We study scalar waves scattered from self-affine and Gaussian correlated surfaces. The simulations are performed using rigorous simulation of the integral equations derived from the Helmholtz equation, describing a scalar wave above a non-penetrable surface with a hard wall or free surface boundary condition.An incident, Gaussian shaped beam is scattered from the surface, and the full angular distribution of the scattered intensity is obtained. Self-affine and Gaussian correlated random surfaces are generated, and the resulting scattered intensity is averaged over a large number of surfaces (in the order $N_s=3000$), using the ergodicity of the surface.Compared with analytical calculation of the scattered intensity in the Kirchhoff approximation, our approach gives similar results for less rough surfaces. Compared with simulations of electromagnetic waves scattered from a perfect conductor, without recording the polarisation of the scattered light, our simulations give similar results when using a hard wall boundary condition.We observe phenomena such as specular scattering for less rough surfaces, diffuse forward scattering for more rough surfaces and enhanced backscattering for surfaces where waves scattered multiple times by the surface roughness gives a large contribution to the scattered intensity.

The behaviour of particles in turbulent flow, with emphasis on particle deposition on both the frontside and backside of a cylinder, was investigated by means of Direct Numerical Simulations. One-way coupling between the fluid and the particles was applied. Simulations of turbulence forced at small, intermediate and large scales were run on a three-dimensional domain. The turbulence was used as inlet on a two-dimensional flow domain, where a Lagrangian tracker was used to compute the particle motions. The Reynolds numbers used were Rec = 421 and Rec = 1685. For intermediate Stokes numbers, or particle sizes, the number of particles deposited increased when the Reynolds number was raised. The presence of turbulence lead to a further increase in the deposition for these Stokes numbers, compared to the deposition in laminar flow. The increase was at its highest for large scale forced turbulence. The increased deposition of intermediate Stokes numbers on the frontside of the cylinder in turbulent flow was found to be related to the variance of the effective Stokes number, resulting from the fluctuating nature of the turbulent velocity. The deposition of particles with small Stokes numbers was also altered by the presence of turbulence, but this could not be explained by the variance of Stokes number. The mechanism leading to deposition of these smallest particles is related to the turbulent eddies close to the boundary layer of the cylinder, and will need further study. At the backside of the cylinder, the increased deposition at raised Reynolds number and at the presence of turbulence was related to the magnitude of vorticity. Furthermore, preferential concentration of particles in turbulence was observed in the Rec = 1685 cases, demonstrating the effect of the vorticity magnitude being sustained throughout the domain.

During the past few decades, the power sectors of several countries have been substantially reorganized, and liberalized markets for trading of electricity have been established. In this report, evidence from six electricity markets are studied in order to identify characteristics of electricity prices. The market structures, statistical quantities, as well as long-term dependence, are investigated. Detrended fluctuation analysis and the average wavelet coefficient method are employed in order to estimate the Hurst exponent, which quantifies the presence of long-termed dependence. Since it is concluded that the price series are periodic on several time scales, all characteristics are investigated for both the original and deseasonalised versions of the time series. In particular, it is confirmed that the electricity prices are volatile, but that a considerable amount of the volatility is caused by the daily and weekly periodicities. Furthermore, the characteristic return distributions, volatility clustering and price spikes are analysed.

This is the Master’s Thesis of Eirik Timo Bøe Vilpponen, and was writtenat the Department of Physics at the Norwegian University of Science andTechnology (NTNU). The thesis is twofold, the first part being the comple-tion of a project undertaken during the fall of 2010. The project concernedthe setup of a solar cell current-voltage characterization lab [4] at the sameDept. of Physics.The second part is an analysis of the current-voltage characteristics ofNTNU-made quantum-dot intermediate band solar cells. A strong focus isput on exploring the possibility of utilizing the Two-Diode Model as a meansof analysis. The two-diode model has been found to have a good potential forthis use, but that it requires a specially made curve fitting computer programto fulfill this potential.

In this thesis the Minimum Ignition Energy, in a hydrogen-air system, is studied by Direct Numerical Simulations (DNS) in a program called the Pencil Code. The heat source used to achieve ignition is modeled by a Gaussian temperature distribution. Three different geometries of the heat source are looked upon, one with spherical geometry in three dimensions, one with cylindrical geometry in two dimensions and the last in one dimension. The results show that the dimensionality of the heat source has a strong impact on ignition.In addition, a new simpler zero dimensional simulation method is proposed with the goal of replicating the results from the Pencil Code. This method needs less calculation power, and uses ignition delay time data together with the heat equation to simulate ignition. The model has proven itself useful since it reproduces the Pencil Code results very well.

The theory of laser-induced liquid-liquid interface deformation has been presented and used to derive a differential equation describing the shape of the deformation. The differential equation has been investigated and solved numerically, and the results have been compared to the experimental results of the Bordeaux group. A model describing the maximum depth of the deformation based on the theory of a sphere in an electric field has also been investigated.The deformations from the numerical solutions of the differential equation are too wide compared to the experimental results. The shoulder-shape that has been observed in the experiments is not present in the numerical solutions. There is reason to believe that the differential equation may be too simple in order to describe the liquid-liquid interface deformation for nonlinear cases. There may be thermal effects that changes the liquid properties due to local temperature variations induced by the laser, causing the liquid parameters to change along the deformation.The model used to estimate the deformation depth does not give reasonable results, as it leads to a deformation that is more than 100 times larger than what is observed in the corresponding experiments. The assumptions made for this model may not be valid, and a discussion on what should be done in order to improve the model is included in this text.

This report is a study of how polarized light can improve our understandings of physical phenomena, such as local organization of anisometric nanoparticles dispersed in a liquid.The first part of the thesis considers the theoretical aspects of polarized light. The Maxwell's equations are considered together with the Stokes formalism and the Mueller matrix. The Mueller matrix is analyzed in depth by looking at different ways it can be decomposed into several matrices, each clearly representing the physical phenomena of depolarization, diattenuation and retardance. The physics behind the phenomena will then be shortly addressed.The second part of the thesis describes the Mueller Matrix Imaging (MMI) ellipsometer, developed in the Applied Optics Group at NTNU. The results of Mueller imaging of air will be presented and discussed in order to get more understanding of the ellipsometer.The third and main part of the thesis, focuses on applying the MMI ellipsometer in order to study complex phenomena in clay dispersion. By looking at the development of samples of aqueous clay dispersions, the creation of different phases will be recorded. Some of those phases have crystalline properties and a Mueller matrix imaging can reveal much about its structure. A decomposition of the Mueller matrix can tell even more about the properties of the phases.

Hyperbolic relaxation systems is an active field of research, with a largenumber of applications in physical modeling. Examples include modelsfor traffic flow, kinetic theory and fluid mechanics. This master’s thesis is a numerical and theoretical analysis of such systems, and consists of two main parts: The first is a new scheme for the stable numerical solution of hyperbolic relaxation systems using exponential integrators. First and second-order schemes of this type are derived and some desirable stability and accuracy properties are shown. The scheme is also used to solve a granular-gas model in order to demonstratethe practical use of the method. The second and largest part of this thesis is the analysis of the solutionsto 2 × 2 relaxation systems. In this work, the link between the the sub-characteristic condition and the stability of the solution of the relaxationsystem is discussed. In this context, the sub-characteristic condition andthe dissipativity of the Chapman–Enskog approximation are shown to beequivalent in both 1-D and 2-D. Also, the dispersive wave dynamics of hyperbolic relaxation systems isanalyzed in detail. For 2 × 2 systems, the wave-speeds of the individualFourier-components of the solution are shown to fulfill a transitional sub-characteristic condition. Moreover, the transition is monotonic in thevariable ξ = kε, where ε is the relaxation time of the system and k is thewave-number. A basic 2 × 2 model is used both as an example-model in the analyticaldiscussions, and as a model for numerical tests in order to demonstratethe implications of the analytical results.

Silicone oil droplets containing synthetic smectite clay submerged in another immiscible organic oil have been studied by observing clay particle movement, oil circulation and drop deformation when an electric field is applied. Results show how electric field strength, electrohydrodynamics, dielectric and conductive properties determines the fluid flow, clay particle formation and drop deformation.

In this thesis we theoretically examine spin-polarized non-local transport in two junctions built up by materials with superconducting and magnetic properties. The first consists of a Zeeman-split superconductor placed between two normal metals. We find that such systems can generate a spin-polarized non-local current even when the injected current is unpolarized. The effect is however mostly geometric and take place also when the superconductor is switched with a normal metal. The second system is built up by two ferromagnetic wires coupled by a superconductor via spin-active interfaces. We investigate the circumstances which allow for an inverse spin-valve effect. For certain parameter ranges we find that a crossover between positive and negative magnetoresistance is possible as a function of temperature.