In theory, the existence of black holes is predicted by general relativity. In reality, there is a general consensus that they exist in space; in particular at the center of many galaxies. The theory of black holes has been around for decades, but there are still interesting questions calling for attention. This doctoral thesis and its four contributions touches upon some of these questions. One challenging theoretical aspect of black holes lies in their definition, the event horizon. For several reasons, this definition is not satisfactory in many contexts, and alternative horizons based on the concept of trapped surfaces have been suggested to take its place. The question raised in Paper I has to do with the location of such surfaces in a simple model of gravitational collapse, the Oppenheimer-Snyder model. A different scenario of gravitational collapse, that of a null shell of dust collapsing in flat spacetime, is the starting point of the original formulation of the Penrose inequality. By a reformulation, this inequality can be turned into a purely geometric relation in Minkowski space. In Paper IV we formulate and prove a (2+1)-dimensional version in anti-de Sitter space. The Penrose inequality sometimes goes under the name of the "isoperimetric inequality for black holes". In Paper III a different kind of isoperimetric inequality is discussed (with less rigour), namely that of the volume contained in a black hole with a given area. In Paper II, the subject of limits of spacetimes is visualized. Again, (2+1)-dimensional anti-de Sitter space finds its use, as a one parameter family of surfaces, capturing the geometry of charged black hole spacetimes, is embedded in it. Thus different limiting procedures are illustrated. Finally, interesting models can be constructed by cutting and gluing in spacetimes, but in doing so one needs to take care, in order to obtain a physically realistic model. With this background as motivation, a study of Lorentzian cones is given. Taken together, all of these contributions make up a collection of interesting aspects of black hole geometry, or, shapes of spacetimes.

In this report a theoretical study have been made in the research field of Materials physics. The system under consideration is based on a similar system from an article. The system consists of a junction between a normal metal and a topological insulator, where one of the materials vibrates. Between the materials there can arise a tunneling current of electrons. The study is to see if an applied voltage over the system can make the vibrating material to exhibit a non-trivial dynamic. From the result we could conclude that the vibrating material were affected by the tunneling current. For different applied voltages we could see a clear difference in the phase and strength of the current when one of the materials vibrated. By studying the Logarithmic Fourier transformation of the current. It was concluded that the system can exhibit resonance, for lower voltages, and that the resonance frequency are dependent on the applied voltage. The calculations of the vibrating material's displacement were done both analytically and numerically. The computations were done using only arbitrary values of the coefficients. / I den här rapporten har en teoretisk studie genomförts inom forsknings området för materialfysik. Systemet som studien utgått ifrån är baserat på ett liknande system ifrån en artikel. Systemet består av en normal metall och en topologisk isolator som är separerade från varandra, där ett av materialen vibrerar. Mellan materialen kan det uppstå en ström av tunnlande elektroner. Studien går ut på att se om en applicerad spänning över systemet kan få det vibrerande materialet att ge upphov till en dynamik som inte är uppenbar. Från resultatet kan vi konstatera att det vibrerande materialet påverkades av tunnelströmmen. För olika applicerade spänningar kunde vi se en tydlig skillnad i strömmens fas och styrka när ett av materialen vibrerade. Genom att studera den Logaritmiska Fourier transformen  av strömmen. Kan vi dra slutsatsen att systemet kan uppvisa resonans för låga spänningar och att resonans frekvensen är beroende av spänningen. Beräkningarna för det vibrerande materialets avvikelse gjordes både analytiskt och numeriskt. Beräkningarna utfördes endast med godtyckliga värden på koefficienterna.

In multibody dynamics simulation of robots and vehicles it is common to model the systems as being composed of mainly rigid bodies with articulation joints. With the trend to more lightweight robots, however, the structural flexibility of the robots link’s needs to be considered for realistic dynamic simulations. The link’s geometries are complex and finite element models (FEM) are required to compute the deformations. However, FEM includes too many degrees of freedom for time-efficient dynamics simulation. A popular method is to generate reduced order models from the FE models, but with much fewer degrees of freedom, for fast and precise simulations. In this thesis a method for introducing reduced order models in rigid multibody systems was developed. The method is to divide a rigid body into two rigid bodies. Their relative movement is described by a six degree of freedom restoration force, determined with a reduced order model from Guyan reduction (static condensation). The method was validated for quasistatic deformation of a homogenous beam, a robot link arm with a more complex geometry and in multibody dynamics simulations. Finally the method was tested in simulation of a complete ABB robot with joint actuators, and any significant differences in the motion of the robot tool centre point due to replacing a rigid link arm by a flexible one was demonstrated.The method show good results for computing deformations of the homogenous beam, of the link arm and in the multibody simulation. The differences observed in simulation of a complete robot was expected and demonstrated the method to be applicable in robotic simulations.

Underbody mine blasts are events during which massive amounts of energy is transferred to a vehicle and its occupants during a very short time. The occupants are usually protected by both external (armor) and internal (seat suspension/belts etc.) features. Here, we aim at improving the safety of vehicles that experience a real threat of mine blasts. Through simulations using the finite element method, modified seat belts, airbags, and vertical seat damping mechanisms were tested. The designs were evaluated through injury criteria established for a virtual test dummy and distance measurements between the occupant and the hull in the simulation model. Modifications to the seat belt geometry that enable faster and stronger response yielded a greater clearance between the occupant’s head and the ceiling of the vehicle. This came at a cost of higher injury values, mainly in the neck. For a test case where the occupant’s head would hit the ceiling, airbags were shown to be able to prevent the impact and decrease injury values that were previously above the acceptance limit. The effect of a proposed damped seat construction was tested with regards to the stiffness and damping constants of the damping mechanism. It was shown that a damped mechanism can decrease the value of the injury criteria related to the acceleration of the spine by over 50 %. / Vid minsprängningar under fordon överförs stora mängder energi till fordonet under väldigt kort tid. Passagerare skyddas av både yttre (pansar) och inre (stolsupphängning, bälten m.m.) åtgärder. Här försöker vi öka säkerheten i fordon för vilka minor är ett reellt hot. Genom simuleringar som använder finita elementmetoden testades och utvärderades modifierade stolsbälten, luftkuddar, och dämpningsmekanismer genom skadekriterier för en virtuell testdocka och avståndsmätningar mellan passageraren och fordonet i simuleringsmodellen. Modifikationer av bältesgeometrin som ger en snabbare respons i bältet resulterade i ökad fri höjd mellan passagerarens huvud och fordonets innertak. Med detta följde dock högre skadevärden, främst i nacken. För ett testfall där passagerarens huvud slog i taket kunde luftkuddar förhindra kollisionen och minska skadevärden som tidigare låg över gränsen. Beteendet av en föreslagen dämpad säteskonstruktion testades med avseende på fjäder- och dämpningskonstanten av den dämpande mekanismen. En dämpad konstruktion visades kunna minska värdet på ett skadekriterium för ryggradens acceleration med över 50 %.

We present a basic introduction to the Super Poincaré algebra in 4D, then constructthe N = 1 Super Yang-Mills in 4D. By analogue we expand to the case of N = 1 Super Yang-Mills in 10D. Then by a method of dimensional reduction we getcertain supersymmetric theories in d <= 7 and restrict to spherical backgrounds. Wethen introduce a localization argument by ways of a cohomology on the configuration space of our theory. Finally we apply both techniques to acquire N = 2 Super Yang-Mills on S3, adding the Chern-Simons term and computing the exact partitionfunction, additionally giving an example for the case of U(N) gauge theories.

No description available.

No description available.

When constructing a marina, one must consider many factors for calculating the mooring forces transferred to the mooring system of the docks. The forces transferred from waves is of course one of the most important. The wave induced forces may be described in different orders, the first-order wave forces from the frequency domain and the second-order wave forces determined from a wave field of different standing waves acting together. All floating objects are subjected to these wave forces, but for different mooring systems the transferred mooring force may vary. To describe the need for different calculations depending on the mooring system, a comparison to a spring system is made for both a Seaflex hawser and a guided pile system, which illustrates a significant difference in transferred mooring load. This is due to the hysteresis giving a low spring constant to the Seaflex hawser, which in turn transfers very little of the frequency induced first-order forces to the mooring system. This gives the conclusion that different methods for scaling the Seaflex mooring system is needed, since the first-order wave forces are not as significant than for a semi-rigid mooring system.

Sheet metal forming is a technique widely used in todays industries as it enables fast transformation of metal sheets into parts of various shapes and sizes. Volvo GTO EBM in Umeå uses sheet metal forming in their production of truck cab body parts, and a challenge common for all industries using this technique is to avoid cracking in the formed metal. The present study has been conducted in order to increase the understanding of why produced articles sometimes crack, so that cracking can be prevented in future production. This has been done by studying how different variations in the production process are affecting the robustness of produced articles, partly by investigating variations in material properties and partly by running robustness simulations of a chosen article prone to crack. Material properties have been gathered for both cracked and non-cracked details of different articles, and thereafter been compared to each other using multivariate analysis. Furthermore, simulations have been run using the software AutoForm with the purpose to investigate factors such as feeding direction of metal sheets, variations in material properties and different forces and velocities used during forming. Experiments have also been conducted in order to compare the simulation model and simulation results with reality. From the material property analysis it could be seen that differences in material properties do exist between cracked and non-cracked materials, but that these differences vary between different articles. The robustness simulations indicated that a certain force called draw cushion force do affect the final robustness of an article the most, compared to the other affecting factors investigated in this study. Moreover, the simulation set-up did seem to agree with reality, while the simulated material thinning deviates more than 20 \% from the real one. This may result from an inadequate modeling of friction in the simulations. In conclusion, material properties are important concerning cracking during sheet metal forming, and the draw cushion force seems to have the strongest influence on article's final robustness.

No description available.