Motivation: Cartilage is a robust but flexible connective tissue found in most joints of the body. The collagen fibres present in the extracellular matrix of cartilage contribute to its tensile strength and stiffness. The purpose of this study is to develop and implement methods to determine the orientation and anisotropy of collagen fibres in 3-D images gen- erated with multi-photon microscopy. The motivation behind developing these techniques is to improve the foundation for further studies on understanding the characteristics of the cartilage matrix. This in turn would give a better foundation for developing artificial matrices and mechanical models, as well as improve diagnostics.Material and methods: The two methods developed in this study are based on analysing the frequency domain. One is an expansion of a previous developed method by Chaudhuri et al. [1]. This method is based on evaluating the average intensity at different directions in the frequency domain. The direction with the least average intensity is equivalent to the direction of the fibres. The other method is based on thresholding the frequency domain according to intensity followed by fitting an ellipsoid to the remaining data set. The direction of the collagen fibres is equivalent to the direction of the shortest axis of the ellipsoid. These methods are called the sector and ellipsoid method, respectively. To determine how robust these methods are a series of tests were developed. The focus of these tests was to determine if the methods are rotational invariant and if the results are influences by different preprocessing techniques. These preprocessing techniques are: median filtering, deconvolution and skeletonization of the original image containing the collagen fibres. It is also important to determine the sensitivity of the ellipsoid method according to the chosen threshold value. In addition data generated fibres and frequency domains were made to determine the accuracy of the methods.Results and conclusion: The sector method was not very robust. For most cases there is not one specific direction that has the least average intensity in the frequency domain. Instead there is a quite large minimum area. The ellipsoid method shows promising results. It managed to find the correct direction both for the data generated data sets, but also for the real images. It seems like no preprocessing nor frequency filtering, except for thresholding, is needed to still find the correct direction and its anisotropy. The only remark is that the automatically chosen threshold value was to low for one of the samples. This can probably be improved by making a slight change in the process for choosing a threshold value.

The effect of thermophoresis on the particle deposition on a cooled cylinderin non-isothermal laminar gas ow has been studied using Direct NumericalSimulations (DNS). Simulations where thermophoresis have been taken intoaccount for different Stokes numbers and particle-to-gas thermal conductivityratios, Λ, have been performed at Reynolds number Re = 380. In additionreference cases, simulations where thermophoresis have not been taken intoaccount, have been performed both for isothermal and non-isothermal owfor Re = 20 and Re = 380.The ratio between the front side particle impaction efficiency in the non-isothermal reference case and the isothermal reference case for the smallestStokes numbers considered was expected to be proportional to the ratio ofthe free stream temperature and the cylinder temperature, according to an-analytical considerations. The simulations for Re = 20 was in good agreementwith this relation, but for Re = 380 the front side particle impaction efficiency for the smallest particles was lower in the non-isothermal referencecase compared to the isothermal reference case. This is believed to havebeen caused by inaccuracies in the numerical method for the non-isothermalsimulation at Re = 380.Thermophoresis was not found to affect the particle impaction for thelargest Stokes numbers. For intermediate and small Stokes numbers the effect of thermophoresis depended on Λ. The particle impaction efficiency wassignificantly higher, both for the front side and the back side, in the ther-mophoretic simulations compared to the non-isothermal reference case forparticles with Λ = 1 and Λ = 100. The particle impaction efficiency forparticles with Λ = 1000 was lower, both for the front side and the back side,in the thermophoretic case compared to the non-isothermal reference case.

A numerical model for predicting icing on offshore structures and vessels has been developed and implemented. The model calculates the icing caused by freezing sea spray, and focuses on two distinct sources of spray - spray from droplets blowing off whitecaps on the sea surface, and spray from waves colliding with the vessel. The implementations of both wind-induced and wave-induced sea spray are based on existing theoretical models, and are combined with a thermodynamic model for the icing process. The model may be used to calculate icing on reference objects or structures on the vessel. In addition, algorithms have been developed so that the model can be applied to polygon-based vessel geometries, calculating the icing distribution over the entire vessel. The model has been applied to meteorological observations and hindcast data for locations in the Norwegian Sea and Barents Sea, in particular at the locations of the Norne field and the undeveloped Skrugard and Shtokman fields. The results indicate that the icing will be comparable at the locations of Skrugard and Shtokman, and that both the frequency and severity of icing events will be far greater for these two locations than for Norne. Although conditions at Shtokman are colder than at Skrugard, the higher winds and waves near Skrugard will increase the available sea spray in the model, thus making the number of severe icing events more similar for the two locations.

Coherent plane-wave compounding is the coherent summation of several successive plane waves incident at different angles. This thesis presents results from simulations and in vitro and in vivo measurements of stationary and moving objects, with focus on loss of resolution and contrast due to object motion. Resolution and contrast results for several angle selections, angle sequences and object velocities with and without motion correction have been compared.It is shown that using a subset of plane-wave tilt angles by decimating the optimal selection introduces grating lobes which degrades the image contrast, while imaging with a lower maximum tilt angle degrades the lateral resolution. The contrast loss for decimation factor 2 was more significant for simulations than for in vitro measurements. While the contrast went from -40 to -30 dB for the simulations, a decimation factor of 4 was needed to degrade the contrast significantly for the measurements. Decimating the angle selection by a factor of 2 doubles the achievable frame rate. A reduction in maximum angle from 13.7 to 8.2 deg., which corresponds to an increase in transmit F-number from 2.1 to 3.5, gives less than 0.3 mm degradation of lateral resolution. The lateral resolution is of the order of 1 mm. This reduction in maximum angle increases the frame rate by a factor of 1.2.Axial point scatterer velocity leads to considerably worse image quality than for stationary scatterers, while the effect of lateral scatterer velocities is limited. The degree of contrast and resolution loss due to object motion is dependent on the selection of plane waves which constitute a frame, and the sequence in which the plane waves are transmitted. Using a subset of the optimal angle selection leads to improvement in image quality for an axial velocity of 10.0 cm/s for decimation factor 4, but not for decimation factor 2, even though the total scatterer movement per frame is reduced by the reduction of transmitted plane-waves. The loss of quality due to motion was less for fewer tilt angles, but the total image quality was still worse for many of these sets of angles due to grating lobes.The unwanted effects of motion for in vivo-measurements were not seen to the same extent as for simulated point scatterers, and working with the coherent plane-wave compound seems promising for moving objects.

In this master thesis I study the extremal positive partial transpose (PPT) states of the three qubit $(2times2times2)$ system using numerical methods. Using two algorithms which locate PPT states of a specified rank and extremal PPT states respectively, I have located numerical examples of extremal PPT states with a variety of ranks. These numerical results confirm the analytical result that all PPT states of rank less than four are separable. I also derive an upper limit on the ranks of extremal PPT states. The extremal PPT states of lowest rank, the rank four states, were studied in more detail. These states were confirmed to be biseparable in accordance with both previous analytical and numerical results. The range and kernel of these states were examined for product vectors, but none were found. In an attempt to parametrize the SL$otimes$SL equivalence classes of these extremal rank four states I have studied an analytical method to construct such states based on unextendible product bases (UPBs). This method can be used to create PPT states from a single equivalence class where, by design, the kernel of all states contain a UPB and the range contains no product vectors. All states where the range is not spanned by a basis of product vectors are necessarily entangled. I also present a numerical method for creating extremal rank four states that are symmetric under various combinations of partial transposes. Numerical examination of these states reveal no product vectors in neither range nor kernel. The existence of rank four states with and without product vectors in their kernel implies the existence of at least two equivalence classes. To get a better impression of these equivalence classes I construct quantities that are invariant under SL$otimes$SL transformations and must therefore have the same value for all states in the same equivalence class. Calculating the values of these invariants for all the rank four extremal states I have generated gives a seemingly continuous range of values. This indicates that there is an infinite number of equivalence classes likely described by one or more continuous variables. The invariants also revealed an interesting set of states that may belong to a single equivalence class, where one invariant is zero and the others have identical values. This was the only equivalence class where more than one of my states were included. There is obviously something special about this class, but I do not know what it is.

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.