Thesis is submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the University of the Witwatersrand, Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2018 / Like any field or topic of research, significant advancements can be made with increasing computational
power - string theory is no exception. In this thesis, an analysis is performed within three areas: Calabi–Yau
manifolds, cosmological inflation and application of conformal field theory. Critical superstring theory is a ten
dimensional theory. Four of the dimensions refer to the spacetime dimensions we see in nature. To account
for the remaining six, Calabi-Yau manifolds are used. Knowing how the space of Calabi-Yau manifolds
is distributed gives valuable insight into the compactification process. Using computational modeling and
statistical analysis, previously unseen patterns of the distribution of the Hodge numbers are found. In
particular, patterns in frequencies exhibit striking new patterns - pseudo-Voigt and Planckian distributions
with high confidence and exact fits for many substructures. The patterns indicate typicality within the
landscape of Calabi–Yau manifolds of various dimensions. Inflation describes the exponential expansion of
the universe after the Big Bang. Finding a successful theory of inflation centres around building a potential
of the inflationary field, such that it satisfies the slow-roll conditions. The numerous ways this can be done,
coupled with the fact that each model is highly sensitive to initial conditions, means an analytic approach
is often not feasible. To bypass this, a statistical analysis of a landscape of thousands of random single and
multifield polynomial potentials is performed. Investigation of the single field case illustrates a window in
which the potentials satisfy the slow-roll conditions. When there are two scalar fields, it is found that the
probability depends on the choice of distribution for the coefficients. A uniform distribution yields a 0.05%
probability of finding a suitable minimum in the random potential whereas a maximum entropy distribution
yields a 0.1% probability. The benefit of developing computational tools extends into the interdisciplinary
study between conformal field theory and the theory of how wildfires propagate. Using the two dimensional
Ising model as a basis of inspiration, computational methods of analyzing how fires propagate provide a new
tool set which aids in the process of both modeling large scale wildfires as well as describing the emergent
scale invariant structure of these fires. By computing the two point and three point correlations of fire
occurrences in particular regions within Botswana and Kazakhstan, it is shown that this proposed model
gives excellent fits, with the model amplitude being directly proportional to the total burn area of a particular
year. / EM2018
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/25803 |
| Date | January 2018 |
| Creators | Pontiggia, Luca Terzio |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (xix, 173 leaves), application/pdf |
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