Fraunhofer Chalmers Research Centre for Industrial Mathematics
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Modelling Methanol Content in Condensates From a Black Liquor Evaporation Plant. A case study of the SCA Östrand pulp mill
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Needs that commercial tenants have regarding future services - A case study at Platzer Fastigheter AB
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Om Gelfand-dualiteten
No full textDetta kandidatarbete är en litteraturstudie inom matematik och specifikt i Gelfand-teori, som huvudsakligen berör kommutativa Banach-algebror. Inledningsvis introduceras notation för algebra och topologi. Därefter följer teoridelen, där spektrum, modulära ideal och multiplikativa linjära funktionaler studeras enskilt för att sedan relateras till varandra. Gelfand-transformen, som kan betraktas som en generalisering av Fouriertransformen, introduceras och kraven för att denna ska vara en, så kallad, isometrisk ∗-isomorfi presenteras med tillhörande bevis. Resultatet kallas för Gelfand-dualiteten och leder till en koppling mellan C∗-algebror och lokalt kompakta Hausdorff-rum. Vid sidan av den rent teoretiska presentationen illustreras många resultat med hjälp av exempel
Spin Dependent Discrimination between Majorana and Dirac Dark Matter
No full textA large number of observations reveal deviations from expected gravitational behaviour
in astrophysical systems. This suggests that something is missing in our
understanding of the Universe. A well established candidate for explaining these
deviations is dark matter, a kind of matter that is not subject to photon interactions
and thus can not be detected by absorbed or emitted light - it is dark. Even
though we can not observe it at any detectable wavelength, dark matter is postulated
to interact via gravitation. These interactions would then account for the
shortcoming of gravitational pull from visible mass, explaining the observed irregular
gravitational behaviour. One leading hypothesis is that the proposed dark matter
component of the Universe is actually made out of massive, weakly interacting particles.
As of today, there has not yet been any detection of such a particle, leaving
the fundamental properties of dark matter unknown.
There are currently several ongoing experimental projects searching for dark matter
particles, and more are being planned. Furthermore, their accuracy is higher
than ever, and if the dark matter particle hypothesis is correct, it is reasonable
to expect a detection signal in the foreseeable future. The different searches take
complementary approaches and exploit either annihilation, production or direct detection
experiments. The latter, which is the focus of this thesis, aims to detect
dark matter by measuring the recoil of a target nucleus in a detector when a dark
matter particle scatters off of it. In case of positive detection at direct detection
experiments, a model describing the interaction between dark matter particles and
baryonic matter is needed in order to be able to draw conclusions about the dark
matter particle properties.
Under the assumption that dark matter is a spin 1/2 particle that only interacts
with baryonic matter via spin dependent interactions, this thesis studies dark
matter-nucleus scattering in order to see if it is feasible to discriminate between
Majorana and Dirac dark matter. I find that, if dark matter particles are detected
at three different experiments, the Majorana dark matter hypothesis can be rejected
in favour of an alternative hypothesis in which dark matter is a Dirac particle. Restrictions
on target elements that are of interest for this test are presented, and the
test procedure is studied for setups containing some of them, namely: 131Xe, 127I,
73Ge, 23Na and 19F