In this thesis we explore several statistical methods for addressing the risk of collision between two petroleum wells. Such a collision is a potentially dangerous but rare event that can occur in situations with directional drilling. In order to extend the usual approach of only considering the two closest points in the two wells in the collision risk calculations, we obtain a joint statistical distribution for the position coordinates of all the survey points in two neighboring wells.The common practice in the petroleum industry today is to use the two closest points in a hypothesis test, in order to make a conclusion on whether we should drill as planned based on the collision risk. We suggest a more accurate version of the hypothesis test, which turns out to be more conservative than the original test.As an alternative measure of the collision risk, we estimate the probability of collision. This is done in two different ways, namely by considering only the two closest points and by considering the whole wells. In the latter case, we use the joint distribution for all the survey points. For some well pair cases, the collision probability is much larger when we consider all the survey points in two wells, than when we only consider the two single closest points.We estimate the probability values by using Monte Carlo simulation methods. Since a well collision is considered to be a rare event, we introduce two methods in order to increase the accuracy in the situations where the original Monte Carlo method need an inconveniently large number of samples. These methods give accurate results even when the collision probability is very small.

A basic overview of mathematical finance and pricing theory is given. The Black-Scholes model and the LIBOR Market Model are explained, and their assumptionsare discussed and tested on historical data. The normality of log-returns of stocksand forward rates is tested for different time periods, and is found to be varyinggreatly over time. The models are calibrated using the Exponentially WeightedMoving Average (EWMA) method and implemented to perform a backtest againsthistorical data of two risk measures, Value at Risk and Expected Shortfall. Thebacktesting is done on five portfolios of varying risk, in the European and Norwegianmarkets. Three unleveraged portfolios consisting of bonds and stocks in differentproportions, and two leveraged portfolios consisting of stocks and interest rate capsrespectively are considered.The performance of the risk measures is found to be not satisfactory for all portfolios, but performance is better for riskier portfolios and assets. Variation ofperformance over different time periods is found. The periods of worst performanceare those of turbulent market conditions, notably in late 2008. These periods arefound to loosely correspond to the time periods in which log-returns of equity andforward rates are least normal.A sensitivity analysis of performances to the weighting parameter in the EWMAis done. The sensitivity is found to be substantial for all portfolios except for theportfolios holding stocks in the Norwegian market.

We have a model for simulating facies values in a rock. We can use the model to find facies structures in a 2-dimensional area, which we can use to find properties of a rock in a petroleum reservoir. The model is a Markov mesh model, with a conditional probability distribution for the facies values, with a set of parameters. By using a training image with known facies values, we can simulate the parameters in the model, and then simulate facies values for a new area. In this text, we simulate the parameters by using a Reversible jump Markov chain Monte Carlo algorithm. This lets us simulate not only the values of the parameters, but also which parameters that should be present in the model. We use the Metropolis-Hastings algorithm in the simulations. We use the model with the simulated parameters to make new images with the Markov mesh model. The images should have similar visual appearance as the training image. We are able to make images with some similar qualities as the training image, even though we are not convinced that the parameter values converge.

Material models has been developed for anionic and/or cationic hydrogels, with a simulation framework implemented in MATLAB and the finite element software ABAQUS. The geometry of the simulations is a hemispheroidal hydrogel, divided into a core with a shell, covalently attached to an optical fiber. The material models have been used to estimate the chemical parameters of poly-acrylamide hydrogels containing anionic or cationic monomer groups. Simulations comparing free and constrained swelling has been conducted in order to determine the effect of the geometrical constriction to the optical fiber. Constrained hydrogel swelling featuring shells with different properties than the core was also investigated.The aim of the study was to validate the material models and examine the effects of geometrical constrictions together with shell-impregnation. The anionic material model was shown to reproduce experimental swelling data, while the cationic material model only reproduced the data for ionic strength greater than 100 mM. Restricting the hydrogel to an optical fiber resulted in decreased change in volume and an increase in the axial swelling. The model was able to reproduce reported reduction in the swelling for an impregnated anionic hydrogel by using a neutral shell in the simulations, but failed to recreate the shape of the swelling curve. With the reduction of swelling as a basis, a new method for estimating thin-layer properties has been developed.

In order to make cost effective solar cells from mc-Si materials, the negative contributions from defects and impurities should be reduced. The analysis of the photogenerated carrier properties is therefore of great importance for characterising carrier processes and hence, for improving the material performance.In this work, pump-probe measurement of a range of silicon wafers have been performed, using anultrafast laser of 800 nm wavelength and 85 fs pulses. The optical response in the samples were analysed by measuring the reflected probe beam initial transient.The purpose of this theses was to explore the use of pump-probe experiment to study carrier dynamics in mc-Si. Measurements of single c-Si samples were used as a basis for developing good experimental skills as well as achieving knowledge about carrier dynamics in c-Si. The initial Delta R/R was studied for a range of input parameters, aiming to characterise important contributions to the measurements.The effects of passivation has been studied, indicating a significant contribution to R~R. Etchingoff the passivated layer of an oxide (SiO2) wafer, showed a radically increased in pump beam reflectivity, from 9% to 32%, and a reduced DeltaR~R from 47×10-6 to 37×10-6 was be observed. Analysis has showed that incident angle may be chose such that the pump reflection loss is at a minimum for the given passivation thickness.The final results showed a R~R is in the range of (14-41)e-6 for bare c-Si, and (47-171)e-6 for passivated c-Si wafers.Ultrafast initial recovery has been observed for mc-Si samples, and attributed to trapping of carriers. Decay times in the range of 1-6 ps are deduced and trapping densities are found as (1:3 - 4:3) × 10^18 cm-3, which is in the same order as the excitation densities.A methodology for using pump-probe measurements to analyse mc-Si samples is established, and the technique is used in characterising the observed defect states, which is of great interest for improving solar cell materials.

A numerical approach to solving the problem of electromagnetic (EM) scattering on a single scatterer is studied. The problem involves calculating the total EM field in arbitrary observation points when a planar EM wave is scattered.The method considered is a surface integral equation (SIE) formulation involving the use of a dyadic Green's function. A theoretical derivation of the magnetic field integral equation (MFIE) and the electric field integral equation (EFIE) from Maxwell's equations are shown. The Method of Weighted Residuals (MWR) and Kirchoff's Approximation (KA) with their respective domains of application are studied as ways of estimating the surface current densities. A parallelized implementation of the SIE method including both the KA and the MWRis written using the FORTRAN language. The implementation is applied in three concrete versions of the scattering problem, all involving a spherical perfectly conducting scatterer, namely the cases of incoming wavelength much larger, much smaller and comparable with the radius of the scatterer. The problems are divided into two separate solution categories, separated by whether or not the KA is assumed valid. A recursive discretization algorithm was found to be superior to a Delaunay triangulationalgorithm due to less spread in element shape and area. The produced resultsfitted well considering the interference pattern and symmetry requirements with relative errors in the order of magnitude $10^{-5}$ and less. The case of having large wavelength compared to the radius was also compared with Rayleigh scattering theory considering the far field dependence on wavelenth, scattering angle and distance from the scatterer. This resulted in relative errors of 2.1 percent and less. The main advantage of the SIE method is only requiring the surface of the scatterer to be discretized thus saving computational time and memory compared to methods requiring discretization of volume. The method is also capable of producing accurate results for observation points arbitrary close to the scatterer surface. A brief discussion on how the program may be modified in order to extend its capabilities is also included.

Studies on sea ice have become increasingly popular among researchers in the last decades, due to its effect on the global climate and the challenges it presents for arctic engineering. The research is in demand of reliable data acquisition on various properties, in this case the temperature gradient in forming sea ice.This project continues the development of a spatial temperature instrument, which intends to provide measurements with an accuracy of 0.01°C, making the researchers able to distinguish between fine variations in melting point due to salinity.The outcome of the project is a complete revision of the probe design, which according to simulations not until now provides an environment for the sensor array that satisfies the accuracy requirement. The design also combines the low thermal resistance between sensor and medium from an earlier steel probe with the low thermal interference of an insulating plastic probe.Manufacturing and assembly of the updated temperature instrument with a new probe is almost finished, and should after completion provide experimental data to back up the claims made by the simulations.

Fixed-abrasive diamond wire sawing is a promising technique for reduction of costs related to sawing of silicon wafers for solar cells. The microscopic mechanisms of material removal in the process are however not fully understood, and must be surveyed in order for costs to be further reduced.An interference microscope for sub-surface inspection of mono-crystalline silicon has been built based on the Linnik configuration, with specific application to in-situ monitoring of moving indentations. The working principles of the instrument are explained from a literature study on relevant theory, combining concepts of optical interference and coherence with imaging theory. The optical system has been experimentally tested in terms of its performance in conventional imaging as well as its interferometric capabilities. Tests on the imaging performance show that a large magnification is accompanied by a lateral resolution with a lower limit of $0.9mumathrm{m}$ and an adequately long depth of field. This provides improved conditions for imaging of internal reflections in silicon, compared to a previously used prototype.Using a light source of low temporal coherence, the capability of the system to measure depth profiles of silicon surfaces has been tested. The technique calculates depths from interferograms recorded by scanning of a reference field. Preliminary results from a flat test surface show that depths are not determined accurately enough for calculated profiles to be considered as reliable reconstructions. It is discussed that the inaccuracy is caused by a number of experimental factors including non-uniform illumination, undesired reflections and non-uniform sampling intervals in scanning.Two experiments with moving indentations on silicon surfaces have been performed, monitored by conventional imaging and calculation of interferometric phase maps, respectively. Results are seen in context with the theoretical understanding of material removal mechanisms in fixed-abrasive diamond wire sawing. The evolution of surface damage is observed as interconnection of chippings in both experiments. In addition, sub-surface lateral cracks are identified from interferometric phase maps. The phase maps of surface damage can, however, only to a limited extent be interpreted as topographic contour lines of surface depth. A deeper knowledge of removal mechanisms requires quantitative measurements of depths. This can be better achieved by calculating accurate depth profiles from interferograms. Future enhancement of the system is dependent on a reevaluation of the optical design as well as better control of sampling intervals in scanning.

This master's thesis is focussed around investigating Massey products as tools for studying properties of links, in particular the Brunnian property. In the literature, there are only a few examples of the Massey product being used to study linking, none of which has any emphasis on links with the Brunnian property, except for computations for the Borromean rings. The result of the work is a number of thorough computations of Massey products in link complements, with the negative conclusion that the Massey product does not detect the Brunnian property.

Self-assembled platinum and gold nanostructures, which are formed by evaporation and subsequent diffusion limited aggregation of metal on highly oriented pyrolytic graphite, have been studied by photoemission spectroscopy and scanning electron microscopy. Dendritic gold nanostructures were observed on samples onto which gold was evaporated at room temperature. For samples onto which gold was evaporated at reduced temperatures, no such dendrites were found. For samples evaporated with platinum, small nano-spiders were seen at low evaporation time, and more complex fractal structures at higher evaporation time. Studying the oxidation of carbon monoxide over the platinum nanostructures yielded no clear corrolation between nanostructure size and oxidation rate.