Groundwater interactions at a regional scale are of great importance to characterize subsurface flow processes. Extensive researches have been conducted previously to determine the main factors controlling the regional implications on groundwater flux circulation. Groundwater circulation occurs due to variation in the groundwater table (hydraulic gradient) across the spatial scale. Previous research highlighted the correlation between groundwater table with both topography variation and the recharge from precipitation. This study aims to highlight the impact of these boundary conditions. Five catchments located across different regions of Sweden with different topographical, hydrological, and meteorological properties considered for this study: Bodalsån, Forsmarksån, Tullstorpsån, Sävaån, and Krycklan. Relevant data were collected and numerical models were set up in steady- state conditions for each of these catchments, using 3D Multiphysics COMSOL. Models were set up for both of the boundary conditions, using 10 m grid resolution.Groundwater flux profiles along the depth of the catchments were obtained as a result, in which significant differences were observed. This was associated predominantly with the difference in the nature of the topography, the slope and soil permeability in these regions. The data thus collected and the models so established have increased the understanding in these regions from a research perspective. / En ökad förståelse för hur grundvatten interagerar med ytvatten är av stor betydelse för att karakterisera underjordiska flödesprocesser. Omfattande undersökningar har tidigare genomförts för att bestämma de viktigaste faktorerna som styr de regionala konsekvenserna för cirkulationen av grundvattenflöde. Grundvattencirkulation uppstår på grund av variationer i grundvattentabellen (hydraulisk gradient) över den rumsliga skalan. Tidigare forskning belyste korrelationen mellan grundvattentabellen med både topografivariation och laddning från nederbörd. Denna studie syftar till att belysa effekterna av dessa gränsförhållanden. Fem avrinningsområden placerade över olika regioner i Sverige med olika topografiska, hydrologiska och meteorologiska egenskaper som beaktas för denna studie: Bodalsån, Forsmarksån, Tullstorpsån, Sävaån och Krycklan. Relevanta data samlades in och numeriska modeller sattes upp under steady-state-förhållanden för vart och ett av dessa avrinningsområden med användning av 3D Multiphysics COMSOL. Modeller konfigurerades för båda gränsförhållandena med 10 m nätupplösning. Grundvattenflödesprofiler längs avrinningsdjupet erhölls som resultat, där signifikanta skillnader observerades. Detta var främst förknippat med skillnaden i topografins natur och lutningen i dessa regioner. De data som samlats in och de så etablerade modellerna har ökat skapat en värdefull grund för vidare hydrologisk forskning i dessa regioner.

Combustion instabilities (thermo-acoustic pressure oscillations) have been recognised for some time as a problem limiting the development of low emissions (e.g., lean burn) gas turbine combustion systems, particularly for aviation propulsion applications. Recently, significant research efforts have been focused on acoustic damping for suppression of combustion instability. Most of this work has either been experimental or based on linear acoustic theory. The last 3-5 years has seen application of density based CFD methods to this problem, but no attempts to use pressure-based CFD methods which are much more commonly used in combustion predictions. The goal of the present work is therefore to develop a pressure-based CFD algorithm in order to predict accurately acoustic propagation and acoustic damping processes, as relevant to gas turbine combustors. The developed computational algorithm described in this thesis is based on the classical pressure-correction approach, which was modified to allow fluid density variation as a function of pressure in order to simulate acoustic phenomena, which are fundamentally compressible in nature. The fact that the overall flow Mach number of relevance was likely to be low ( mildly compressible flow) also influenced the chosen methodology. For accurate capture of acoustic wave propagation at minimum grid resolution and avoiding excessive numerical smearing/dispersion, a fifth order accurate Weighted Essentially Non-Oscillatory scheme (WENO) was introduced. Characteristic-based boundary conditions were incorporated to enable accurate representation of acoustic excitation (e.g. via a loudspeaker or siren) as well as enable precise evaluation of acoustic reflection and transmission coefficients. The new methodology was first validated against simple (1D and 2D) but well proven test cases for wave propagation and demonstrated low numerical diffusion/dispersion. The proper incorporation of Characteristic-based boundary conditions was validated by comparison against classical linear acoustic analysis of acoustic and entropy waves in quasi-1D variable area duct flows. The developed method was then applied to the prediction of experimental measurements of the acoustic absorption coefficient for a single round orifice flow. Excellent agreement with experimental data was obtained in both linear and non-linear regimes. Analysis of predicted flow fields both with and without bias flow showed that non-linear acoustic behavior occurred when flow reversal begins inside the orifice. Finally, the method was applied to study acoustic excitation of combustor external aerodynamics using a pre-diffuser/dump diffuser geometry previously studied experimentally at Loughborough University and showed the significance of boundary conditions and shear layer instability to produce a sustained pressure fluctuation in the external aerodynamics.

In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Kapranov-Zelevinsky hypergeometric systems. This proves the abelian case of a conjecture of Bullimore, Gaiotto, Dimofte, and Hilburn on the behavior of generic Dirichlet boundary conditions in 3d N=4 SUSY gauge theories.

The objective of this research was to evaluate the capabilities of ALEGRA, a Sandia National Labs hydrocode, and Forge3, a Transvalor S.A. product, to accurately model the Friction Stir Welding Process. ALEGRA and Forge3 are discussed in light of the inherent challenges of modeling Friction Stir Welding, and a rotational boundary condition is added to ALEGRA. Results are presented from Friction Stir Welding modeling outputs from both ALEGRA and Forge3. ALEGRA is shown to be incapable of modeling the Friction Stir Welding process, in large part due to its focus on shock propagation, which causes extremely small time steps. Forge3 is shown capable of modeling of the FSW plunge process in a transient manner, but overestimates the temperature profiles 90% to 100% in comparison to experimentally measured values. It appears that the adiabatic boundary condition is the source of much of the error. It is recommended that future work focus on improving estimates of the boundary conditions utilized in the Forge3 model.

Efficiency is one of the key issues in numerical simulation of large-scale problems with complex 3-D geometry. Traditional domain based methods, such as finite element methods, may not be suitable for these problems due to, for example, the complexity of mesh generation. The Boundary Element Method (BEM), based on boundary integral formulations (BIE), offers one possible solution to this issue by discretizing only the surface of the domain. However, to date, successful applications of the BEM are mostly limited to linear and continuum problems. The challenges in the extension of the BEM to nonlinear problems or problems with non-continuum boundary conditions (BC) include, but are not limited to, the lack of appropriate BIE and the difficulties in the treatment of the volume integrals that result from the nonlinear terms. In this thesis work, new approaches and techniques based on the BEM have been developed for 3-D nonlinear problems and Stokes problems with slip BC. For nonlinear problems, a major difficulty in applying the BEM is the treatment of the volume integrals in the BIE. An efficient approach, based on the precorrected-FFT technique, is developed to evaluate the volume integrals. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh to evaluate volume integrals. The cubes enclosing part of the boundary are partitioned using surface panels. No volume discretization of the interior cubes is necessary. This grid is also used to accelerate volume integration. Based on this approach, accelerated BEM solvers for non-homogeneous and nonlinear problems are developed and tested. Good agreement is achieved between simulation results and analytical results. Qualitative comparison is made with current approaches. Stokes problems with slip BC are of particular importance in micro gas flows such as those encountered in MEMS devices. An efficient approach based on the BEM combined with the precorrected-FFT technique has been proposed and various techniques have been developed to solve these problems. As the applications of the developed method, drag forces on oscillating objects immersed in an unbounded slip flow are calculated and validated with either analytic solutions or experimental results.

Photonic crystals have allowed unprecedented control of light and have allowed bringing new functionalities on chip. Photonic crystal waveguides (PCWs), which are linear defects in a photonic crystal, have unique features that distinguish these waveguides from other waveguides. The unique features include very large dispersion, existence of slow light, and the possibility of tailoring the dispersion properties for guiding light. In my research, I have overcome some of the challenges in using slow light in PCWs. In this work, I have demonstrated (i) high efficiency coupling of light into slow group velocity modes of a PCW, (ii) large bandwidth high transmission and low dispersion bends in PCWs, (iii) accurate modeling of pulse propagation in PCWs, (iv) high efficiency absorbing boundary conditions for dispersive slow group velocity modes of PCWs. To demonstrate the utility of slow light in designing high efficiency devices, I have demonstrated refractive index sensors using slow light in PCWs. In the end, a few high efficiency devices based on slow light in PCWs are mentioned. The remaining issues in the widespread use of PCW are also discussed in the last chapter.

The objective of this dissertation is to develop robust and accurate numerical methods for solving the compressible, non-linear Euler equations of gas dynamics in one and two space dimensions. In theory, solutions of the Euler equations can display various characteristics including shock waves, rarefaction waves and contact discontinuities. To capture these features correctly, highly accurate numerical schemes are designed. In this thesis, two different projects have been studied to show the accuracy and utility of these numerical schemes. Firstly, the compressible, non-linear Euler equations of gas dynamics in one space dimension are considered. Since the non-linear partial differential equations (PDEs) can develop discontinuities (shock waves), the numerical code is designed to obtain stable numerical solutions of the Euler equations in the presence of shocks. Discontinuous solutions are defined in a weak sense, which means that there are many different solutions of the initial value problems of PDEs. To choose the physically relevant solution among the others, the entropy condition was applied to the problem. This condition is then used to derive a bound on the solution in order to satisfy L2-stability. Also, it provides information on how to add an adequate amount of diffusion to smooth the numerical shock waves. Furthermore, numerical solutions are obtained using far-field and no penetration (wall) boundary conditions. Grid interfaces were also included in these numerical computations. Secondly, the two dimensional compressible, non-linear Euler equations are considered. These equations are used to obtain numerical solutions for compressible ow in a shock tube with a 90° circular bend for two channels of different curvatures. The cell centered finite volume numerical scheme is employed to achieve these numerical solutions. The accuracy of this numerical scheme is tested using two different methods. In the first method, manufactured solutions are used to the test the convergence rate of the code. Then, Sod's shock tube test case is implemented into the numerical code to show the correctness of the code in both ow directions. The numerical method is then used to obtain numerical solutions which are compared with experimental data available in the literature. It is found that the numerical solutions are in a good agreement with these experimental results.

In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21551号 / 理博第4458号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 准教授 藤 定義, 准教授 荒木 武昭 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22047号 / 工博第4628号 / 新制||工||1722(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 後藤 仁志, 教授 細田 尚, 准教授 KHAYYER,Abbas / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM