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 U(N) 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 Z2 orbifolds of the SU(2) WZW-model and to the D-series of unitary minimal models. In Paper 3 two different descriptions of an invariant star-product on S² 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</p>

Mapping dynamical motion to neural brain activity is one of many challenges in the field of neuroscience. Further knowledge in this area could provide useful insights in fields such as medical treatment of brain disorders. However, progress in the field is halted by the immense complexity of the human brain and the diversity of unique dynamical behaviours. In this project the stereotypical grooming behaviour of mice is analysed to gain knowledge of its dynamical features. Properties such as the dimensionality of the underlying dynamical system and trajectories of state space reconstructions are analysed using tools such as Taken's delayed embedding theorem, Principal Component Analysis and Locally Linear Embedding. / Att sammankoppla motorik med hjärnans neurala aktivitet är en av många utmaningar inom neurovetenskapen. En bättre förståelse inom området kan vara till stor nytta för behandling av till exempel neurologiska sjukdomar. Komplexiteten av den mänskliga hjärnan och den stora mängden av unika rörelsebeteenden gör dock processen svårare. I det här projektet analyseras det stereotypiska skötselbeteendet hos möss för att få en djupare förståelse om dess dynamiska egenskaper. Dimensionaliteten av skötselbeteendet och rekonstruktioner av det dynamiska flödet undersöks med hjälp av exempelvis Taken's delayed embedding Theorem, Principal Component Analysis och Locally Linear Embedding.

Nonequilibrium Statistical Mechanics focuses on the branch of physics that studies large systems that are out of equilibrium. These systems are inherently difficult to model due to the complex paths available through state space depending on initial configurations and external force fields. Langevin dynamics is a stochastic differential equation used by physicists to model and capture these dynamics. By sampling individual particles from any given distribution, and allowing these particles to follow a Langevin path as t → ∞, we can demonstrate that the Boltzmann distribution is recovered for any stationary field. Thus Langevin dynamics can be seen as a path through state space that leads to equilibrium.In this master’s thesis, we use these properties of Langevin dynamics in a machine learning setting to perform time-series forecasting of large systems. Langevin dynamics gives us the ability to not only capture expectation values from datasets, but instead models an approximate distribution representing the data. This leads us to believe that using diffusion models inspired by Langevin dynamics will allow us to model complex multivariate datasets with temporal, spatial, local &amp; global correlations.Modeling the electric grid is an inherently challenging problem due to the compli- cated and subtle correlations that exist with for example historical usage, weather, and economic effects. Thanks to this, we chose to forecast the American power grid using a diffusion based machine learning model. In this thesis, a diffusion based architecture has been developed to forecast this problem and includes several components such as recur- rent neural networks, graph attention networks, and diffusion processes in conjunction.Our architecture has demonstrated superior performance, outperforming current state- of-the-art methods, including gradient boosting decision tree models. Detailed perfor- mance comparisons between our diffusion model and XGBoost have shown that our diffusion model consistently outperforms it.Looking ahead, our work suggests many potential areas of improvement to further advance the performance of diffusion based models in time-series forecasting. Examples of this include incorporating physics inspired conservation laws into the model, and im- proved sampling methods. We hope that these methods will be applied in industries that could benefit from more advanced forecasting, such as the increasingly renewable-based power grids. / Icke-jämnviktsstatistisk mekanik är den delen av fysik som studerar stora partikel system som ej är i jämnvikt. Det är svårt att modellera dessa system på grund av de komplexa banorna genom systemets tillståndsrums som finns tillgängliga. Langevin-dynamik är en stokastisk differentialekvation som används av fysiker för att modellera och fånga dessa beteende. Genom att låta partiklar i sådana system följa en Langevin process, kan man demonstrera att det går att återfå en Boltzmann distribution. Således kan Langevin- dynamik ses som en väg genom ett systems tillståndsrymd som leder till jämnvikt.I denna masteruppsats används dessa egenskaper hos Langevin-dynamik i en mask- ininlärningsmiljö för att utföra tidsserieprognoser av stora system. Langevin-dynamik ger oss möjlighet att inte bara fånga väntevärden från datan, utan istället modellera en approximativ fördelning som representerar datan. Detta får oss att tro att diffu- sionsbaserade modeller inspirerade av Langevin-dynamik tillåter oss att modellera dessa komplexa dataset med tidsmässiga, rumsliga, lokala och globala korrelationer.Att modellera elnätet är ett i grunden utmanande problem på grund av de komplicer- ade och subtila korrelationer som finns i datan. Exempel inkluderar historisk användning, väder samt ekonomiska effekter. Vi valde därför att utveckla en diffusionsbaserad mask- ininlärningsmodell för att prognostisera det amerikanska elnätet.xArkitekturen som utvecklats visar på överlägsen prestanda och överträffar nuvarande använda metoder, inklusive s.k. gradient boosted decision trees. Detaljerade prestanda- jämförelser mellan vår diffusionsmodell och XGBoost har visat att vår diffusionsmodell konsekvent presterar bättre.Om vi blickar frammåt pekar vårt arbete på många potentiella förbättringsområden för att ytterligare öka prestandan hos diffusionsbaserade modeller inom tidsserieprog- noser. Exempel på detta inkluderar att integrera fysikinspirerade konservationslagar i modellen samt förbättrade samplingsmetoder. Vi hoppas att dessa metoder kommer att tillämpas i industrier som kan dra nytta av mer avancerade prognoser, såsom de alltmer förnyelsebaserade elnäten.

<p>Ab-initio results of the core-level shift and the distribution about the average for the 3<i>d</i>_5/2 electrons of Ag, Pd and 2<i>p</i>_3/2 of Cu are presented for the face-centered-cubic AgPd and CuPd random alloys. The complete screening model, which includes both initial and final states effects in the same scheme, has been used in the investigations. </p><p>The alloys have been modeled with a supercell containing 256 atoms. Density-functional theory calculations are carried out using the locally self consistent Green's function approach. </p><p>Results from the calculations clearly shows that the core-level shift distributions characteristic is Gaussian, but the components reveals a substantial difference in the FWHM (Full-Width at Half-Maximum). Comparison between the experimental and the calculated broadening shows a remarkable agreement.</p>

<p>For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level.</p><p>A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only.</p><p>We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.</p>

<p>One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties.</p><p>Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS₅×S⁵ is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.</p>

<p>String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.</p>

<p>This thesis investigates aspects of field theories and soliton solutions with nontrivial topology. In particular we explore the following effective models: a limited sector of the scalar Electroweak theory called extended Abelian Higgs model, and a classical mechanics model derived from the low energy SU(2) Yang-Mills theory.</p><p>The extended Abelian Higgs model applied on two-component plasma of charged particles is studied numerically. We find evidence that the model admits straight twisted line vortices. The result is described by an energy function that acquires a minimum value for a non-trivial twist. In addition to the twisted line vortices the result also suggests that stable torus shaped solitons are solutions of the theory. </p><p>Furthermore we construct a classical mechanics model exhibiting some of the key properties of the low-energy Yang-Mills theory. The dynamics of the model is studied numerically. We find that its classical equations of motion support stable periodic orbits. In a three dimensional projection these trajectories are self-linked in a topologically non-trivial manner suggesting the existence of knotted configurations in low energy SU(2) Yang-Mills theory. </p><p>We calculate the one-loop effective action for the Abelian Higgs model with extended Higgs sector. The resulting first order quantum corrected model shows close resemblance to a modified model where texture stabilizing term has been added to the system. In the limit where the gauge field can be entirely expressed by the scalar fields, the both models become identical suggesting that the theories are closely connected. This implies that quantum corrections have stabilising effect on the soliton solutions. </p><p>These studies have contributed to a better understanding of the dynamics of non-linear low energy systems, and brought us a step closer to exploring full scale physically realistic models.</p>

<p>In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models.</p><p>The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first mentioned, it is still quite poorly understood. We discuss how tensionless strings give rise to exact solutions to supergravity and solve closed tensionless string theory in the ten dimensional maximally supersymmetric plane wave background, a contraction of AdS(5)xS(5) where tensionless strings are of great interest due to their proposed relation to higher spin gauge theory via the AdS/CFT correspondence.</p><p>For a sigma model, the amount of supersymmetry on its worldsheet restricts the geometry of the target space. For N=(2,2) supersymmetry, for example, the target space has to be bi-hermitian. Recently, with generalized complex geometry, a new mathematical framework was developed that is especially suited to discuss the target space geometry of sigma models in a Hamiltonian formulation. Bi-hermitian geometry is so-called generalized Kähler geometry but the relation is involved. We discuss various amounts of supersymmetry in phase space and show that this relation can be established by considering the equivalence between the Hamilton and Lagrange formulation of the sigma model. In the study of generalized supersymmetric sigma models, we find objects that favor a geometrical interpretation beyond generalized complex geometry.</p>