## Mathematics MSc dissertations

The Department of Mathematics and Statistics was host until 2014 to the MSc course in the Mathematics of Scientific and Industrial Computation (previously known as Numerical Solution of Differential Equations) and the MSc course in Mathematical and Numerical Modelling of the Atmosphere and Oceans. A selection of dissertation titles are listed below, some of which are available online:

2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

### 2014: Mathematics of Scientific and Industrial Computation

Amanda Hynes - Slow and superfast diffusion of contaminant species through porous media

### 2014: Applicable and Numerical Mathematics

Emine Akkus - Estimating forecast error covariance matrices with ensembles

Rabindra Gurung - Numerical solution of an ODE system arising in photosynthesis

### 2013: Mathematics of Scientific and Industrial Computation

**Zeinab Zargar** - Modelling of Hot Water Flooding as an Enhanced Oil Recovery Method

**Siti Mazulianawati Haji Majid** - Numerical Approximation of Similarity in Nonlinear Diffusion Equations

### 2013: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**Yu Chau Lam **- Drag and Momentum Fluxes Produced by Mountain Waves

**Josie Dodd **- A Moving Mesh Approach to Modelling the Grounding Line in Glaciology

### 2012: **Mathematics of Scientific and Industrial Computation**

**Chris Louder - Mathematical Techniques of Image Processing**

**Jonathan Muir - Flux Modelling of Polynyas**

**Naomi Withey - Computer Simulations of Dipolar Fluids Using Ewald Summations**

### 2012: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**Jean-Francois Vuillaume - Numerical prediction of flood plains using a Lagrangian approach**

### 2011: **Mathematics of Scientific and Industrial Computation**

**Tudor Ciochina - The Closest Point Method**

**Theodora Eleftheriou - **Moving Mesh Methods Using Monitor Functions for the Porous Medium Equation

**Melios Michael - Self-Consistent Field Calculations on a Variable Resolution Grid**

### 2011: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**Peter Barnet - Rain Drop Growth by Collision and Coalescence**

**Matthew Edgington - Moving Mesh Methods for Semi-Linear Problems**

**Samuel Groth - **Light Scattering by Penetrable Convex Polygons

**Charlotte Kong - Comparison of Approximate Riemann Solvers**

**Amy Jackson - Estimation of Parameters in Traffic Flow Models Using Data Assimilation**

**Bruce Main - Solving Richards' Equation Using Fixed and Moving Mesh Schemes**

**Justin Prince -** Fast Diffusion in Porous Media

**Carl Svoboda - **Reynolds Averaged Radiative Transfer Model

### 2010: **Mathematics of Scientific and Industrial Computation**

**Tahnia Appasawmy - Wave Reflection and Trapping in a Two Dimensional Duct**

**Nicholas Bird - Univariate Aspects of Covariance Modelling within Operational Atmospheric Data Assimilation**

**Michael Conland **- Numerical Approximation of a Quenching Problem

**Katy Shearer - Mathematical Modelling of the regulation and uptake of dietary fats**

**Peter Westwood - A Moving Mesh Finite Element Approach for the Cahn-Hilliard Equation**

**Kam Wong - Accuracy of a Moving Mesh Numerical Method applied to the Self-similar Solution of Nonlinear PDEs**

### 2010: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**James Barlow - Computation and Analysis of Baroclinic Rossby Wave Rays in the Atlantic and Pacific Oceans**

**Martin Conway** - __Heat Transfer in a Buried Pipe__

**Simon Driscoll - The Earth's Atmospheric Angular Momentum Budget and its Representation in Reanalysis Observation Datasets and Climate Models**

**George Fitton - A Comparative Study of Computational Methods in Cosmic Gas Dynamics Continued**

**Fay Luxford - Skewness of Atmospheric Flow Associated with a Wobbling Jetstream**

**Jesse Norris - A Semi-Analytic Approach to Baroclinic Instability on the African Easterly Jet**

**Robert J. Smith - Minimising Time-Stepping Errors in Numerical Models of the Atmosphere and Ocean**

**Amandeep Virdi - The Influence of the Agulhas Leakage on the Overturning Circulation from Momentum Balances**

### 2009: **Mathematics of Scientific and Industrial Computation**

**Charlotta Howarth - Integral Equation Formulations for Scattering Problems**

**David Fairbairn - Comparison of the Ensemble Transform Kalman Filter with the Ensemble Transform Kalman Smoother**

**Mark Payne - Mathematical Modelling of Platelet Signalling PathwaysMesh Generation and its application to Finite Element Methods**

**Mary Pham - Mesh Generation and its application to Finite Element Methods**

**Sarah Cole - Blow-up in a Chemotaxis Model Using a Moving Mesh Method**

### 2009: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**Danila Volpi - Estimation of parameters in traffic flow models using data assimilation**

**Dale Partridge - Analysis and Computation of a Simple Glacier Model using Moving Grids**

**David MacLeod - Evaluation of precipitation over the Middle East and Mediterranean in high resolution climate models**

**Joanne Pocock - Ensemble Data Assimilation: How Many Members Do We Need?**

**Neeral Shah - Impact and implications of climate variability and change on glacier mass balance in Kenya**

**Tomos Roberts - Non-oscillatory interpolation for the Semi-Lagrangian scheme**

**Zak Kipling - Error growth in medium-range forecasting models**

**Zoe Gumm - Bragg Resonance by Ripple Beds**

### 2008: **Mathematics of Scientific and Industrial Computation**

**Muhammad Akram - Linear and Quadratic Finite Elements for a Moving Mesh Method**

**Andrew Ash - Examination of non-Time Harmonic Radio Waves Incident on Plasmas**

**Cassandra Moran - Harbour modelling and resonances**

**Elena Panti - Boundary Element Method for Heat Transfer in a Buried Pipe**

**Juri Parrinello - Modelling water uptake in rice using moving meshes**

**Ashley Twigger - Blow-up in the Nonlinear Schrodinger Equation Using an Adaptive Mesh Method**

**Chloe Ward - Numerical Evaluation of Oscillatory Integrals**

**Christopher Warner - Forward and Inverse Water-Wave Scattering by Topography**

### 2008: Mathematical and Numerical Modelling of the Atmosphere and Oceans

**Fawzi Al Busaidi - Fawzi_Albusaidi**

**Christopher Bowden - A First Step Towards the Calculation of a Connectivity Matrix for the Great Barrier Reef**

**Evangelia-Maria Giannakopoulou - Flood Prediction and Uncertainty**

**Victoria Heighton - 'Every snowflake is different'**

**Thomas Jordan - Does Self-Organised Criticality Occur in the Tropical Convective System?**

**Gillian Morrison - Numerical Modelling of Tidal Bores using a Moving Mesh**

**Rachel Pritchard - Evaluation of Fractional Dispersion Models**

### 2007: **Numerical solution of differential equations**

**Tamsin Lee -** New methods for approximating acoustic wave transmission through ducts (PDF 2.5MB)

**Lee Morgan -** Anomalous diffusion (PDF-1.5MB)

**Keith Pham -** Finite element modelling of multi-asset barrier options (PDF-3MB)

**Alastair Radcliffe -** Finite element modelling of the atmosphere using the shallow water equations (PDF-2.5MB)

**Sanita Vetra -** The computation of spectral representations for evolution PDE (PDF-3.2MB)

### 2007: Mathematical and numerical modelling of the atmosphere and oceans

**Laura Baker -** Properties of the ensemble Kalman filter (PDF-3.8MB)

**Alison Brass -** A moving mesh method for the discontinuous Galerkin finite element technique (PDF-916KB)

**Daniel Lucas -** Application of the phase/amplitude method to the study of trapped waves in the atmosphere and oceans (PDF-1.1MB)

**Duduzile Nhlengethwa -** Petrol or diesel (PDF-1MB)

**Rhiannon Roberts -** Modelling glacier flow (PDF-406KB)

**David Skinner -** A moving mesh finite element method for the shallow water equations (PDF-4.3MB)

**Jovan Stojsavljevic -** Investigation of waiting times in non-linear diffusion equations using a moving mesh method (PDF-538KB)

### 2006: **Numerical solution of differential equations**

**Bonhi Bhattacharya -** A moving finite element method for high order nonlinear diffusion problems

**Jonathan Coleman -** High frequency boundary element methods for scattering by complex polygons

**Rachael England -** The use of numerical methods in solving pricing problems for exotic financial derivatives with a stochastic volatility

**Stefan King -** Best fits with adjustable nodes and scale invariance

**Edmund Ridley -** Analysis of integral operators from scattering problems

**Nicholas Robertson -** A moving Lagrangian mesh model of a lava dome volcano and talus slope

### 2006: Mathematical and numerical modelling of the atmosphere and oceans

**Iain Davison -** Scale analysis of short term forecast errors

**Richard Silveira -** Electromagnetic scattering by simple ice crystal shapes

**Nicola Stone -** Development of a simplified adaptive finite element model of the Gulf Stream

**Halina Watson -** The behaviour of 4-D Var for a highly nonlinear system

### 2005: **Numerical solution of differential equations**

**Jonathan Aitken -** Data dependent mesh generation for peicewise linear interpolation

**Stephen Arden -** A collocation method for high frequency scattering by convex polygons

**Shaun Benbow -** Numerical methods for american options

**Stewart Chidlow -** Approximations to linear wave scattering by topography using an integral equation approach

**Philip McLaughlin -** Outdoor sound propagation and the boundary element method

**Antonis Neochoritis -** Numerical modelling of islands and capture zone size distributions in thin film growth

**Kylie Osman -** Numerical schemes for a non-linear diffusion problem

**Shaun Potticary -** Efficient evaluation of highly oscillatory integrals

**Martyn Taylor -** Investigation into how the reduction of length scales affects the flow of viscoelastic fluid in parallel plate geometries

**Aanand Venkatramanan -** American spread option pricing

### 2005: Mathematical and numerical modelling of the atmosphere and oceans

**Richard Fruehmann -** Ageostrophic wind storms in the central Caspian sea

**Gemma Furness -** Using optimal estimation theory for improved rainfall rates from polarization radar

**Edward Hawkins -** Vorticity extremes in numerical simulations of 2-D geostrophic turbulence

**Robert Horton -** Two dimensional turbulence in the atmosphere and oceans

**David Livings -** Aspects of the ensemble Kalman filter

**David Sproson -** Energetics and vertical structure of the thermohaline circulation

### 2004: **Numerical solution of differential equations**

**Rakhib Ahmed -** Numerical schemes applied to the Burgers and Buckley-Leverett equations

**James Atkinson -** Embedding methods for the numerical solution of convolution equations

**Catherine Campbell-Grant -** A comparative study of computational methods in cosmic gas dynamics

**Paresh Prema -** Numerical modelling of Island ripening

**Mark Webber -** The point source methods in inverse acoustic scattering

### 2004: Mathematical and numerical modelling of the atmosphere and oceans

**Oliver Browne -** Improving global glacier modelling by the inclusion of parameterised subgrid hypsometry within a three-dimensional, dynamical ice sheet model

**Petros Dalakakis -** Radar scattering by ice crystals

**Eleanor Gosling -** Flow through porous media: recovering permeability data from incomplete information by function fitting.

**Sarah Grintzevitch -** Heat waves: their climatic and biometeorological nature in two north american reigions

**Helen Mansley -** Dense water overflows and cascades

**Polly Smith -** Application of conservation laws with source terms to the shallow water equations and crowd dynamics

**Peter Taylor -** Application of parameter estimation to meteorology and food processing

### 2003: **Numerical solution of differential equations**

**Kate Alexander -** Investigation of a new macroscopic model of traffic flow

**Luke Bennetts -** An application of the re-iterated Galerkin approximation in 2-dimensions

**Peter Spence -** The Position of the free boundary formed between an expanding plasma and an electric field in differing geometries

**Daniel Vollmer - ** Adaptive mesh refinement using subdivision of unstructured elements for conservation laws

### 2003: Mathematical and numerical modelling of the atmosphere and oceans

**Clare Harris -** The Valuation of weather derivatives using partial differential equations

**Emma Quaile -** Rotation dominated flow over a ridge

**Jemma Shipton -** Gravity waves in multilayer systems

### 2002: **Numerical solution of differential equations**

**Winnie Chung -** A Spectral Method for the Black Scholes Equations

**Penny Marno -** Crowded Macroscopic and Microscopic Models for Pedestrian Dynamics

**Malachy McConnell -** On the numerical solution of selected integrable non-linear wave equations

**Stavri Mylona -** An Application of Kepler's Problem to Formation Flying using the StÃ¶rmer-Verlet Method

### 2002: Mathematical and numerical modelling of the atmosphere and oceans

**Sarah Brodie -** Numerical Modelling of Stratospheric Temperature Changes and their Possible Causes

**Matt Sayer -** Upper Ocean Variability in the Equatorial Pacific on Diurnal to Intra-seasonal Timescales

**Laura Stanton -** Linearising the Kepler problem for 4D-var Data Assimilation

### 2001: **Numerical solution of differential equations**

**R.B. Brad -** An Implementation of the Box Scheme for use on Transcritical Problems

**D. Garwood -** A Comparison of two approaches for the Approximating of 2-D Scattered Data, with Applications to Geological Modelling

**R. Hawkes -** Mesh Movement Algorithms for Non-linear Fisher-type Equations

**P. Jelfs -** Conjugate Gradients with Rational and Floating Point Arithmetic

**M. Maisey -** Vorticity Preserving Lax-Wendroff Type Schemes

**C.A. Radcliffe -** Positive Schemes for the Linear Advection Equation

### 2000: **Numerical solution of differential equations**

**D. Brown -** Two Data Assimilation Techniques for Linear Multi-input Systems.

**S. Christodoulou -** Finite Differences Applied to Stochastic Problems in Pricing Derivatives.

**C. Freshwater -** The Muskingum-Cunge Method for Flood Routing.

**S.H. Man -** Galerkin Methods for Coupled Integral Equations.

**A. Laird -** A New Method for Solving the 2-D Advection Equation.

**T. McDowall -** Finite Differences Applied to Joint Boundary Layer and Eigenvalue Problems.

**M. Shahrill -** Explicit Schemes for Finding Soliton Solutions of the Korteweg-de Vries Equation.

**B. Weston -** A Marker and Cell Solution of the Incompressible Navier-Stokes Equations for Free Surface Flow.

### 1999: **Numerical solution of differential equations**

**M. Ariffin -** Grid Equidistribution via Various Algorithmic Approaches.

**S.J. Fletcher -** Numerical Approximations to Bouyancy Advection in the Eddy Model.

**N.Fulcher -** The Finite Element Approximation of the Natural Frequencies of a Circular Drum.

**V. Green -** A Financial Model and Application of the Semi-Lagrangian Time-Stepping Scheme.

**D.A. Parry -** Construction of Symplectic Runge-Kutta Methods and their Potential for Molecular Dynamics Application.

**S.C. Smith -** The Evolution of Travelling Waves in a Simple Model for an Ionic Autocatalytic System

**P. Swain -** Numerical Investigations of Vorticity Preserving Lax-Wendroff Type Schemes.

**M. Wakefield -** Variational Methods for Upscaling.

### 1998: **Numerical solution of differential equations**

**C.C. Anderson -** A dual-porosity model for simulating the preferential movement of water in the unsaturated zone of a chalk aquifer.

**K.W. Blake -** Contour zoning.

**M.R. Garvie -** A comparison of cell-mapping techniques for basins of attraction.

**W. Gaudin -** HYDRA: a 3-d MPP Eulerian hydrocode.

**D. Gnandi -** Alternating direction implicit method applied to stochastic problems in derivative finance.

**J. Hudson -** Numerical techniques for conservation laws with source terms..

**H.S. Khela -** The boundary integral method.

**K. Singh -** A comparison of numerical schemes for pricing bond options.

### 1997: **Numerical solution of differential equations**

**R.V. Egan -** Chaotic response of the Duffing equation. A numerical investigation into the dynamics of the non-linear vibration equation.

**R.G. Higgs -** Nonlinear diffusion in reservoir simulation.

**P.B. Horrocks -** Fokker-Planck model of stochastic acceleration: a study of finite difference schemes.

**M.A. Wlasek -** Variational data assimilation: a study.

### 1996: **Numerical solution of differential equations**

**A. Barnes -** Reaction-diffusion waves in an isothermal chemical system with a general order of autocatalysis.

**S.J. Leary -** Mesh movement and mesh subdivision.

**S. McAllister -** First and second order complex differential equations.

**R.K. Sadhra -** Investigating dynamical systems using the cell-to-cell mapping.

**J.P. Wilson -** A refined numerical model of sediment deposition on saltmarshes.

### 1995: **Numerical solution of differential equations**

**M. Bishop -** The modelling and analysis of the equations of motion of floating bodies on regular waves.

**J. Olwoch -** Isothermal autocatalytic reactions with an immobilized autocatalyst.

**S. Stoke -** Eulerian methods with a Lagrangian phase in gas dynamics.

**Diploma**

**R. Coad -** 1-D and 2-D simulations of open channel flows using upwinding schemes.

### 1994: **Numerical solution of differential equations**

**M. Ali -** Application of control techniques to solving linear systems of equations.

**M.H. Brookes -** An investigation of a dual-porosity model for the simulation of unsaturated flow in a porous medium.

**A.J. Crossley -** Application of Roe's scheme to the shallow water equations on the sphere.

**D.A. Kirkland -** Huge singular values and the distance to instability..

**B.M. Neil -** An investigation of the dynamics of several equidistribution schemes.

### 1993: **Numerical solution of differential equations**

**P.A. Burton -** Re-iterative methods for integral equations.

**J.M. Hobbs -** A moving finite element approach to semiconductor process modelling in 1-D..

**L.M. Whitfield -** The application of optimal control theory to life cycle strategies.

**S.J. Woolnough -** A numerical model of sediment deposition on saltmarshes.

### 1992: **Numerical solution of differential equations**

**I. MacDonald -** The numerical solution of free surface/pressurized flow in pipes..

**A.D. Pollard -** Preconditioned conjugate gradient methods for serial and parallel computers..

**C.J. Smith -** Adaptive finite difference solutions for convection and convection-diffusion problems.

### 1991: **Numerical solution of differential equations**

**K.J. Neylon -** Block iterative methods for three-dimensional groundwater flow models.