DSpace Collection:http://theses.ncl.ac.uk/jspui/handle/10443/892023-03-30T02:03:40Z2023-03-30T02:03:40ZMagnetohydrodynamics in hot JupitersHindle, Alexander Williamhttp://theses.ncl.ac.uk/jspui/handle/10443/54652022-06-24T14:04:04Z2021-01-01T00:00:00ZTitle: Magnetohydrodynamics in hot Jupiters
Authors: Hindle, Alexander William
Abstract: Hot Jupiters are Jupiter-like exoplanets found in close-in orbits. This subjects them
to high levels of stellar irradiance and is believed to tidally-lock them to their host stars,
causing extreme day-night temperature differentials which in-turn drive atmospheric dynamics. A ubiquitous feature of hydrodynamic models of hot Jupiter atmospheres is
equatorial superrotation, which advects their hotspots (equatorial temperature maxima)
eastwards (prograde). Observational studies generally find eastward hotspot/brightspot
offsets. However, recent observations of westward hotspot/brightspot offsets suggest that
this is not ubiquitous. Prior to these observations, three-dimensional magnetohydrodynamic simulations predicted that westward hotspots could result from magnetohydrodynamic effects in the hottest hot Jupiters, yet the mechanism driving such reversals is not
well understood.
We study the underlying physics of magnetically-driven hotspot reversals using a
shallow-water magnetohydrodynamic model. This captures the leading order physics
of hot Jupiter atmospheres, but with reduced mathematical complexity. The model’s
hydrodynamic counterpart is well-established and has successfully been used to explain
equatorial superrotation in hydrodynamic models of hot Jupiter atmospheres in terms of
planetary scale equatorial wave interactions. However, until now, shallow-water magnetohydrodynamic models have not been applied to hot Jupiters. Firstly, we find that the
model can indeed capture the physics of magnetically-driven hotspot reversals. We use
non-linear numerical simulations to understand the dominant force balances that drive
the reversals and use a linear analysis of the system’s planetary scale equatorial waves to
understand the reversal mechanism in terms of wave interactions. We then use the developed theory to place physically motivated observational constraints on the magnetic field
strengths of hot Jupiters exhibiting westward hotspot/brightspot offsets, finding that on
the hottest of these the observations can be explained by moderate planetary magnetic field
strengths. Finally, we identify candidates that are likely to exhibit magnetically-driven
hotspot reversals to help guide future observational missions.
Description: PhD Thesis2021-01-01T00:00:00ZBayesian optimal design using stochastic gradient optimisation and surrogate utility functionsHarbisher, Sophiehttp://theses.ncl.ac.uk/jspui/handle/10443/53612022-04-07T13:59:11Z2021-01-01T00:00:00ZTitle: Bayesian optimal design using stochastic gradient optimisation and surrogate utility functions
Authors: Harbisher, Sophie
Abstract: Experimental design is becoming increasingly important to many applications from genetic
research to robotics. It provides a structured way of allocating resources in an e cient
manner prior to an experiment being conducted. Assuming a model for the data, one
approach is to introduce a utility function to quantify the worth of a design given some
data and parameters. Typically experiment-speci c utility functions are di cult to elicit
and hence a pragmatic choice of utility concerning the information gained about the model
parameters is used. Bayesian experimental design aims to maximise the expected utility
accounting for uncertainty in the model parameters and the data which could be observed.
For this approach, di culties arise as the expected utility is typically intractable and
computationally costly to approximate.
Modern applications often seek high dimensional designs. In these settings existing
algorithms such as the MCMC scheme of Müller (1999) and ACE (Overstall and Woods,
2017), require a high number of utility evaluations before they converge. For the most
commonly used utility functions this becomes a computationally costly exercise.
Therefore there is a need for an e cient and scalable method for nding the Bayesian
optimal design.
The contributions of this thesis are as follows. Firstly, stochastic gradient optimisation, a
scalable method widely used in the eld of machine learning, is applied to the Bayesian
experimental design problem. The second contribution is to consider a utility function
based on the Fisher information matrix as a Bayesian utility function by showing it has a
decision theoretic justi cation. These utilities are often available in a closed-form so are
fast to compute. The nal contribution is to investigate surrogate functions for expensive
utilities as an e cient way of nding promising regions of the design space.
Description: PhD Thesis2021-01-01T00:00:00ZModelling Voxel Dependent Hemodynamic Response FunctionFletcher, Darrenhttp://theses.ncl.ac.uk/jspui/handle/10443/53202022-03-18T14:49:04Z2020-01-01T00:00:00ZTitle: Modelling Voxel Dependent Hemodynamic Response Function
Authors: Fletcher, Darren
Abstract: An important challenge of contemporary neuroscience is the detection and understanding of significant brain activity using functional
magnetic resonance imaging (fMRI). One of the many motivations of
this research, related to the data set used in this thesis, is to investigate brain activation and connectivity patterns aimed at identifying
associations between these patterns and regaining motor functionality following a stroke. Much statistical modelling has attempted to
interpret noisy fMRI data and detect changes in response to activity.
However due to the large data sets usually involved in fMRI modelling,
here as many as 150, 000 measurements in localised spatial volumes
known as voxels at each time point, many simplifying assumptions are
usually made to make computation feasible. This is known to have a
negative impact on detecting voxel activation. In this work we fit a
space-time model to a fMRI data set using a sequential approach to
allow for scalability. However, the main contribution of this work is
an alternative method to detect activation in the brain. Here we take
the novel approach of using topological data analysis to investigate
the model residuals to detect changes in the fMRI data. In particular
we analyse the spatial distribution of topological features of the residuals to provide a test for normality, and also by providing a method
to analyse how the spatial distribution of such features change over
time, we are able to detect changes in the data in response to activity
where conventional methods cannot. A recommendation for future
work is to also investigate how topological features change for different filtration levels of the field, as this may provide new insights on
brain activation.
Description: Ph. D. Thesis.2020-01-01T00:00:00ZBayesian inference for linear stochastic differential equations with application to biological processesMcLean, Ashleigh Taylorhttp://theses.ncl.ac.uk/jspui/handle/10443/53112022-03-04T16:15:57Z2020-01-01T00:00:00ZTitle: Bayesian inference for linear stochastic differential equations with application to biological processes
Authors: McLean, Ashleigh Taylor
Abstract: Stochastic differential equations (SDEs) provide a natural framework for describing the
stochasticity inherent in physical processes that evolve continuously over time. In this
thesis, we consider the problem of Bayesian inference for a specific class of SDE – one
in which the drift and diffusion coefficients are linear functions of the state. Although
a linear SDE admits an analytical solution, the inference problem remains challenging,
due to the absence of a closed form expression for the posterior density of the parameter
of interest and any unobserved components. This necessitates the use of sampling-based
approaches such as Markov chain Monte Carlo (MCMC) and, in cases where observed data
likelihood is intractable, particle MCMC (pMCMC). When data are available on multiple
experimental units, a stochastic differential equation mixed effects model (SDEMEM) can
be used to further account for between-unit variation. Integrating over this additional
uncertainty is computationally demanding.
Motivated by two challenging biological applications arising from physiology studies
of mice, the aim of this thesis is the development of efficient sampling-based inference
schemes for linear SDEs. A key contribution is the development of a novel Bayesian
inference scheme for SDEMEMs.
Description: Ph. D. Thesis.2020-01-01T00:00:00Z