Mastergradsoppgaver i matematikk
http://hdl.handle.net/10037/225
2018-02-16T14:13:25ZOn the Ewald-Oseen scattering formulation for linear and nonlinear transient wave scattering
http://hdl.handle.net/10037/11305
Kuzmina, Anastasiia<br />
In this thesis work we develop and apply EOS formulation to three scattering problems:
two of them are 1D problems and one is 2D. The first chapter comprises EOS
formulations and numerical implementation for 1D scattering problems.
Also in this chapter we use different numerical methods to solve test problem and
choose the most stable and accurate method for solving of the given 1D problems.
In the second chapter we discuss EOS formulation for 2D scattering problem.<br />
2017-05-16T00:00:00ZAlmost affine codes and matroids
http://hdl.handle.net/10037/11301
Diachkov, Konstantin<br />
In this thesis we study various types of block codes, like linear, mutlti-linear, almost affine codes. We also look at how these codes can be described by associated matroids. In addition we look at flags (chains) of codes and see how their behavior can be described using demi-matroids. We also introduce weight polynomials for almost affine codes.<br />
2017-05-15T00:00:00ZA complex contour based perfectly matched layer applied to a pattern generating model equation.
http://hdl.handle.net/10037/10841
Jenssen, Amund<br />
The observable universe consists of several non equilibrium systems that generate spatiotemporal behaviour in the form of various patterns. As the elementary laws of physics and chemistry are unable to explain the pattern forming behaviour of such systems, scientists have turned to desktop experiments and model equations to gain further insight. The model equations that generate numerical solutions similar to real world systems are computationally intensive, and this thesis discusses the possibility of designing a numerical scheme which are to reduce the computation time for a specific model equation.
The design is based on the perfectly matched layer (PML), a mathematical-numerical technique that works as an artificial absorbing layer within the discretized grid boundaries.
The thesis discuss how to impose a PML version of the model equation into the numerical method of lines(MOL) procedure, and various numerical and mathematical techniques are discussed in order to build this scheme.
The numerical simulations for the PML-equation fail to produce the correct spatiotemporal behaviour, and the discussed analysis states that a PML does not apply to the model equation discussed in the thesis.<br />
2017-02-17T00:00:00ZSeparable representations of the Poisson, Helmholtz and complex Helmholtz kernels
http://hdl.handle.net/10037/10840
Bjørgve, Magnar<br />
For high accuracy applications of integral operators in higher dimensions the
complexity of operation and storage usually grows exponentially with dimensions.
One method that has proven successful for handling these difficulties are the
separation of the integral kernels as linear combinations of products of
one-dimensional kernels, commonly referred to as separation of variables.
In this thesis we optimize the existing separable forms of the Poisson and
complex Helmholtz kernels used in the program package MRCPP. We then find a new
separable representation of the (non-complex) Helmholtz kernel.<br />
2017-02-15T00:00:00ZInsulating the Vacuum. Calculating the Casimir force using the boundary integral method with von Neumann boundary conditions
http://hdl.handle.net/10037/9778
Utheim, Marius<br />
In 2012, a new method for calculating the Casimir force between compact objects was developed, expressing the force in terms of a boundary integral equation. The case of perfectly conducting objects with Dirichlet boundary conditions in two dimensions was treated by Isak Kilen. The method was later extended to three dimensions by Karl Øyvind Mikalsen.
The contribution of this thesis will be to develop the method in two dimensions for the case when the objects are perfectly insulating, meaning von Neumann boundary conditions. A formula for the Casimir force in terms of a boundary integral problem is derived and shown to correctly predict the force between two parallel plates, except for a missing factor of 2 that was also observed for Dirichlet boundary conditions. The developed formula contains a coefficient that is dependent on the regularization scheme used, and it is not clear whether this coefficient is geometry-independent.<br />
2016-08-15T00:00:00ZModelling laser-matter interactions using resonant states
http://hdl.handle.net/10037/9300
Juhász, Dávid<br />
Studying how light interacts with materials has become important for many technological applications from optical communication to developing of new materials. Therefore scientists have always tried to improve their understanding of these effects. The primary goal has always been to microscopically describe the pertinent processes. This paper provides a brief introduction into the interactions of atoms with laser fields. Precisely this interaction, photoelectric effect and the blackbody radiation were those findings which started off the development of quantum mechanics. This theory allowed better description of atoms and it will be used in this work to handle the problem we are confronting. We will consider two of the simplest potentials and let the atom interact with a strong laser pulse in these potentials. From this interaction the so called resonant states will arise. The goal of this thesis is to investigate to what extent and in what meaning these resonant states form a complete set of functions and consequently can be used for expansion of atomic states of physical importance.<br />
2016-05-12T00:00:00ZHigh frequency financial time series prediction: machine learning approach
http://hdl.handle.net/10037/9255
Zankova, Ekaterina<br />
Machine learning is a rapidly evolving subfield of computer science. It has enormous amount of applications. One of the application domains is financial data analysis. Machine learning was usually applied for analysis and forecasting of daily financial time series. Availability of high frequency financial data became another challenge with its own specifics and difficulties. Regressors, being a significant part of machine learning field, have been selected as study subjects for this project. The purpose of this research is to apply machine learning techniques for predicting high frequency financial time series. Experiments are conducted using several regressors which are evaluated with respect to prediction quality and computation cost. The obtained results were analysed in order to reveal parameter combination for particular regressor that yields the best results according to chosen performance criteria.<br />
2016-05-13T00:00:00ZModelling the evolution of ideal, infinite domain patterns, on a finite domain using a Perfectly Matched Layer
http://hdl.handle.net/10037/9192
Antrushin, Andrey<br />
The Swift-Hohenberg equation is an evolution equation which can produce a Pattern, or a pattern-like picture, to be more precise. For example, it could be used to model some simple natural patterns, like stripes and rolls that one may observe in a Rayleigh-Benard convection experiment.
But for any pattern formation obtained by an evolution equation to look ideal, we have to consider this equation analytically on the infinite domain. If one wants to calculate and present the results numerically, the problem has to be discretized, the number of steps turns out to be finite then, and at some point the lateral boundaries appear. These boundaries cause a backward reflection and destroy the pattern eventually.
The idea of using a Perfectly Matched Layer in order to obtain some reflectionless boundaries was suggested. It should let us model the evolution of an ideal, infinite domain pattern, on an actual finite domain. From a set of numerical methods the most suitable ones will be chosen. The MATLAB environment is used to write a code to visualise the results.
Any investigations that could concern the fact of applying a Perfectly Matched Layer to an evolution Swift-Hohenberg equation seem to be absolutely new and yet untouched. This Thesis might be considered as a first step, as an introduction to the problem and its possible solutions.<br />
2016-01-28T00:00:00ZThe Unidirectional Pulse Propagation Equation for Cylindrical Vector modes
http://hdl.handle.net/10037/7996
Nilsen, Vegard<br />
A new model for the unidirectional pulse propagation equations (UPPE) was developed by Per Jacobsen[1], this model is based on the assumption of cylindrical vector (CV) modes. The model will be strong for CV type electrical eld representations where only a few modes will be excited. In this thesis we will investigate the model further. The model will be implemented as a pseudo spectral method where both the Fourier and Hankel transform are necessary.<br />
2015-07-27T00:00:00ZArctic tipping points
http://hdl.handle.net/10037/7763
Smolkova, Valentina<br />
The Arctic is warming much faster than the entire planet, and this causes severe melting of sea ice. However, the climate of different regions of the Earth is interconnected, and changes in the amount of ice in the Arctic can dramatically affect the climate across the whole planet. Some scientists claim that a possible tipping point is the event of the ice-free Arctic Ocean in summer. Certain predictions point towards ice-free Arctic summers around the year 2050, whereas others pre- dict this will occur in 2016. There are also others arguing that only a year-round sea ice loss can represent a tipping point in the Arctic. The disagreement between scientists on this topic is an indication that more detailed studies of tipping points are needed to be done.
In this thesis, we use five different models to explore possible tipping points of sea ice loss in the Arctic Ocean. The results show that the tipping point will most probably occur between years 2017 and 2021, with sea ice loss average from 11 million km sq to 4 million km sq during one seasonal cycle.<br />
2015-05-15T00:00:00Z