This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS5 x S5 and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS5 rotate quickly around the equator of the S5 and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order. Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers from the problem of fermion doubling, a general pathology of fermions on a lattice. In paper II we show how to adjust the theory in order to avoid this problem and, in fact, use the fermion doubling to our advantage. The second part of the thesis studies the low energy behaviour of SU(2) Yang-Mills theory in 4 space-time dimensions. In paper I we perform numerical calculations on an effective action for this theory. We propose the existence of a knotted trajectory within the dynamics of this effective action.

Neutrino oscillations in matter can be studied in different regimes, depending on the energy of the incoming neutrinos and the matter density of the medium. In this thesis we investigate neutrino oscillations in dense matter at very high energy (TeV-PeV range), taking into account the absorption that the neutrinos may undergo in such dense media. This absorption phenomenon is relevant for neutrino telescope measurements of astrophysical neutrinos. We begin with a brief reminder on neutrino oscillations in vacuum and the construction of the PMNS matrix. Then, we proceed with calculations for dense matter. We then explore the accuracy of the resulting effective 2-neutrino mixing formulas. They present a good accuracy for Earth-like densities in our range of energies. We develop the calculations for oscillation probabilities in dense matter with absorption through charged-current inelastic scattering for both the two-neutrino and three-neutrino case. We find that in dense media, astrophysical neutrinos indeed undergoabsorption, which reduces signicantly the fluxes for each flavor, with a resonant absorption of electron-anti-neutrinos around E_{res}\simeq 6.3PeV. We discuss the impact of neutrino absorption in the Earth for neutrino telescopes measurements. We find that solar and lunar shadowing is not problematic for current telescopes but could be a good angular resolution indicator for new telescopes to come. / Neutrinooscillationer i materia kan studeras i olika regimer beroende på inkommande neutrinernas energi och densiteten hos det bakomliggande mediet. I detta examensarbete undersöker vi neutrinooscillationer i gränsen av tät materia och mycket hög energi (TeV-PeV-intervall), och tar hänsyn till den absorption av neutriner som då kan inträffa i sådant materia. Detta absorptionsfenomen är relevant för neutrino-teleskopmätningar av astrofysiska neutriner. Vi börjar med att kort påminna oss om neutrinooscillationer i vakuum och konstruktionen av PMNS-matrisen. Vi försätter sedan med beräkningar av neutrinooscillationer i tät materia. Vi undersöker noggrannheten i resulterande effektiva 2-neutrino-blandningsformlerna. De uppvisar en god noggrannhet i jordlika materieprofiler i vårt intervall av energier. Vi utvecklar beräkningarna av oscillationssannolikheterna i tät materia inklusive absorption genom laddad ström oelastisk spridning i båda två- och tresmaksfallen. Vi finner att astrofysiska neutriner i tät materia absorberas, vilket minskar betydligt flödena för varje smak, med en resonansabsorption av elektron-antineutrino omkring E_res\simeq 6.3PeV. Vi diskuterar sedan effekterna av neutrinoabsorption på jorden för neutrino-teleskopmätningar. Vi finner att sol- och månskuggning är inte problematisk för nuvarande teleskop och kunde vara en bra vinkelupplösningsindikator för kommande teeskop.

Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.

<p>Gravitational waves and electromagnetic waves are important as carriers of energy and information. This thesis is devoted to the study of the propagation and interaction of these waves in plasmas, with emphasis on nonlinear effects and applications within astrophysics.</p><p>The physical systems are described by the Einstein-Maxwell-fluid equations or Einstein-Maxwell-Vlasov equations, when a kinetic treatment is required. The small amplitude and high-frequency approximation is employed for the gravitational waves, such that perturbative techniques can be applied and space-time can be considered locally flat, with a gravitational radiation field superimposed on it. The gravitational waves give rise to coupling terms that have the structure of effective currents in the Maxwell equations and an effective gravitational force in the equation of motion for the plasma. The Einstein field equations describe the evolution of the gravitational waves, with the perturbed energy-momentum density of the plasma and the electromagnetic field as a source.</p><p>The processes that are investigated are gravitational waves exciting electromagnetic waves in plasmas, altering the optical properties of plasmas and accelerating charged particles. The thesis also deals with the propagation propertities of gravitational and electromagnetic waves, e.g. effects due to resonant wave-particle interactions, plasma inhomogeneties and nonlinear self-interactions. It is also shown that plasmas that are not in thermodynamical equilibrium may release their free energy by emitting gravitational waves.</p>

<p>Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.</p>

<p>The overall aim of this thesis is to compare different methods for calculation of Core-Level shifts in metallic alloys. The methods compared are the Initial State model, the Complete screening and the Transition state model. Core-level shifts can give information of chemical bonding and about the electronic structure in solids.</p><p>The basic theory used is the so-called Density-Functional-Theory, in conjunction with the Local-Density Approximation and the Coherent-Potential- Approximation. The metallic alloys used are Silver-Palladium, Copper-Palladium, Copper-Gold and Copper-Platinum, all inface-centered-cubic configuration.</p><p>The complete screening- and the transition-state model are found to be in better agreement with experimental results than those calculated with the initial state model. This is mainly due to the fact that the two former models includes final-state effects, whereas the last one do not. The screening parameters within the Coherent-Potential approximation are also investigated. It is found that the Screened-Impurity Model can extend the validity of the Coherent-Potential-Approximation and increase it's accuracy.</p>

<p>This thesis describes some aspects of noncommutative geometry and conformal field theory. The motivation for the investigations made comes to a large extent from string theory. This theory is today considered to be the most promising way to find a solution to the problem of unifying the four fundamental interactions in one single theory. The thesis gives a short background presentation of string theory and points out how noncommutative geometry and conformal field theory are of relevance within the string theoretical framework. There is also given some further information on noncommutative geometry and conformal field theory. The results from the three papers on which the thesis is based are presented in the text. It is shown in Paper 1 that, for a gauge theory in a flat noncommutative background only the gauge groups <i>U(N)</i> can be used in a straightforward way. These theories can arise as low energy limits of string theory. Paper 2 concerns boundary conformal field theory, which can be used to describe open strings in various backgrounds. Here different orbifold theories which are described using simple currents of the chiral algebra are investigated. The formalism is applied to ``branes´´ in <b>Z</b>₂<b> </b>orbifolds of the <i>SU(2)</i> WZW-model and to the <i>D</i>-series of unitary minimal models. In Paper 3 two different descriptions of an invariant star-product on <i>S²</i> are compared and the characteristic class that classifies the star-product is calculated. The Fedosov-Nest-Tsygan index theorem is used to compute the characteristic class.</p>

The increased use of the diesel engine in the passenger car, truck and bus market is due to high efficiency and lower fuel costs. This growing market share has brought with it several environmental issues for instance soot particle emission. Different technologies to remove the soot have been developed and are normally based on some kind of soot trap. In particular for automobiles the use of diesel particulate traps or filters (DPF:s) based on ceramic monolithic honeycombs are becoming a standard. This new exhaust system component will affect the acoustics and also work as a muffler. To properly design exhaust systems acoustic models for diesel particulate traps are needed. The first part of this thesis considers the modelling of sound transmission and attenuation for traps that consist of narrow channels separated by porous walls. This work has resulted in two new models an approximate 1-D model and a more complete model based on the governing equations for a visco-thermal fluid. Both models are expressed as acoustic 2-ports which makes them suitable for implementation in acoustic software for exhaust systems analysis. The models have been validated by experiments on clean filters at room temperature with flow and the agreement is good. In addition the developed filter models have been used to set up a model for a complete After Treatment Device (ATD) for a passenger car. The unit consisted of a chamber which contained both a diesel trap and a Catalytic Converter (CC). This complete model was also validated by experiments at room temperature. The second part of the thesis focuses on experimental techniques for plane wave decomposition in ducts with flow. Measurements in ducts with flow are difficult since flow noise (turbulence) can strongly influence the data. The difficulties are also evident from the lack of good published in-duct measurement data, e.g., muffler transmission loss data, for Mach-numbers above 0.1-0.2. The first paper in this part of the thesis investigates the effect of different microphone mountings and signal processing techniques for suppressing flow noise. The second paper investigates in particular flow noise suppression techniques in connection with the measurement of acoustic 2-ports. Finally, the third paper suggests a general wave decomposition procedure using microphone arrays and over-determination. This procedure can be used to determine the full plane wave data, e.g., the wave amplitudes and complex wave numbers k+ and k-. The new procedure has been applied to accurately measure the sound radiation from an unflanged pipe with flow. This problem is of interest for correctly determining the radiated power from an engine exhaust outlet. The measured data for the reflection coefficient and end correction have been compared with the theory of Munt [33] and the agreement is excellent. The measurements also produced data for the damping value (imaginary part of the wavenumber) which were compared to a model suggested by Howe [13]. The agreement is good for a normalized boundary layer thickness less than 30-40

Gravitational waves and electromagnetic waves are important as carriers of energy and information. This thesis is devoted to the study of the propagation and interaction of these waves in plasmas, with emphasis on nonlinear effects and applications within astrophysics. The physical systems are described by the Einstein-Maxwell-fluid equations or Einstein-Maxwell-Vlasov equations, when a kinetic treatment is required. The small amplitude and high-frequency approximation is employed for the gravitational waves, such that perturbative techniques can be applied and space-time can be considered locally flat, with a gravitational radiation field superimposed on it. The gravitational waves give rise to coupling terms that have the structure of effective currents in the Maxwell equations and an effective gravitational force in the equation of motion for the plasma. The Einstein field equations describe the evolution of the gravitational waves, with the perturbed energy-momentum density of the plasma and the electromagnetic field as a source. The processes that are investigated are gravitational waves exciting electromagnetic waves in plasmas, altering the optical properties of plasmas and accelerating charged particles. The thesis also deals with the propagation propertities of gravitational and electromagnetic waves, e.g. effects due to resonant wave-particle interactions, plasma inhomogeneties and nonlinear self-interactions. It is also shown that plasmas that are not in thermodynamical equilibrium may release their free energy by emitting gravitational waves.

The overall aim of this thesis is to compare different methods for calculation of Core-Level shifts in metallic alloys. The methods compared are the Initial State model, the Complete screening and the Transition state model. Core-level shifts can give information of chemical bonding and about the electronic structure in solids. The basic theory used is the so-called Density-Functional-Theory, in conjunction with the Local-Density Approximation and the Coherent-Potential- Approximation. The metallic alloys used are Silver-Palladium, Copper-Palladium, Copper-Gold and Copper-Platinum, all inface-centered-cubic configuration. The complete screening- and the transition-state model are found to be in better agreement with experimental results than those calculated with the initial state model. This is mainly due to the fact that the two former models includes final-state effects, whereas the last one do not. The screening parameters within the Coherent-Potential approximation are also investigated. It is found that the Screened-Impurity Model can extend the validity of the Coherent-Potential-Approximation and increase it's accuracy.