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- PostEffects of electron trapping and ion collisions on electrostatic shocks(2018) Sundström, Andréas; Chalmers tekniska högskola / Institutionen för fysik, Subatomär fysik och plasmafysik (Chalmers); Chalmers University of Technology / Department of Physics, Subatomic and Plasma Physics (Chalmers)Electrostatic shocks in plasmas have been observed to be able to accelerate particles to twice the shock velocity with a very low energy spread. Shock phenomena are often modeled as exactly collisionless, which is a very good approximation for astrophysical shocks. However, collisions might play a role in shocks created in laboratory plasmas, since very sharp features of the ion distribution function develop due to ions being reflected at the shock front; this ion reflection results in empty regions of phase space with discontinuities at their boundaries. In this thesis the effects of a weak but finite ion collisionality are considered in a time dependent, semi-analytical treatment. The amplitude of the downstream potential oscillation is found to increase approximately as the square root of time as particles are scattered into the originally empty regions of phase space. The corresponding changes in the electrostatic potential lead to an increased size of the trapping regions in the ion phase space. This thesis also studies the effect of electron trapping in the potential oscillations downstream of the shockfront. Two model electron distributions, which are flat in the trapped regions of phase space, are considered. The two models only differ in where the potential threshold for trapping is set; one model allows for trapping at a freely set threshold in order to emulate the effects of far downstream behavior of the shock, while the other model only allows for trapping inside the downstream potential oscillation. In general the effects of electron trapping are to reduce the maximum electrostatic potential, but at the same time increase the range of shock propagation speeds for which electrostatic shock solutions exist. The second electron trapping model also exhibits multiple shock solutions for the same temperature ratio and Mach number in certain parameter regions.
- PostGPU Implementation of the Feynman Path-Integral Method in Quantum Mechanics(2011) Carlsson, Kristoffer; Gren, Martin; Bohlin, Gustav; Holmvall, Patric; Säterskog, Petter; Ahlén, Olof; Chalmers tekniska högskola / Extern; Chalmers University of Technology / ExternalThe Path-Integral Formulation of Quantum Mechanics is introduced along with a detailed mathematical description of how it is used in quantum computations. The important concept of the kernel is explained, along with the free particle and harmonic oscillator as examples. Furthermore, the method for calculating expectation values of quantum operators is explained. The expectation values are naturally calculated by importance sampled Monte Carlo integration and by use of the Metropolis algorithm. This is due to the discretization of the path integral results in an integral with a high number of integration variables. The mathematical concepts of this calculation are explained. Also, a method for obtaining the probability density of the treated system is presented. The calculations are performed by a GPU, due to its high capabilities for numerical operations. This requires the mathematical computations to be parallelized and is done by use of the free software PyOpenCL. A thorough introduction to these concepts are given. The resulting ground state energies and probability densities for many particle systems interacting with harmonic as well as attractive and repulsive gaussian potentials are presented. The calculations worked exceedingly well for many particle systems. Source code is available at https://sourceforge.net/projects/ feynmangpu/files/
- PostSOFC Modeling in Femlab(2003) Nordelöf, Anders; Salsing, Christofer; Chalmers tekniska högskola / Institutionen för experimentell fysik; Chalmers University of Technology / Department of Experimental PhysicsThis report describes a graduate thesis project for the Master of Science diploma from the Engineering Physics program at Chalmers University of Technology. It has been performed at Volvo Technology Corporation with the primary aim to model a given Solid Oxide Fuel Cell design, the Rutquist cell, in Femlab. The model is intended to provide information on current-voltage characteristics, power development and the temperature profile, both during startup and operation. The secondary purpose was to evaluate the suitability of Femlab for this kind of task. The project was initiated with a bibliographic research, which gave several theories and parameters useful for modeling the different processes in the SOFC design. These models were then implemented in Femlab. Two separate modes were created where the startup and the operation of the cell respectively, were simulated. The cell was assumed to be a part of a larger system and receive hot gases from a fuel reformer. The heating in the startup process was achieved by letting warm gas, 1073 K, enter the electrodes via the gas channels. The chemical reactions were assumed to begin when all parts of the structure had reached 1023 K. The calculations showed that the heating to this temperature takes about one minute, and that most of the heat exchange takes place in the electrodes. The resulting temperature profiles from the operation mode model demonstrate that the temperature is in the same range as other SOFC structures and that the design is very compact. The dimensions of a cubic stack developing 10 kW at maximum power would be less than one cubic decimeter. The computational software Femlab has advantages, but also several shortcomings. Among the advantages are the flexibility in the module based system and the short learning period needed for solving simple problems. The weaknesses include the necessity of good knowledge of numerical solution methods, since many settings have to be adjusted when the models become more complex; especially the error report system is poor and occasionally even missing. The report also presents the theory of the physical and chemical processes ceramic fuel cells. Suggestions for improvements and the effects of the delimitations and approximations used in the modeling work are discussed. Finally, recommendations for future work are put forward.
- PostUndersökning av radiogalaxer i kartläggningen XXL-North(2017) Nilsson, Andreas; Krook, Christoffer; Tolliner, Lukas; Karlsson, Frida; Chalmers tekniska högskola / Institutionen för rymd-, geo- och miljövetenskap; Chalmers University of Technology / Department of Space, Earth and EnvironmentThis report aims at investigating two newly discovered radio galaxies in a 47 deg2 region of the sky labeled XXL-North. In the first step, a sensitive, high angular resolution radio map obtained with the Giant Meterwave Radio Telescope in India is scanned for interesting radio galaxies; in the second step, two of the found radio galaxies are analyzed in detail and additional data at radio frequencies and in other parts of the electromagnetic spectrum (X-ray, optical) are used. The spectral flux densities, spectral indices and spectral luminosities of the two radio galaxies are computed and related to their morphology. The host galaxies are identified and their redshifts and distances are established. Both have the same redshift z ' 0.14. The extents of the radio structures are, respectively, 35300 and 18000, which amounts to projected sizes of 850 kpc and 439 kpc, respectively. The derived luminosities are, respectively, (1.27 ± 0.13) · 1025 W Hz−1 and (6.30 ± 0.63) · 1024 W Hz−1. These are reasonable luminosity values for radio galaxies of morphological class FR II. Their structural appearance, with lobes containing distinct hot spots, supports this classification.