DSpace Collection:http://theses.ncl.ac.uk/jspui/handle/10443/53742024-02-04T02:46:38Z2024-02-04T02:46:38ZThe strong-field regime of the geodynamoMason, Stephen Jameshttp://theses.ncl.ac.uk/jspui/handle/10443/60252024-01-24T12:07:16Z2023-01-01T00:00:00ZTitle: The strong-field regime of the geodynamo
Authors: Mason, Stephen James
Abstract: The Earth’s magnetic field is generated in the Earth’s outer core from convective
motions via a dynamo mechanism. Convective flows in the Earth’s core are under the
influence of magnetic forces strong enough to significantly affect their dynamics (known
as being in the “strong field regime”). The aim of this PhD work is to explore the strong
field regime using magnetoconvection, where a magnetic field is externally imposed on the
convective system.
We are studying the effect of an imposed uniform axial field on convection in a rapidlyrotating spherical shell. The numerical code Parody has been used to run simulations of
thermal convection and magnetic field generation, with increasing imposed magnetic field
strength B0.
In the first part of this thesis, we consider the effect of the imposed field on the
onset of convection, finding three regimes classified via the corresponding force balance
(rotationally-dominated, magnetically-dominated, and a MAC balance, in which the Coriolis, Lorentz and buoyancy forces are the dominant terms). Critical parameters including
the Rayleigh number and azimuthal wavenumber are reduced when the strength of the imposed field is of order one, which corresponds to an Elsasser number (the ratio of Lorentz
and Coriolis forces) of unity. We explore the changes in the flow for more supercritical values of the Rayleigh number. We find that strong zonal flows form for intermediate values
of B0 for Rayleigh numbers a few times critical, driven by magnetic and thermal winds
as a result of more efficient heat transfer in the equatorial region. We also investigate the
mechanisms of magnetic field generation, finding that the induced magnetic field supports
the imposed field when the imposed field has strength of order one. We find that the
lengthscales involved in the production of the axisymmetric field vary with the strength of
the imposed field, with small scales being involved in the rotationally-dominated regime
and large scales in the MAC regime.
In the second part of the thesis, we study the effects of varying the magnetic Prandtl
number. We first focus on the effects of the imposed field on the flow at the onset of
convection. Here we find further changes in the critical parameters: magnetoconvection at
low Pm require significantly stronger field strengths than at high Pm for the magnetic field
to influence the onset of convection, and appears to depend on Λ0 = PmB2
0
, rather than
Pm and B0 individually. The reduction of the critical Rayleigh number is more marked
at high Pm, and there is also a more drastic reduction in the azimuthal wavenumber mc
compared to Pm ≤ 1. For high Pm, we establish a correlation between the axial vorticity
and induced axial field; for example, we find that there is a strong asymmetry between
the cyclones and anticyclones at onset. When considering values of the Rayleigh number
away from the onset, we find that the induced axisymmetric poloidal field opposes the
imposed field at high Pm.
Description: Ph. D. Thesis.2023-01-01T00:00:00ZThe irreducible representations of rational Cherednik algebras associated to the symmetric groups S2 and S3 in positive characteristicBarnes, Jordanhttp://theses.ncl.ac.uk/jspui/handle/10443/60042024-01-12T15:10:45Z2023-01-01T00:00:00ZTitle: The irreducible representations of rational Cherednik algebras associated to the symmetric groups S2 and S3 in positive characteristic
Authors: Barnes, Jordan
Abstract: Let k be an algebraically closed field of positive characteristic p. Given parameters
t, c ∈ k we form the rational Cherednik algebra Ht,c(Sn, h) for n = 2, 3 and consider its
representation theory over k. For each irreducible representation τ of Sn there is a Verma
module Mt,c(τ ) which is a module for Ht,c(Sn, h) and this module has a unique maximal
proper graded submodule Jt,c(τ ). The quotient Mt,c(τ )/Jt,c(τ ) is a graded, irreducible
representation Lt,c(τ ) of Ht,c(Sn, h) in category O and all simple objects in O are of this
form. Our goal is to describe the representations Lt,c(τ ) for all possible values of p, t, c,
and τ , by calculating their characters, Hilbert polynomials, and specifying the generators
of Jt,c(τ ). We achieve this goal, filling gaps in the literature and describing these modules
completely and explicitly, in all cases except one where we provide a conjecture.
Description: PhD Thesis2023-01-01T00:00:00ZConfined Bose superfluids: a study of vorticity in a rotating bucket, and phase transitions and sound in a trap from two to three dimensionsKeepfer, Nickhttp://theses.ncl.ac.uk/jspui/handle/10443/59682023-12-04T11:25:28Z2022-01-01T00:00:00ZTitle: Confined Bose superfluids: a study of vorticity in a rotating bucket, and phase transitions and sound in a trap from two to three dimensions
Authors: Keepfer, Nick
Abstract: Quantum fluids are a fascinating state of matter, permitting extraordinary insights into the
behaviour of macroscopic quantum systems. Most strikingly, they possess the property of
superfluidity, enabling inviscid flow. Whilst irrotational in nature, singularities in the fluid
provide localised vorticity in the form of quantised vortex filaments. Interaction between
these vortex structures provides rich dynamical behaviour which is interrogated within the
first part of this thesis. Furthermore, one expects the equilibrium and dynamical proper ties of a trapped superfluid system to vary in response to changes in dimensionality.
Whilst dimensionality crossovers have previously been considered both experimentally and
theoretically, the nature of the dimensional crossover between the 2D and 3D phase tran sitions in a trapped Bose gas remains relatively unexplored and forms the secondary focus
of this thesis.
Initially, we consider the effects of disordered potentials, protuberances and remnant vor tices for a zero temperature weakly interacting Bose gas under rotation. Focusing partic ularly on a rough bucket potential we draw parallels with superfluid helium experiments,
where such effects must be considered. Our findings elucidate important insights on the
effects of vortex proliferation in the spin-up dynamics of a quiescent system towards the
simple and well-reproduced vortex lattice structure.
We then go on to discuss the effects of dimensionality on the finite temperature weakly
interacting Bose gas, this time concentrating on a hybridised optical trap that allows one
to modify the trapping strength along a singular direction. Utilising the stochastic pro jected Gross-Pitaevskii equation (SPGPE) we validate our approach based on previous
findings at the dimensional extremes before considering in greater detail, the precise na ture of the crossover region. We introduce a novel mixed basis numerical scheme to solve
the SPGPE in the hybridised geometry. Using this, we identify and numerically extract a
phase transition temperature as a function of dimensionality using a collection of equilib rium statistics. Building on this work, we subsequently conduct a numerical investigation
into the propagation of sound as a function of dimensionality in the trapped Bose gas.
We discover new insights on the properties of the sound across the phase transition at the
dimensional extremes. We then extend our work into the dimensionality crossover region,
paying particular attention to the behaviour of the sound at the phase transition critical
point.
Description: PhD Thesis2022-01-01T00:00:00ZFunctional Data Analysis for Earth ObservationAustin, Julianhttp://theses.ncl.ac.uk/jspui/handle/10443/59522023-11-29T11:04:18Z2022-01-01T00:00:00ZTitle: Functional Data Analysis for Earth Observation
Authors: Austin, Julian
Abstract: Earth observation data, that is data observed over the surface of the earth, is often
characterised by its spatial and temporal dependency. Such datasets are being collected
more frequently and over larger spatial domains as remote sensing and in-situ collection
methodologies become more sophisticated. However, they often include large amounts of
missing observations. There is a high demand for models which can help interpret and
interpolate to aid in the use of these datasets for a vast array of disciplines. Often the
most challenging aspect of such data is how to interpolate missing observations. In this
work, we consider such datasets from a functional data perspective. In particular, we focus
on methods which can help explain the datasets variation in a parsimonious way whilst
maintaining predictive accuracy for missing observations.
We begin by discussing the current methods available to earth observation datasets
from both a spatio-temporal and functional data perspective. Following this, we introduce
an interim functional time series model, based on a functional data decomposition which
considers the spatial dimension as our functional domain. We discuss the consequences of
taking this approach from a practical perspective.
Finally, we develop a novel framework which treats the temporal dimension as the
functional domain. We maintain parsimony by basing this model on the main modes
of variation using a functional principal components analysis and incorporate spatial
dependency between functional observation using a structured Gaussian process. We
present the validity of this methodology under spatial correlation of the observed data and
evidence the ability of this framework using various spatial dependency models on both a
simulation and real world study. We show that such a model performs well on sparsely
observed datasets and also highlight the approaches used to make the model applicable to
large datasets.
Description: PhD Thesis2022-01-01T00:00:00Z