On the one hand, it deals with the characterization of the young groundwater components of the discharge of four major springs of Wadi Qilt and Jericho, as well as of sampled deep wells of three important well fields. All of these objects discharge or abstract water from the Upper and Lower Judea Group Aquifer. With a thickness of about 750 m it is one of the most important groundwater reservoirs of the region and comprises mainly to varying degrees karstified and fractured limestones and dolomites. These formations underwent uplift during Senonian to Eocenian times forming a pair of double-plunging anticlinal structures (Hebron and Ramallah or Judea and Samaria Mountains, respectively) that are again subdivided into minor anticlines and synclines. The groundwater replenishment is restricted to the winter season between October and April, and to the crestal area of the mountains, where the otherwise covered aquifer rocks crop out. A strategy was developed to interpret the applied tracers for all locations in a similar way using a lumped parameter approach, which enables a direct comparison. On the other hand, the work investigates salinization processes in the Shallow Aquifer of Jericho and their discrimination. Potential sources for salinization are remnant brines that are activated to flow into the range of well extraction due to groundwater overexploitation, dissolution of salts, or formation waters from the Lisan formation. These layers represent the sediments of Lake Lisan, the Pleistocene precursor of the Dead Sea. A discrimination of the salinization mechanisms is important to develope reasonable measures to limit or lower the salt concentration in the affected wells. Consequently, the relevant measured but also potential main hydrochemical indicators and isotope tracers are identified. The large uncertainties with respect to the establishment of a well-founded water balance and to the insuffcient knowledge about the geology of the small-scale area of Jericho are discussed. Because the interpretation of the measured helium samples from the fractured and karstified aquifer of the Cretaceous Judea Group is limited, the dependencies of the He-4 accumulation in groundwater in an idealized dual-continuum aquifer are investigated with respect to the relation of the He-4 mass fluxes and the system response time to the varied parameters (groundwater head gradient, hydraulic conductivities, dispersivities, porosities) by means of a sensitivity analysis. Although the system response time is not a system variable as such it clearly turned out that knowledge about it may be an important information for the interpretation of He concentrations in groundwaters of non-stationary systems. To enhance the visual post-processing of the parameter sensitivity analysis an easily interpretable way of data presentation is introduced. / Semiaride und aride Gebiete stellen aufgrund des niedrigen oder ungünstig verteilten Niederschlagsdargebots eine besondere Herausforderung bezüglich Erkundung, Bereitstellung, nachhaltiger Nutzung und Schutz sich neu bildender, aber auch fossiler Wasserresourcen dar. Abgesehen von wenigen natürlichen oder künstlich angelegten Oberflächenreservoiren ist der poröse Untergrund dabei gleichzeitig Hauptspeicher und Transportmedium für Wasser und bietet einen Schutz gegen Verdunstung und bis zu einem gewissen Grade gegen oberflächig einwirkende Verunreinigungen. Diese Situation ist charakteristisch für den Nahen Osten und damit für die im Rahmen der vorliegenden Arbeit beschriebenen Teiluntersuchungsgebiete, die sich in Israel und der West Bank befinden. Die Arbeit behandelt drei Hauptthemen. Einerseits geht sie auf die Charakterisierung der Jungwasseranteile im Abfluß vier bedeutender Quellen des Wadi Qilts und Jerichos sowie in beprobten tiefen Brunnen dreier wichtiger Brunnenfelder ein. Alle diese Objekte entwässern bzw. entnehmen Wasser aus dem Oberen oder Unteren Judea Group Aquifer. Mit ca. 750 m Mächtigkeit stellt dieser eines der bedeutensten Grundwasserreservoire der Region dar und besteht hauptsächlich aus unterschiedlich stark verkarsteten und gestörten Kalkstein- und Dolomitformationen, welche zwischen dem Senon und Eozän in Form einer in sich weiter gegliederten, beid-seitig abtauchenden Doppelantiklinalstruktur herausgehoben wurde (Hebron und Ramallah bzw. Judea und Samaria Mountains). Die Grundwasserneubildung ist beschränkt auf die Zeit zwischen Oktober und April sowie auf die Kammlagen des Gebirges, wo die sonst bedeckten Schichten des Aquifers ausstreichen. Es wurde eine Strategie entwickelt, die eingesetzten Tracer auf ähnliche Weise mit Hilfe von Lumped Parameter-Modellen für alle Lokationen zu interpretieren und somit eine Vergleichbarkeit zu gewährleisten. Andererseits untersucht die Arbeit Versalzungsprozesse im Shallow Aquifer von Jericho und deren Abgrenzung untereinander. Mögliche Hauptquellen der Versalzung sind durch überhöhte Grundwasserentnahme verstärke Zuflüsse von Solen, die Lösung von Salzen aus der Lisan-Formation oder Formationswässer der Lisan-Formation, welche die Ablagerungen des Lisan-Sees, des Pleistozänen Vorgängers des heutigen Toten Meeres, repräsentieren. Eine Unterscheidung der Mechanismen hat dabei durchaus Bedeutung für die Festlegung geeigneter Gegenmaßnahmen. Demzufolge werden die ermittelten, aber auch weitere, potentielle hydrochemische Hauptindikatoren und Tracer benannt. Unsicherheiten sowohl hinsichtlich der Aufstellung einer Wasserbilanz, als auch einer unzureichend bekannten Geologie für das sehr kleinräumige Gebiet von Jericho werden diskutiert.

This thesis investigates shallow gas hazards in Queen Charlotte Basin, a sedimentary basin situated offshore British Columbia. The work presented here provides the first detailed gas hazard assessment in Queen Charlotte Basin and the first evidence that gas has migrated from basin sediments into surficial sediments to be expelled in the water column. A unique method of geophysical surveying is used to investigate hazards due to shallow gas at two sites within Queen Charlotte Basin: high-resolution multichannel seismic, Huntec Deep-Towed Seismic and multibeam bathymetry data were collected over two 2-D grids and interpreted concurrently to yield a comprehensive understanding of the geology at each site. Numerous features related to both ice-cover and shallow gas has been identified. Pockmarks, iceberg ploughmarks and seafloor mounds are observed in the multibeam data; acoustically turbid and vertical blank zones are imaged in the Huntec data and faulted anticlines containing bright spots as well as low frequency shadow zones are seen in the multichannel data. Combining and interpreting all three geophysical datasets concurrently provided the means to discriminate features related to ice-cover from features related to gas in the shallow sediments. In addition, this method of geohazards assessment has enabled links between surficial and basin geology to be made. Based on the results obtained gas and other geohazards were identified at each of the two sites. Based on observations in high-resolution multichannel seismic data, gas is determined to have migrated along structural pathways within basin sediments and into surficial sediments. The level of hazard posed by shallow gas has been assessed qualitatively for each of the two study sites and gas hazard regions have been identified elsewhere in Queen Charlotte Basin.

Les courants turbulents de bord ouest sont l'un des phénomènes les plus dominants des océans, il en existe aux faibles latitudes aussi. Ils sont caractérisés par une dynamique très turbulente avec une forte production d'énergie cinétique, et une forte variabilité interne. Plusieurs régions existent où les courants de bord ouest se rétrofléchissent (décollage de la côte) pour former des structures cohérentes: des anticyclones, des bursts (arrachements) et des dipoles. Circulant le long de la côte, les courants de bord ouest interagissent très fortement avec le bord ouest et la bathymétrie et sont donc un problème de couche limite. Cependant aucune étude du point de vue de la théorie de couche limite n'a été jamais été faite. Cette thèse aborde le problème d'un point de vue de couche limite par l'utilisation d'un modèle idéalisé "shallow water" à très haute résolution (2.5km) afin d'isoler et de comprendre les processus. Les résultats sont ensuite appliqués à des sorties de modèle réaliste Drakkar (~10km) basé sur le code NEMO. Le courant de Somali est ensuite pris pour cette application. / Strong western boundary currents are one of dominant features of the world oceans, also at low latitudes. They exhibit a turbulent dynamics and their region is a source of strong kinetic energy production and internal variability of the worlds oceans. Several places exists where the western boundary currents retrofect (i.e separation from the coast) and generate coherent structures as anticyclonic eddies, bursts and dipoles. The dynamics of turbulent western boundary currents has so far not been extensively studied in the viewpoint of turbulent boundary-layer theory. The approach followed in this thesis is to use a fine resolution (2.5km) reduced-gravity shallow water model to understand the turbulent boundary-layer processes and then apply these findings to the Ocean General Circulation Model NEMO in the Drakkar configuration (~10km). The case of the Somali Currentis considered for this application.