Diese Doktorarbeit behandelt die bosonische Einbettung der geeichten N = 8 Supergravitation in elf Dimensionen. Die höher dimensionalen Felder müssen zuerst nichtlinear umdefiniert werden, sodass ihre supersymmetrischen Transformationen mit denen der vierdimensionalen Felder verglichen werden können. So wurden in der Literatur nichtlineare Beziehungen zwischen den neu definierten elfdimensionalen Feldern und den Feldern der N = 8 Supergravitation gefunden. Darauf basierend können nun direkte Ansätze gefunden werden, die eine vierdimensionale in eine elfdimensionale Lösung der Supergravitation einbetten. Die Arbeit präsentiert alle Ansätze für die skalaren internen Felder. Zuerst werden die schon bekannten Einbettungsformeln für die inverse Metrik, das Dreiform-Potential mit gemischter Indexstruktur sowie das Sechsform-Potential zusammengefasst. Danach werden neue Ansätze für die explizite interne Metrik, das vollständige Dreiform-Potential, den Warp Faktor, die Vierform Feldstärke sowie den Freund-Rubin Faktor gefunden. Die Einbettung der Vektorbosonen hängt dann nur von den skalaren Feldern ab. Der zweite Teil der Arbeit benutzt die gefundenen Einbettungsformeln, um gruppeninvariante Lösungen der elfdimensionalen Supergravitation zu finden. In solchen Fällen hängen die höherdimensionalen Felder ausschließlich von speziellen gruppeninvarianten Tensoren ab, die auf die jeweilige interne Geometrie angepasst sind. Als Beispiel wird zuerst die schon bekannte Einbettung der G2 invarianten Supergravitation zusammengefasst. Dann wird eine neue SO(3)×SO(3) invariante Löung der elfdimensionalen Supergravitation gefunden. Schließlich wird die Konsistenz der gefundenen Lösungen für eine maximal symmetrische Raumzeit überprüft. Die Ergebnisse können auf andere Kompaktifizierungen verallgemeinert werden, z.B. auf die nichtkompakten CSO(p,q,r) Eichungen oder auf die Reduzierung der Typ IIB Supergravitation zu fünf Dimensionen. / This thesis presents the complete embedding of the bosonic section of gauged N = 8 supergravity into 11 dimensions. The fields of 11-dimensional supergravity are reformulated in a non-linear way, such that their supersymmetry transformations can be compared to the four-dimensional ones. In this way, non-linear relations between the redefined higher-dimensional fields and the fields of N = 8 supergravity were already found in the literature. This is the basis for finding direct uplift Ansätze for the bosonic fields of 11-dimensional supergravity in terms of the four-dimensional ones. This work gives the scalar Ans¨atze for the internal fields. First, the well known uplift formulae for the inverse metric, the three-form potential with mixed index structure and the six-form potential are summarized. Secondly, new embedding formulae for the explicit internal metric, the full three-form potential and the warp factor are presented. Additionally, two subsequent non-linear Ansätze for the full internal four-form field strength and the Freund-Rubin term are found. Finally, the vector uplift can simply be found in terms of the obtained scalar fields. The second part of this thesis uses the obtained embedding formulae in order to construct group invariant solutions of 11-dimensional supergravity. In such cases, the higher-dimensional fields can be written solely in terms of certain group invariant tensors that are adapted to the particular geometry of the internal space. Two such examples are discussed in detail. The first one is the well-known uplift of G2 gauged supergravity. Furthermore, a new SO(3)×SO(3) invariant solution of 11-dimensional supergravity is found. In particular, the consistency of both solutions is explicitly checked for a maximally symmetric spacetime. The results may be generalized to other compactifications, e.g. the non-compact CSO(p, q, r) gaugings or the reduction from type IIB supergravity to five dimensions.

<p>The elastic constants of Mg_(1-x)Al_xB₂ have been calculated in the regime 0<x<0.25. The calculations show that the ratio, B/G, between the bulk- and the shear-modulus stays well below the empirical ductility limit, 1.75, for all concentrations, indicating that the introduction of Al will not change the brittle behaviour of the material considerably. Furthermore, the tetragonal elastic constant C’ has been calculated for the transition metal alloys Fe-Co, Mo-Tc and W-Re, showing that if a suitable tuning of the alloying is made, these materials have a vanishingly low C'. Thermal expansion calculations of the 4d transition metals have also been performed, showing good agreement with experiment with the exception of Nb and Mo. The calculated phonon dispersions of the 4d metals all give reasonable agreement with experiment. First principles calculations of the thermal expansion of hcp Ti have been performed, showing that this element has a negative thermal expansion along the c-axis which is linked to the closeness of the Fermi level to an electronic topological transition. Calculations of the EOS of fcc Au give support to the suggestion that the ruby pressure scale might underestimate pressures with ~10 GPa at pressures ~150 GPa. The high temperature bcc phase of the group IV metals has been calculated with the novel self-consistent ab-initio dynamical (SCAILD) method. The results show good agreement with experiment, and the free energy resolution of < 1 meV suggests that this method might be suitable for calculating free energy differences between different crystallographic phases as a function of temperature.</p>

The objectives of this dissertation were to find a principal domain of promising and technologically feasible reactor physics characteristics for a multi-purpose, modular-sized, lead-cooled, fast neutron spectrum reactor fueled with an advanced uranium-transuranic-nitride fuel and to determine the principal limitations for the design of an autonomous long-term multi-purpose fast reactor (ALM-FR) within the principal reactor physics characteristic domain. The objectives were accomplished by producing a conceptual design for an ALM-FR and by analysis of the potential ALM-FR performance characteristics. The ALM-FR design developed in this dissertation is based on the concept of a secure transportable autonomous reactor for hydrogen production (STAR-H2) and represents further refinement of the STAR-H2 concept towards an economical, proliferation-resistant, sustainable, multi-purpose nuclear energy system. The development of the ALM-FR design has been performed considering this reactor within the frame of the concept of a self-consistent nuclear energy system (SCNES) that satisfies virtually all of the requirements for future nuclear energy systems: efficient energy production, safety, self-feeding, non-proliferation, and radionuclide burning. The analysis takes into consideration a wide range of reactor design aspects including selection of technologically feasible fuels and structural materials, core configuration optimization, dynamics and safety of long-term operation on one fuel loading, and nuclear material non-proliferation. Plutonium and higher actinides are considered as essential components of an advanced fuel that maintains long-term operation. Flexibility of the ALM-FR with respect to fuel compositions is demonstrated acknowledging the principal limitations of the long-term burning of plutonium and higher actinides. To ensure consistency and accuracy, the modeling has been performed using state-of-the-art computer codes developed at Argonne National Laboratory. As a result of the computational analysis performed in this work, the ALM-FR design provides for the possibility of continuous operation during about 40 years on one fuel loading containing mixture of depleted uranium with plutonium and higher actinides. All reactor physics characteristics of the ALM-FR are kept within technological limits ensuring safety of ultra-long autonomous operation. The results obtained provide for identification of physical features of the ALM-FR that significantly influence flexibility of the design and its applications. The special emphasis is given to existing limitations on the utilization of higher actinides as a fuel component.

The elastic constants of Mg(1-x)AlxB2 have been calculated in the regime 0&lt;x&lt;0.25. The calculations show that the ratio, B/G, between the bulk- and the shear-modulus stays well below the empirical ductility limit, 1.75, for all concentrations, indicating that the introduction of Al will not change the brittle behaviour of the material considerably. Furthermore, the tetragonal elastic constant C’ has been calculated for the transition metal alloys Fe-Co, Mo-Tc and W-Re, showing that if a suitable tuning of the alloying is made, these materials have a vanishingly low C'. Thermal expansion calculations of the 4d transition metals have also been performed, showing good agreement with experiment with the exception of Nb and Mo. The calculated phonon dispersions of the 4d metals all give reasonable agreement with experiment. First principles calculations of the thermal expansion of hcp Ti have been performed, showing that this element has a negative thermal expansion along the c-axis which is linked to the closeness of the Fermi level to an electronic topological transition. Calculations of the EOS of fcc Au give support to the suggestion that the ruby pressure scale might underestimate pressures with ~10 GPa at pressures ~150 GPa. The high temperature bcc phase of the group IV metals has been calculated with the novel self-consistent ab-initio dynamical (SCAILD) method. The results show good agreement with experiment, and the free energy resolution of &lt; 1 meV suggests that this method might be suitable for calculating free energy differences between different crystallographic phases as a function of temperature.

The thesis investigates the elements of a consistent strategy for favorable acquisition and utilization of Flight Simulation Training Devices (FSTD), thus Full Flight Simulators (FFS) and Flight Training Devices (FTD). The primary purpose is to determine a knowledge-based strategy for the end-user, acquisition professional, aviation firms and institutions. Hence, it could be possible to shed a light for cooperative groups and main institutions of national innovation system involved in entrepreneurial and innovative efforts regarding complex technologies like FSTD. In the sample study, 114 pilots from varied sources were administered a questionnaire and their FFS and FTD perceptions were statistically tested regarding each &ldquo / technology&rsquo / s usefulness&rdquo / in four types of training. Another variable, each &ldquo / technology&rsquo / s ease of operation and use&rdquo / was also tested additionally via agent-based model whether it had any effect on technologies&rsquo / selection processes. It could be inferred that that aviation institutions and firms could acquire and utilize FTD as a complementary to both aircraft and FFS within a range of 30-60% depending upon type of the training. Moreover, FTD could be acquired and utilized as a substitute to FFS for Instrument Flight Training (IFT). The FTD&rsquo / s usefulness for IFT was rated as 67% by the military pilots. The research also asserts that the aviation institutions and firms as well as cooperative groups and organizations could favor the established strategy and policy during their FSTD related efforts at &ldquo / micro and meso-level&rdquo / . The final aim is to create a collaborative medium and a synergy for those agents.

Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in finance is developed, with application to asset allocation. The numerical scheme has the following properties: it is unconditionally stable; convergence to the viscosity solution is guaranteed; there are no restrictions on the underlying stochastic process; it can be easily extended to include features as needed such as uncertain volatility and transaction costs; and central differencing is used as much as possible so that use of a locally second order method is maximized. In this thesis, continuous time mean variance type strategies for dynamic asset allocation problems are studied. Three mean variance type strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic variation, are investigated. The numerical method can handle various constraints on the control policy. The following cases are studied: allowing bankruptcy (unconstrained case), no bankruptcy, and bounded control. In some special cases where analytic solutions are available, the numerical results agree with the analytic solutions. These three mean variance type strategies are compared. For the allowing bankruptcy case, analytic solutions exist for all strategies. However, when additional constraints are applied to the control policy, analytic solutions do not exist for all strategies. After realistic constraints are applied, the efficient frontiers for all three strategies are very similar. However, the investment policies are quite different. These results show that, in deciding which objective function is appropriate for a given economic problem, it is not sufficient to simply examine the efficient frontiers. Instead, the actual investment policies need to be studied in order to determine if a particular strategy is applicable to specific investment problem.

Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in finance is developed, with application to asset allocation. The numerical scheme has the following properties: it is unconditionally stable; convergence to the viscosity solution is guaranteed; there are no restrictions on the underlying stochastic process; it can be easily extended to include features as needed such as uncertain volatility and transaction costs; and central differencing is used as much as possible so that use of a locally second order method is maximized. In this thesis, continuous time mean variance type strategies for dynamic asset allocation problems are studied. Three mean variance type strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic variation, are investigated. The numerical method can handle various constraints on the control policy. The following cases are studied: allowing bankruptcy (unconstrained case), no bankruptcy, and bounded control. In some special cases where analytic solutions are available, the numerical results agree with the analytic solutions. These three mean variance type strategies are compared. For the allowing bankruptcy case, analytic solutions exist for all strategies. However, when additional constraints are applied to the control policy, analytic solutions do not exist for all strategies. After realistic constraints are applied, the efficient frontiers for all three strategies are very similar. However, the investment policies are quite different. These results show that, in deciding which objective function is appropriate for a given economic problem, it is not sufficient to simply examine the efficient frontiers. Instead, the actual investment policies need to be studied in order to determine if a particular strategy is applicable to specific investment problem.

Acoustic plane wave intearctions with a rough seabed with a continuously varying density and sound speed in a fluid-like sediment layer overlying an elastic basement is considered in this thesis. The acoustic properties in the sediment layer possess an exponential type of variation in density and one of the three classes of sound speed profiles, which are constant, k^2-linear, or inverse-square variations. Analytical solutions for the Helmholtz equation in the sediment layer, combined with a formulation based upon boundary perturbation theory, facilitate numerical implementation for the solution of coherent field. The coherent reflection coefficients corresponding to the aformentioned density and sound speed profiles for various frequencies, roughness parameters, basement stiffness, are numerically generated and analyzed. Physical interpretations are provided for various results. This simple model characterizes three important features of an realistic sea floor, including seabed roughness, sediment inhomogenieties, and basement shear property,%Two dimensions is considered in the seafloor environment and the random roughness is belong to one dimension space.% , therefore, provides a canonical model for the study of seabed acoustics. The variation of the acoustic properties takes such a form that it is not only geologically realistic, but also renders analytical solutions for the Helmholtz equation, thus facilitating the formulation of the problem. The computational algorithm for the spatial spectrum of the scattered field due to random seabed has been developed based upon a boundary perturbation method. %About scattering field, only one time reflection from the sediment is taked account of, because the higher numerical order is, the lower scattering energy exist.% The results have shown that, while the coherent field mainly depends upon the gross structure of the rough seabed represented by the RMS roughness, the scattered field heavily depends upon the details of the roughness structure specialized by the roughness power spectrum and the spatial correlation length of the rough surface. The dependence of the spatial spectrum on the sediment stratification is also carefully examined.

Past studies (primarily on steady state problems) that have compared the penalty and the velocity-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of one method over the other is dictated by which of the two is more efficient. In this work, we show that the penalty finite element method yields inaccurate solutions at large times on a class of transient problems, while the velocity-pressure formulation yields solutions that are in good agreement with the analytical solution. Numerical studies are conducted on various problems to compare these two formulations on the basis of rates of convergence, total number of equations to be solved and accuracy of results. We found that both formulations give almost the same rates of convergence in all problems, however the penalty formulation involves lesser number of equations than the velocity-pressure formulation due to implicit treatment of pressure field, and hence is more efficient. In some of the problems we have also compared a finite volume method with the penalty and velocity-pressure formulations on the basis of accuracy and computational cost.

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