We present a method for finding the optimal decision on Random Variables in a graphical model. Upper and lower bounds on the exact value for each decision are used to reduce the complexity of the algorithm, while we still ensure that the decision chosen actually represents the exact optimal choice. Since the highest lower bound value is also a lower bound on the value of the optimal decision, we rule out any candidate with an upper bound of lower value than the highest lower bound. By this strategy, we try to reduce the number of candidates to a number we can afford to do exact calculations on.We generate five Bayesian Networks with corresponding value functions, and apply our strategy to these. The bounds on the values are obtained by use of an available computer program, where the complexity is controlled by an input constant. We study the number of decisions accepted for different values of this input constant. From the first Network, we learn that the bounds does not work well unless we split the calculations into parts for different groups of the nodes. We observe that this splitting works well on the next three Networks, while the last Network illustrates how the method fails when we add more edges to the graph. We realize that our improved strategy is successful on sparse graphs, while the method is unsuccessful when we increase the density of edges among the nodes.

In dielectric insulating materials subjected to alternating electric fields there are energy losses associated with polarization mechanisms and resistivity. A typical dielectric material used for insulation of high voltage sub-marine cables is cross-linked polyethylene (XLPE) produced from polyethylene (PE). Under production, PE can stagnate in high temperature thermal zones and consequently be subjected to thermal oxidation that introduces polar carbonyl groups to the polyethylene chain, which leads to increased energy losses, inferior insulating properties and subsequent degradation and eventually breakdown and failure of the cable.The oxidized polyethylene can contaminate the insulating material in the form of microscopic particles embedded in the material, that are difficult to detect and separate from the polyethylene granulate. In this work the focus have been on documenting the fundamental properties of the oxidized XLPE contaminations, such as complex permittivity, associated energy losses and breakdown strengths, compared to that of un-oxidized XLPE.In this thesis the thermal oxidation process of XLPE and PE has been studied in order to determine the degree of oxidation and carbonyl contents, using Fourier transform infra red spectroscopy. Three real contaminations was found, investigated and categorized. The contaminations was replicated through thermal oxidation of XLPE samples in a ventilated heat cabin at 170˚C.The electrical properties of replicated contaminations has been investigated using dielectric spectroscopy and breakdown strength-tests. At 50Hz the real relative per- mittivities is measured to be ε' = 2.30 for un-oxidized XLPE, ε' = 2.57 for category 1 samples, ε' = 2.72 for category 2 samples and ε' = 4.19 for category 3 samples.The lossy polarization process is characterized by the imaginary part of the permittivity ε''. It is seen that the dielectric losses are indeed increasing with the presence of polar carbonyl group, as expected from theoretical considerations. It is also seen that ε'' in oxidized samples increases as the frequency decreases, which indicates that the conductive process dominates the low frequency domain, and that the DC conductivity is higher in contaminations than in un-oxidized XLPE. Break- down tests was preformed using the ASTM D149 standard for dielectric breakdown testing.It was observed a decrease in breakdown strength in oxidized XLPE. The breakdown strengths decreased from (55.31±31)kV/mm in un-oxidized XLPE to (24.07±12.88) kV/mm in the most oxidized category 3 XLPE sample.As a consequence of the theories and experimental results presented in this work, it can be said that there is a causal relation between dielectric losses and breakdown strengths in oxidized XLPE material which can be sumerized as follows: The intro- duction of polar carbonyl groups through thermal oxidation to polyethylene causes increased permittivities and dielectric losses. Subsequently there will be a decrease in electric breakdown strength of the XLPE insulation. Contaminations of oxidized material embedded in a solid insulation system may pose a reliability issue and may eventually be the cause of breakdown and failure of the cable.

The van der Waals interaction energy is derived for a homogenous fluid of polarizable particles. Low-temperature corrections to the van der Waals interaction energy are computed numerically for three cases: Dilute media with radiative interactions, arbitrarily dense media without radiative interactions, and arbitrarily dense media with radiative interactions. The validity of the model used to calculate the corrections at arbitrary densities is argued for, by comparison with the results for low densities.

Resent research indicates that there might be a connection between perturbation of the Earth's geomagnetic field caused by solar wind, and the atmospheric circulation. In this project the mesospheric meridional and zonal wind, obtained from the SuperDARN radars Goose Bay, Hankasalmi, Kapuskasing, King Salmon, Kodiak, Pykkvibær, Saskatoon and Stokkseyri in the northern hemisphere was compared with the global Ap index along with the measure for solar radiance, the F10.7 index. Wind data from the SuperDARN radars were available for every hour and geomagnetic and irradiance data for every month. The solar atmospheric tides along with seasonal effects were removed from the wind data and the perturbation of the residual wind due to Ap and F10.7 was used to see if any connection between the mesospheric wind and Ap/F10.7 could be found, and if they influenced the wind in a similar manner. A tendency for more equatorwards and eastwards winds during periods of high geomagnetic activity was found. In addition, this effect was observed to increase with increasing geomagnetic latitude for the zonal wind. Ap and F10.7 often affected the wind in a similar manner, making it hard to distinguish the two. Using linear regression, the correlation between them was found to be high over the timescales of this study.

This master thesis presents a new experimental way to dynamically determinerheological properties of a complex fluid. The fluid investigated is asuspension of the synthetic clay mineral laponite of 3 wt%. This is mixedtogether with distilled water or a NaCl solution with concentrations bellow10^2 M. Laponite gels are thixotropic and shear thinning with a yield stress.In the experiments done during this thesis the transition between liquid andsolid behavior is investigated using a Hele-Shaw cell and a rheometer. Threedifferent phases is observed with respect to waiting time and NaCl concentration.These are recognized as a liquid phase for small concentration ofNaCl and short waiting times and a solid phase for high concentration ofNaCl and long waiting time. In the intermediate range a viscoelastic phaseis observed.Some experiments were done with the sample placed between crossed polarizers,and birefringence was observed in all three phases. In the solid phaseit is observed only a small area around the fracture tip. In the liquid phasethis is observed in front of the finger, but this is not a stable phase. Inthe viscoelastic regime a stable nematic phase occur along the stress fieldaround the interface of the bubble. This nematic phase will align normal tothe glass surface. Fracture like patterns in the nematic phase are observed.This is an elastic behavior with the clay platelets aligning normal to thestress field to prepare for fractures to propagate there.Different NaCl concentrations will give different arrested states, respectivelya repulsive glass and a attractive gel. It is expected that glass and gels behavedifferently in this experiment, but this was not confirmed. A gel phasehave been observed in concentrations of NaCl above 5*10^3 for waitingtimes up to 605 hours. For smaller concentrations a even longer waitingtime is expected and experiments on this needs to be performed in futurestudies.In addition this experiment could investigate and give insight of flow incomplex fluid. To investigate this further, tracer particles have been usedin a few experiments. The results are promising for further studies.In this thesis work, a large range in waiting times and concentrations of NaClhave been investigated. In future studies it should be carried out experimentsin a smaller range of these parameters along with other parameters.Also a more quantitative analysis should be carried out. Especially thetransitions between fluid/viscoelastic and viscoelastic/solid is interesting toinvestigate further.

We show experimentally that CO2 intercalates into the interlayer spaceof the synthetic smectite clay Li-fluorohectorite (LiFh). The intercalationoccurs for a range of conditions in terms of pressure (5 bar to 20 bar) andtemperature (-20'C to 5'C). The mean basal spacing of the clay layersin LiFh intercalated by CO2 is found to be approximately 12.0 Å.We observe that the dynamics depends on the pressure, with a higherintercalation rate at increased pressure. Even under pressure of 20 bar,intercalation of CO2 is slower than H2O intercalation in fluorohectoritesby orders of magnitude.In situ observations show that LiFh is able to retain CO2 in the interlayerspace at room temperature, and the CO2 only starts leaving the clay attemperatures exceeding 30'C. Hydrated and CO2-intercalated clays areindistinguishable by use of X-ray diffraction alone. The difference in behaviorat higher temperatures is used as an additional confirmation thatintercalation of residual water is not the cause of the observed swelling.Furthermore, we report a new intercalation state corresponding to intercalationof more than one layer of CO2 into the interlamellar space, andhave also observed changes in the intercalation state of a monohydratedLiFh sample under exposure to CO2.We believe that the findings, concerning both intercalation and deintercalation,could be relevant for application of clays related to capture, transportor storage of CO2.

Starting from a super saturated solid solution and two different conditions withβ′′ precipitates (T6) an Al-Mg-Si alloy was heat treated at 200◦C and investigated byhardness measurements. One of the T6 conditions was investigated with transmissionelectron microscopy (TEM). The phase transformation to post-β′′ was studiedwith TEM and there was found that post-β′′ phases nucleated on the β′′ particles.After longer overaging times the growths were larger. A simple model was proposed, and it suggested that the growth of post- β′′ phases was the first steps in thetransformation of β′′, and that the final result was a microstructure consisting onlyof post- β′′ particles

In this thesis we study time series containing pressure measurements from a three phase flow pipeline at the Ekofisk oil field. The pipeline transports a mixture of oil, water and gas from $15$ wells for approximately 2.5km to a production facility. Our aim is to develop techniques that allow the selection and (to some extent) prediction of "non-standard" behavior in the system (sharp pressure changes and other type of instabilities). To advice this aim we perform a scalewise decomposition of the input signal/time series and investigate the behavior of each scale separately. We introduce the Sliding Window Wavelet Transform (SWWT) method. The method evaluate the variability on different scales within the time interval of a characteristic length (a window) and then trace these characteristics as the window slides in time.We use the discrete wavelet transform (DWT) in order to obtain the scalewise decomposition within the window. Using orthonormal discrete wavelets, we show that the variability of such sequences can be decomposed into their corresponding scales. Based on this, a thresholding algorithm is applied, characterizing the state of the system any given time. The results we find are promising and we show that different parameters in the thresholding algorithm extracts different types of special events. We also show that in some cases, this approach allows to predict special events before they really occur.While we investigate one particular system in this thesis, the procedures developed can be applied to other complicated systems where instability in system parameters is important.

We study the effect of an impurity potential on spin-memory loss in graphene. Various general methods for finding the spin-orbit related effect of a slowly varying impurity potential on a semiconductor have been examined. We have also revisited problems concerning electronic properties and spin relaxation in graphene. To this end, the bandstructure for graphene has been calculated through analytical and computational methods. The following results have been reproduced: Low energy excitations behave like massless relativistic particles with an effective speed of light at roughly 10^6 m/s. Intrinsic spin-orbit coupling splits the bands at the Fermi level. The importance of the $d$ orbitals for this effect is also shown. Extrinsic spin-orbit coupling induced by a perpendicular electric field give rise to a Rashba type Hamiltonian. Our novel results are related to extrinsic effects from an impurity. We have calculated the renormalised impurity induced spin-orbit coupling due to mixing of the conduction bands and the other bands. This renormalisation is at most comparable to the vacuum term, and thus cannot explain the experimental results on spin relaxation.

The Cauchy problem for a two-component Hunter-Saxton equation, begin{align*}(u_t+uu_x)_x&=frac{1}{2}u_x^2+frac{1}{2}rho^2,rho_t+(urho)_x) &= 0,end{align*}on $mathbb{R}times[0,infty)$ is studied. Conservative and dissipative weak solutions are defined and shown to exist globally. This is done by explicitly solving systems of ordinary differential equation in the Lagrangian coordinates, and using these solutions to construct semigroups of conservative and dissipative solutions.