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I am happy to offer PhD project in any area related to my research interests

 
At the end of any of these projects you would have a good mix of practical computational and analytic skills.
These projects would suit someone with an interest in dynamical systems and computational mathematics.
Potential route either into further research or for a position in industry in science, engineering or finance.
Please contact me for more information or an informal chat.

Numerics for Stochastic DEs

 This project would look at developing new methods to solve stochastically forced differential equations - these are equations which are subject to noise. The inclusion of the effects of stochastic forcing on physical and biological systems is of great interest at present in mathematical biology, computational chemistry, fluid dynamics, finance, physics, numerical analysis to mention a few areas. The noise often provides more realistic models and allows bounds to be obtained on the uncertainty in predictions. In applications I am particularly interested in systems arising in neurodynamics, metrology and from flow in porous media, such as ground water flow (for whcih there might be the possibility to work with people from PET.

Neural Modelling

 In this project you would have the opportunity to look at models of neurons and investigate wave propagation. Of interest are models of single neurons as well as coupled neurons. Possibilities include improving existing models, performing numerical compuations on the models, investigating existence and stability of travelling wave solutions, examining wave propagation in different media - looking at the effects of noise and delays.
Related group at Heriot-Watt in Modelling in Medicine

Cylinder buckling

 In this project you would have the opportunity to look at both the static and dynamics of a buckling shell and to investigate a and analyse a variety of different solution techniques. Further developments would be to look at composite shells which are much used in engineering for light and strong structures.

Dynamics and PDEs

 I would like to look at the stability of travelling waves in heterogeneous media and subject to stochastic forcing. One equation of interest is the complex Ginzburg-Landau equation this is a parabolic equation that arises in many areas of physics ranging from fluid flow to superconductivity.

 

Fronts and localized solutions in differential equations

This project would look at the computation and analysis of localized solutions and propagating fronts. These types are often physically relevent solutions to differential equations as they determine the spread of information. A typical example is the FitzHugh-Nagumo equation which describes neural activity in nerve axons. There are a number of avenues that can be followed : developing and analysing efficient computational methods in 2 dimensions; studying the effect of noise on the stability and computation of waves and improving the current models of neural behaviour.