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An elliptic regularity theorem for fractional partial differential operators
(Computational and Applied Mathematics, 2018-09-01)
Avalanching on dunes and its effects: Size statistics, stratification, & seismic surveys
(University of CambridgeApplied Mathematics and Theoretical PhysicsSt. Catharine's College, 2018-10-20)
Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true ...
Spiral density waves and vertical circulation in protoplanetary discs
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2018-06-01)
Spiral density waves dominate several facets of accretion disc dynamics – planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, ...
A Variational Model for Joint Motion Estimation and Image Reconstruction
(Society for Industrial and Applied MathematicsSIAM Journal on Imaging Sciences, 2018-01)
The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set ...
Analytic solutions for reduced leading-edge noise aerofoils
(American Institute of Aeronautics and Astronautics2018 AIAA/CEAS Aeroacoustics Conference, 2018-01-01)
This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a piecewise linear periodic leading edge. The Wiener-Hopf method is used in conjunction ...
Modelling non-linear exposure-disease relationships in a large individual participant meta-analysis allowing for the effects of exposure measurement error
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 2012-10-09)
This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a
large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...
Extremal and probabilistic bootstrap percolation
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-11-12)
In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ...
Maximum likelihood parameter estimation in time series models using sequential Monte Carlo
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryDarwin College, 2013-06-11)
Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...
Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-10)
Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...
Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-02-05)
The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...