Fraunhofer Chalmers Research Centre for Industrial Mathematics
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Artins förmodan: p-adiska tal, ändliga kroppar och ekvationer utan heltalslösningar
No full textThis paper is based on Artin's conjecture concerning homogeneous polynomial equations.
The conjecture is false in general but it is still true in many cases. One of our goals is to
motivate why the conjecture is formulated the way it is. Moreover, we present a counterproof
to the conjecture and we prove the conjecture in one specific case. We construct the p-adic
numbers as the conjecture is expressed in terms of p-adic numbers and we introduce theory
on finite fields, as it is needed in the motivation of the conjecture, the counterproof and in the
proof of the specific case
Att mäta SVT-program
No full textThe purpose of this study is to examine whether or not the concept of informational
advantage in series has a correlation with the popularity of the series. Informational advantage
as a dramaturgical tool means that the viewer, at any given point throughout the series, either
knows more, less or the same amount as the character in the show; these stages are called
dramatic irony, mystery, and suspence respectively. Three different questions were examined.
The time spent in one stage before switching to the next is examined with an Anderson-Darling
test to see if it fits any statistical distribution, and if there is a difference between series with
high and low viewership numbers. The conclusion is that it cannot be rejected that the time
follows a log-normal distribution and that the expected time a program will spend in one stage
before switching is shorter in programs with high viewership numbers. Furthermore, whether
the total percentage of time spent in the different stages has a linear relationship with the
viewership numbers is examined with linear regression using the method of least squares. With
the collected data it was difficult to make a definitive conclusion, however the data implies that
the relationship is stronger for the time spent in dramatic irony and viewership numbers, than
the relationship for mystery. The relationship is especially stronger for the online viewership.
Lastly it is examined whether the percentage of switches between the different states has a
linear relationship with the viewership numbers, also with the method of least squares. The
result points towards switches between dramatic irony and suspence correlating positively with
viewership, while switches between mystery and suspence seem to correlate negatively with
viewership
Hårdvaruutveckling på en autonom formelbil
No full textThe autonomous driving industry is currently growing rapidly due to the large demand
created by our society. Formula student, the largest student engineering contest
in the world, assesses the automobile production by developing and competing
with formula cars. Formula student driverless is one of the branches of the large
competition, Chalmers University of Technology is one of the represented universities
with two attending teams. The role of this bachelor’s group is to be a part of
the 2019 Chalmers formula student driverless team and maintain and develop the
hardware of the car.
The thesis is separated into three different sections, where each section describes
a problem solving process. The sections are: the aerodynamic package, the steering
actuation and the computer case.
The aerodynamic package was designed for a formula car driven manually at a
different speed than the current autonomous system. Therefore, an analysis of the
current aerodynamic package was performed. The results were generated through
simulation methodologies and it was decided that the aerodynamic package was sufficiently
valuable to the car’s performance.
To analyse the steering actuation, tests were made comparing sent steering requests
to readings of potentiometers mounted on the linear actuator and on the steering
rack. The conclusion was that the steering system had drawbacks such as play and
complexity, but it was kept since it is robust and the time needed to rebuild the
system could not be justified.
The computer case’s function is to protect the computer from water and dust while
also enabling cooling of the components. The case created in 2018 was deemed
inadequate for the competition. Therefore a new case where developed to replace
the old one. Different concepts were generated and condensed into a final prototype
which was manufactured. The final product fulfilled the requirements to confine the
computer in a water and dust proof casing.
By implementing a quantitative and qualitative analysis of the three projects, a
conclusion was drawn deciding that the aerodynamic package was the most valuable
project to score points in the formula student driverless competition. All things
considered, the entire result generated an advantageous score to the competition
Electrification of the heat treatment process for iron ore pelletization at LKAB
No full textLKABisaSwedishstate-ownedminingcompanythatextractsandrefinesironoreforthe global steel industry. Their main product is iron ore pellets which accounts for around 83 % of LKAB’s iron ore products. The straight-grate process is used for heat treatment of the pellets and is the most energy-intensive part of the refining process. The heat is supplied by fossil fuel burners with considerable emissions of greenhouse gases and pollutants such as nitrogen oxides, which should be reduced to comply with emission targets set by LKAB as well as the Swedish government.
This project investigates electrical heating alternatives in the form of plasma torches and microwaves to replace the fossil fuel burners, providing potential for a CO2-neutral productionprocess. Theworkfocusonhowprocessconditionsareaffectedwhenswitchingto anelectricheatsource. Processperformanceisevaluatedthroughproductquality, energy efficiency, emissions of CO2 and NOx. Furthermore, new potential process optimization measures as a result of the implementation of electric heating are discussed. A previously established process model of the straight-grate process was used to establish a reference case and several new cases where modifications were made to simulate the implementation of electric heating. NOx emissions from plasma torches were studied by reaction modelling in Chemkin and results were evaluated against data from previous practical experiments.
Results showed that electric heating through microwaves may supply energy at low temperature to the drying process, which would allow for a more compact drying zone and replacement of up to 1 MW of fossil fuels. However, the total power demand of the process increased by 15 - 20 %. To supply heat at the high temperature required in the firing zones, plasma torches have the potential to replace the entire fossil fuel demand and achieve a CO2 neutral process. The implementation of plasma torches only had a slight effect on pellet quality and energy efficiency. Simulations regarding NOx emissions from plasma torches when mixing hot plasma gases with air shows that the formation of NOx may be higher than from a fossil fuel burner. The most important factor for determining the NOx emissions is the gas residence time at high temperatures. Reburning using small amounts of natural gas was the most efficient NOx reduction strategy with NOx reduction of up to 65 %. Future work should be directed towards financial analyses of the implementation of electric heating and experimental tests to prepare for practical implementation
