PhD projects in Physics and Chemistry
Below are some examples of PhD projects in physics and chemistry. Alternative projects might be formulated following discussions with individual staff members, just contact the staff member or PhD admissions tutor Dr Gianne Derks.
Estimating the cost of phase nucleation in shape-memory crystals (Supervisor: Dr Jon Bevan)
Certain shape-memory crystals rearrange themselves `internally' in response to a change in temperature. As a result, you can bend and twist them into all sorts of shapes at room temperature and, on heating in a cup of hot tea, for example, they spring back into their original shape. They are the subject of a huge amount of research and their applications are numerous.
There is a widely accepted mathematical model, due to Ball and James, which explains why this change happens as the temperature decreases: roughly speaking, the material minimizes its free energy differently at high temperatures compared to low. But this theory does not explain all features. At low temperatures in two space dimensions, for example, the material prefers to deform according to a certain map u such that
∇u ∈ SO(2)A∪SO(2)B
where A and B are fixed 2x2 matrices dictated by the particular material under consideration. (SO(2) is the group of rotations in the 2x2 matrices; ∇u is the matrix of partial derivatives of the map u: R2 → R2.) The patterns typically observed show material where bands of ∇u = A alternate with bands of ∇u = B. The Ball-James model correctly predicts the ratio of A to B, but it does not limit the fineness of these bands. The `minimum energy' state does not exist. However, the model can be improved by adding a so-called surface energy term. The aim of this project is to extend the mathematical analysis of these enhanced material models using tools from the Calculus of Variations. In particular, we would focus on finding the activation energy of one (new) material phase in another, i.e. the least energy required to transform the material from one phase to another. No background in materials science is needed for this project.
Stress-induced twinned microstructure - image courtesy of R D James
Faraday waves (Supervisor: Dr Anne Skeldon)
Patterns can be made to form on the surface of a container of fluid by shaking the container up and down. The shaking has to be at the right frequency and right amplitude for any patterns to form - if you move a container of fluid up and down very slowly then the surface of the fluid will remain flat. There are a wealth of experimental results showing a variety of different possible patterns. On the theoretical front, arguments based on symmetries and the way different patterns interact has led to some knowledge of the mechanisms that cause particular patterns to become dominant. Although these have been tested on mathematical models describing the fluid, there are still significant gaps in our understanding. The aim of this project is to investigate further the theory underlying pattern selection in the Faraday and related problems. This will require using a variety of different dynamical systems techniques both theoretical and computational.
Soliton Switching in Fibres (Supervisor: Dr Gianne Derks)
For the optical transmission of data across a cable, one can use two (or more) coupled fibre cables. Experiments have shown that if a certain type of signal is put at one end of the cable, it will go to the other end of this cable and hardly anything happens in the other cable. However, if one puts other types of signals on the cable, the signal will switch to the other cable. This gives a convenient way of sending data consisting of zeros and ones. In this project we will aim for a better understanding of this experimentally observed process by investigating the family of soliton-like solutions, especially issues like existence, stability, bifurcations and invariant manifolds will be investigated.
Patterns in Surface Chemistry (Supervisor: Dr Rebecca Hoyle)
Regular patterns arise naturally in many physical, chemical and biological systems - from hexagonal convection cells on the surface of the sun to stripes on a zebra's back. Constantly changing irregular patterns of carbon monoxide (CO) and oxygen are seen during CO oxidation on platinum crystals in the [100] orientation. Recently a reaction-diffusion model is developed to reproduce this pattern formation and created numerical simulations that show patterns made up of moving CO and oxygen fronts. Possible PhD projects in this area include: extending the model to include the formation of subsurface oxygen at higher pressures or developing a similar model for the NO + NH3 reaction on Pt{100}. These interdisciplinary projects are great opportunities for Maths graduates to apply their skills in a new area, or for Chemistry graduates with good maths and computing skills to move into theory.
Molecular Motors (Supervisor: Dr Rebecca Hoyle)
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Molecular motors are proteins that transform chemical energy into mechanical work on a molecular level, generating forces and leading to motion. We are studying myosin V, a motor involved in intracellular transport in animal cells. It has two heads that bind to an actin filament and a long neck that attaches to its cargo, such as vesicles and organelles. The myosin molecule walks hand-over-hand along the actin track via the coordinated binding and release of its heads. We have used energetics to model the interaction of external load and intramolecular strain with the ATP hydrolysis cycle that drives the stepping action, and performed a detailed quantitative fit to experimental data. Possible PhD projects include: applying the same methodology to a variety of other molecular motors to determine how well the established models compare with experimental data, and how the evolved physical characteristics of the motors relate to their biological function. This is interdisciplinary work in an exciting and fast-moving area of biophysics. An enthusiasm for learning about biophysics and communicating with experimentalists is essential. This project would suit a graduate in Applied Maths or Physics, or possibly a Biology graduate with strong quantitative skills. Programming skills are needed to adapt existing codes.