<p>Directional wave-field decomposition for heterogeneousanisotropic media with in-stantaneous response is establishedfor both the acoustic and the electromagnetic equations.</p><p>We derive a sufficient condition for ellipticity of thesystem's matrix in the Laplace domain and show that theconstruction of the splitting matrix via a Dunford-Taylorintegral over the resolvent of the non-compact, non-normalsystem's matrix is well de ned. The splitting matrix also hasproperties that make it possible to construct the decompositionwith a generalized eigenvector procedure. The classical way ofobtaining the decomposition is equivalent to solving analgebraic Riccati operator equation. Hence the proceduredescribed above also provides a solution to the algebraicRiccati operator equation.</p><p>The solution to the wave-field decomposition for theisotropic wave equation is expressed in terms of theDirichlet-to-Neumann map for a plane. The equivalence of thisDirichlet-to-Neumann map is the acoustic admittance, i.e. themapping between the pressure and the particle velocity. Theacoustic admittance, as well as the related impedance aresolutions to algebraic Riccati operator equations and are keyelements in the decomposition. In the electromagnetic case thecorresponding impedance and admittance mappings solve therespective algebraic Riccati operator equations and henceprovide solutions to the decomposition problem.</p><p>The present research shows that it is advantageous toutilize the freedom implied by the generalized eigenvectorprocedure to obtain the solution to the decomposition problemin more general terms than the admittance/impedancemappings.</p><p>The time-reversal approach to steer an acoustic wave eld inthe cavity and half space geometries are analyzed from aboundary control perspective. For the cavity it is shown thatwe can steer the field to a desired final configuration, withthe assumption of local energy decay. It is also shown that thetime-reversal algorithm minimizes a least square error forfinite times when the data are obtained by measurements. Forthe half space geometry, the boundary condition is expressedwith help of the wave-field decomposition. In the homogeneousmaterial case, the response of the time-reversal algorithm iscalculated analytically. This procedure uses the one-wayequations together with the decomposition operator.</p>

Cette thèse porte sur le couplage chimie-transport pour la modélisation et la simulation du stockage géologique de CO2. Nous présentons un modèle d'écoulement multiphasique et un modèle géochimique permettant de décrire un modèle couplé d'écoulement multiphasique réactif. Nous proposons ensuite deux méthodes de résolution, l'une est une méthode globale, l'autre est une méthode de splitting utilisée à l'IFP dans le logiciel COORES. Le splitting effectué pour cette méthode repose sur des hypothèses physiques. La méthode de couplage utilisée est une méthode de couplage non itérative dans laquelle l'erreur de splitting est corrigée à l'aide d'un terme de pénalisation. Une étude de convergence sur un cas simplifié permet de montrer que le schéma pénalisé est convergent vers la même solution que le schéma global. Une partie de cette thèse est consacrée à l'étude des phénomènes de diffusion-dispersion. On s'intéresse particulièrement à ce terme car il ne peut être intégré facilement dans un schéma de splitting si l'on souhaite résoudre le modèle de transport réactif de façon locale (nécessaire pour l'utilisation de sous-pas de temps locaux). Après avoir mis en évidence l'importance de ce terme sur un cas test représentatif, nous montrons la difficulté de l'intégrer dans le schéma de splitting. Finalement, on étudie un problème d'écoulement miscible en 1D d'un point de vue mathématique. Les difficultés proviennent de la non linéarité due à la solubilité non nulle du gaz dans l'eau. Nous proposons une définition d'une solution faible pour ce problème dont l'existence est montrée à l'aide de la convergence d'un schéma volumes finis de type Godunov.

In dieser Arbeit wird das asymptotische Verhalten der Approximationszahlen für Operatorfolgen aus einer speziellen Klasse von Banachalgebren untersucht. Es werden bemerkenswerte Eigenschaften der Folgen und der Approximationszahlen ihrer Operatoren gezeigt, darunter die so genannte splitting-Eigenschaft. Ein typisches Beispiel solcher Operatorfolgen stellen die Finite Sections von Toeplitzoperatoren dar, die exemplarisch behandelt werden. Dabei werden hier auch die Folgenräume l1 und l-unendlich betrachtet.

In this thesis we investigate experimentally certain aspects of the interaction of terahertz (THz) radiation with intersubband transitions and excitonic transitions in semiconductor quantum wells. The first part deals with a more fundamental view on an intersubband transition in a symmetric, undoped GaAs/AlGaAs multiple quantum well. After optical excitation of carriers, the considered electronic conduction intersubband transition is probed in the low-intensity linear regime using broadband THz pulses. These pulses are detected via field-resolved electro-optic sampling. While the sample’s terahertz absorption shows the expected single peak of the resonant intersubband transition, the differential transmission spectra, i.e. the photoexcitation-induced changes in transmission, display strong Fano signatures. On the basis of a microscopic theory, we show that they originate from a phase sensitive superposition of THz current and ponderomotive current. The latter one results from the wiggling motion of carriers induced by the accelerating THz field. Our findings demonstrate for the first time that the ponderomotive contribution has to be taken into account also at the lowest THz intensities. The following issues consider the interaction with THz pulses of higher intensity from the free-electron laser (FEL) of the Forschungszentrum Dresden-Rossendorf. In one experiment we investigate efficient second order sideband generation in the GaAs/AlGaAs multiple quantum well mentioned above. To this end a near-infrared laser tuned to excitonic interband transitions is mixed inside the sample with the inplane polarized FEL beam to create the sum- and difference-frequencies between them. We compare the sideband efficiencies for the THz beam tuned to the interexcitonic heavy-hole light-hole transition and to the intraexcitonic heavy-hole 1s-2p transition. In the latter case we achieve a ten times higher n=+2 low-temperature efficiency around 0.1%. This value is comparable to previous studies in the literature, but our approach involves different transitions in a much simpler geometry. At room temperature the efficiency drops only by a factor of 7 for low THz powers. The last part of this thesis addresses another fundamental quantum-mechanical phenomenon: the splitting of an absorption line in a strong THz field. In the same abovementioned quantum well sample the FEL wavelength is tuned near the intraexcitonic 1s-2p heavy-hole transition. The THz radiation induces a power-dependent splitting of the heavy-hole 1s exciton absorption line which manifests itself in the transmitted spectrum of a broadband near-infrared probe beam. The FEL-wavelength-dependent strength of this so-called Autler-Townes splitting is discussed on the basis of a simple two-level model.

Carbon based materials, including porous carbons and carbon layer composites, are finding increased usage in latest environmental and energy related research. Among porous carbon materials, hierarchical porous carbons with multi-modal porosity are proving out to be an effective solution for applications where the traditional activated carbons fail. Thus, there has been a lot of recent interest in developing low-cost, facile, easy to scale-up, synthesis techniques for producing such multi-modal porous carbons. This dissertation offers two novel synthesis techniques: (i) ice templating integrated with hard templating, and (ii) salt templating coupled with hard templating, for producing such hierarchically porous carbons. The techniques offer tight control and tunability of porosity (macro- meso- and microscale) in terms of both size and extent. The synthesized multi-modal porous carbons are shown to be an effective solution for three important environment related applications – (i) Carbon dioxide capture using amine supported hierarchical porous carbons, (ii) Reduction in irreversible fouling of membranes used for wastewater reuse through a deposition of a layer of hierarchical porous carbons on the membrane surface, (iii) Electrode materials for electrosorptive applications. Finally, because of their tunability, the synthesized multi-modal porous carbons serve as excellent model systems for understanding the effect of different types of porosity on the performance of porous carbons for these applications. Also, recently, there has been a lot of interest in developing protective layer coatings for preventing photo-corrosion of semiconductor structures (in particular Cu2O) used for photoelectrochemical water splitting. Most of the developed protective strategies to date involve the use of metals or co-catalyst in the protective layer. Thus there is a big need for developing low-cost, facile and easy to scale protective coating strategies. Based on the expertise gained in synthesizing porous carbon materials, and owing to our group’s interest in developing suitable photoelectrode materials, this dissertation also proposes a novel carbon-Cu2O composite comprising of a carbon layer coated Cu2O nanowire array structure as a high performance and stable photoelectrode material for photoelectrochemical water splitting.

Solar energy is the most abundant source of renewable energy available. The relatively high cost prevents solar photovoltaic (PV) from replacing fossil fuel on a larger scale. In solar PV power generation the cost is reduced with more efficient PV technologies. In this dissertation, methods to improve PV conversion efficiency with holographic optical components are discussed. The tandem multiple-junction approach has achieved very high conversion efficiency. However it is impossible to manufacture tandem PV cells at a low cost due to stringent fabrication standards and limited material types that satisfy lattice compatibility. Current produced by the tandem multi-junction PV cell is limited by the lowest junction due to series connection. Spectrum-splitting is a lateral multi-junction concept that is free of lattice and current matching constraints. Each PV cell can be optimized towards full absorption of a spectral band with tailored light-trapping schemes. Holographic optical components are designed to achieve spectrum-splitting PV energy conversion. The incident solar spectrum is separated onto multiple PV cells that are matched to the corresponding spectral band. Holographic spectrum-splitting can take advantage of existing and future low-cost technologies that produces high efficiency thin-film solar cells. Spectrum-splitting optical systems are designed and analyzed with both transmission and reflection holographic optical components. Prototype holograms are fabricated and high optical efficiency is achieved. Light-trapping in PV cells increases the effective optical path-length in the semiconductor material leading to improved absorption and conversion efficiency. It has been shown that the effective optical path length can be increased by a factor of 4n2 using diffusive surfaces. Ultra-light-trapping can be achieved with optical filters that limit the escape angle of the diffused light. Holographic reflection gratings have been shown to act as angle-wavelength selective filters that can function as ultra-light-trapping filters. Results from an experimental reflection hologram are used to model the absorption enhancement factor for a silicon solar cell and light-trapping filter. The result shows a significant improvement in current generation for thin-film silicon solar cells under typical operating conditions.

During the past few years there has been a significant interest in spectrum splitting systems to increase the overall efficiency of photovoltaic solar energy systems. However, methods for comparing the performance of spectrum splitting systems and the effects of optical spectral filter design on system performance are not well developed. This dissertation first establishes a method to analyze and compare spectrum splitting systems with different filters, PV cells types and geometries. The method examines the system conversion efficiency in detail and the role of optical spectral filters. A new metric termed the Improvement over Best Bandgap is defined which expresses the efficiency gain of the spectrum splitting system with respect to a similar system that contains the highest constituent single bandgap photovoltaic cell. Also, this work expands the analysis on dispersive spectrum splitting systems. The dispersive effects of transmission type filters are evaluated using a cross-correlation analysis. Lastly, this work presents a grating-over-lens design for dispersive spectrum splitting. In this geometry, a transmission grating is placed at the entrance of a lens. Part of the incident solar spectrum is diffracted off-axis from normal incidence to the lens. The diffracted spectral range comes to a focus at an off-axis point and the undiffracted spectrum comes to a focus at the paraxial focus of the lens. Since the diffracted wave is planar and off-axis, the off-axis focal points suffer from aberrations that increase system loss. In this work, a novel aberration compensation technique is presented using non-planar transmission gratings recorded using a conjugate object beam to modify the off-axis wavefront. Diverging sources are used as conjugate object and reference beams. The spherical waves are incident at the lens and the grating is recorded at the entrance aperture of the solar concentrator. The on-axis source is adjusted to produce an on-axis planar wavefront at the hologram plane. The off-axis source is approximated to a diffraction limited spot producing a non-planar off-axis wavefront on the hologram plane. Illumination with a planar AM1.5 spectrum reproduces an off-axis diffraction-limited spot on the focal plane. Models and experimental data are presented to quantify the reduction in losses achieved with aberration correction.

An initial-value problem consists of an ordinary differential equation subject to an initial condition. The right-hand side of the differential equation can be interpreted as additively split when it is comprised of the sum of two or more contributing factors. For instance, the right-hand sides of initial-value problems derived from advection-diffusion-reaction equations are comprised of the sum of terms emanating from three distinct physical processes: advection, diffusion, and reaction. In some cases, solutions to initial-value problems can be calculated analytically, but when an analytic solution is unknown or nonexistent, methods of numerical integration are used to calculate solutions. The runtime performance of numerical methods is problem dependent; therefore, one must choose an appropriate numerical method to achieve favourable performance, according to characteristics of the problem. Additive methods of numerical integration apply distinct methods to the distinct contributing factors of an additively split problem. Treating the contributing factors with methods that are known to perform well on them individually has the potential to yield an additive method that outperforms single methods applied to the entire (unsplit) problem. Splittings of the right-hand side can be physics-based, i.e., based on physical characteristics of the problem, such as advection, diffusion, or reaction terms. Splittings can also be based on linearization, called Jacobian splitting in this thesis, where the linearized part of the problem is treated with one method and the rest of the problem is treated with another. A comparison of these splitting techniques is performed by applying a set of additive methods to a test suite of problems. Many common non-additive methods are also included to serve as a performance baseline. To perform this numerical study, a problem-solving environment was developed to evaluate permutations of problems, methods, and their associated parameters. The test suite is comprised of several distinct advection-diffusion-reaction equations that have been chosen to represent a wide range of common problem characteristics. When solving split problems in the test suite, it is found that additive Runge–Kutta methods of orders three, four, and five using Jacobian splitting generally outperform those same methods using physics-based splitting. These results provide evidence that Jacobian splitting is an effective approach when solving such initial-value problems in practice.

The increasing demand for energy and the pressure to reduce reliance on fossil fuels encourages the development of devices to harness clean and renewable energy. Solar energy is a large enough source to fulfill these demands, however, in order to overcome its daily and seasonal variability, it has been proposed that sunlight be harvested and stored in the form of chemical fuels. One potential approach is the photosynthetic splitting of water to store solar energy in the simplest chemical bond, H–H, using a device that includes: semiconducting microwire arrays as light harvesting components, redox catalysts, and a membrane barrier for separating the products of water redox reactions.. However, the harvested solar energy can be lost across the system and it is critical to characterize the electrical properties of each component within the system to quantify how much of this energy will ultimately be coupled to the water splitting reactions. The aim of this research is to develop approaches for characterization of a proposed system of this kind, incorporating individual semiconductor microwires as photoelectrodes (with no redox catalysts) embedded into a candidate conducting polymer membrane to form a single functional unit. Semiconductor microwires were isolated and using a novel contact formation approach with tungsten probes in a standard probe station, and their current versus voltage properties were characterized. This approach is of particular interest when ii considering the limitations of conventional contact formation approaches (e.g. thermal evaporation of contact metals), arising from the small dimensions of the microwires and also the incompatibility of these techniques with many microwire/polymer structures due to the unwanted interactions between polymers, photoresists, etchants and the high temperature lithographic processes. The electrical properties of different microwires and also the junctions between microwires and two candidate polymers were studied. Specifically, the combination of methyl-terminated silicon microwires and PEDOT:PSS:Nafion demonstrated promising behavior, with a total DC resistance of approximately 720 kΩ (i.e. losses < 16 mV at maximum available photocurrent), making it a suitable candidate for the use in the proposed system. The outcome of these research may be applied to many applications including semiconducting microstructures and conducting polymers.

The Forsmark area, the main study area in this thesis, is located about 140 km north of Stockholm, central Sweden. It belongs to the Paleoproterozoic Svecokarelian orogen and contains several major ductile and brittle deformation zones including the Forsmark, Eckarfjärden and Singö zones. The bedrock between these zones, in general is less deformed and considered suitable for a nuclear waste repository. While several site investigations have already been carried out in the area, this thesis focuses primarily on (i) re-processing some of the existing reflection seismic lines to improve imaging of deeper structures, (ii) acquiring and processing high-resolution reflection and refraction data for better characterization of the near surface geology for the planning of a new access ramp, (iii) studying possible seismic anisotropy from active sources recorded onto sparse three-component receivers and multi-offset-azimuth vertical seismic profiling data (VSP). Reflection seismic surveys are an important component of these investigations. The re-processing helped in improving the deeper parts (1-5 km) of the seismic images and allowing three major deeper reflections to be better characterized, one of which is sub-horizontal while the other two are dipping moderately. These reflections were attributed to originate from either dolerite sills or brittle fault systems. First break traveltime tomography allowed delineating an undulating bedrock-surface topography, which is typical in the Forsmark area. Shallow reflections imaged in 3D, thanks to the acquisition design were compared with existing borehole data and explained by fractured or weak zones in the bedrock. The analysis of seismic anisotropy indicates the presence of shear-wave splitting due to transverse isotropy with a vertical symmetry axis in the uppermost hundreds of meters of crust. Open fractures and joints were interpreted to be responsible for the large delays observed between the transverse and radial components of the shear-wave arrivals, both on surface and VSP data.