Research
As a member of the Solar Physics and Space Plasma Research Centre at the University of Sheffield, I currently research in solar magnetohydrodynamic waves under the supervision of Prof. Róbert von Fáy-Siebenbürgen. I have previously completed research in meterology and photovoltaics.
Solar Magnetohydrodynamic waves
Waves are a ubiquitous feature of the magnetically dominated solar atmosphere. This is continually demonstrated with ever-improving spacial and temporal resolution observations of ground- and space-based solar telescopes. To understand the context of these observations, we use analytical models of simplified solar environments that we can use mathematics to understand.
Magnetohydrodynmics (MHD) is the mathematical study of the motion of electrically conduction fluids and provides the appropriate mathematical framework to study many solar structures because the Sun is made up of plasma, which, due to atom dissociation, is electrically conducting. The equations that govern the motion of an electrically conducting fluid (under a few assumptions that can be made for the dynamics of the Sun) are the MHD equations: \[ \begin{aligned} \frac{\textrm{D}\mathbf{v}}{\textrm{D}t} &= -\frac{1}{\rho}\nabla{}p - \frac{1}{\mu}\mathbf{B}\times(\nabla\times\mathbf{B}) + \mathbf{g}, \\ \frac{\partial\rho}{\partial{}t} &= - \nabla\cdot(\rho\mathbf{v}), \\ \frac{\partial\mathbf{B}}{\partial{}t} &= \nabla\times(\mathbf{v}\times\mathbf{B}). \end{aligned} \] Under the framework of MHD, we can understand the types of waves supported by solar magnetic structures. In my research, I have completed a definitive study into the magnetoacoustic eigenmodes of an asymmetric magnetic slab, demonstrating how the sausage and kink modes are modified (now quasi-sausage and quasi-kink modes) by asymmetry in the background plasma (see blog post here). I further showed that the ratio of the amplitudes of oscillation on each side of a magnetised slab has the potential to be used as a diagnostic tool in solar magneto-seismology to give an approximation to the magnetic field strength of solar structures.
Meteorology
To a good approximation, the Earth's atmosphere is not influenced by its magnetic field. However, the Earth rotates at a faster rate than the Sun and is significantly smaller so the Coriolis force (a strange force due to the rotation of a system) is much more significant. Therefore, the dynamics of the Earth's atmosphere are governed by the Navier Stokes Equations with a Coriolis force term, given by: \[ \begin{aligned} \frac{\textrm{D}\mathbf{v}}{\textrm{D}t} &= -\frac{1}{\rho}\nabla{}p - 2\mathbf{\Omega}\times\mathbf{v} + \mathbf{g}, \\ \frac{\partial\rho}{\partial{}t} &= - \nabla\cdot(\rho\mathbf{v}). \end{aligned} \]
The effect of the Coriolis force is to give a fluid element a force perpendicular to its velocity that makes the element curve to the right (left) in the northern (southern) hemisphere. This rotational effect introduces some interesting phenomena such as Rossby waves which are large scale waves that oscillate around the globe which can break, causing violent cyclones. Rossby wave breaking has been linked to the extreme weather in Australia.
For weather and climate forecasting, the Navier Stokes Equations are solved numerically using the current weather and climate as initial conditions. During a visit to Monash University, I worked with the School of Earth and Atmospheric Science to assess and compare the simulation of a heat low in central Australia using the Australian Community Climate and Earth-System Simulator (ACCESS). We showed how crucial the lower boundary conditions are to the accurate simulation of this heat low; in particular, how parameters such as the soil moisture content and surface albedo are to the precipitation cycle that is interwoven into the formation of the heat low. This research allows scientists to improve their global climate models for better climate predictions in the future. See publications.
Photovoltaics
I am interested in renewable energy alternatives and have previously completed research into optimising the geometry of photovoltaic panels, using analytical and numerical methods, to see whether alternative curved geometries would increase the incident radiation gathered by a planar geometry.Publications
Research
- Allcock, M., and Erdelyi, R., 2017. Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab, Solar Physics, 292: 35, 20 pages.
- Allcock, M., and Ackerley, D., 2016. Representing the Australian Heat Low in a GCM Using Different Surface and Cloud Schemes, Advances in Meteorology, vol. 2016, Article ID 9702607, 16 pages.
See ResearchGate and OrcID.
Outreach
- Allcock, M., 2017. 1,000,000 degrees with a chance of solar flares: a Pint of Science solar weather report, Mendeley Blog.
Conferences, workshops, and seminars
Below is a list of the conferences, workshops, and significant seminars I have attended.
Date | Meeting | Venue | Contribution |
---|---|---|---|
3-6/07/17 | National Astronomy Meeting 2017 | University of Hull | |
19-21/04/17 | UKMHD conference | Durham University | Talk (large file: 22.5MB) |
16/02/17 | School of Mathematics and Statistics postgraduate student seminar | University of Sheffield | Talk (large file: 69.8MB) |
4-9/09/2016 | STFC Advanced Summer School in Solar System Physics 2016 | University of Sheffield | |
28-2/09/2016 | STFC Introductory Course in Solar System Plasma Physics 2016 | University of St. Andrews | |
28/06/2016 | National Astronomy Meeting 2016 | University of Nottingham | Talk |
11-15/01/2016 | OpenAstronomy - Software Carpentry Workshop | University of Sheffield | |
11/12/2015 | Solar Physics and Space Plasma Research Centre (SP2RC) seminar | University of Sheffield | Talk |
17/02/2015 | Sheffield Undergraduate Research Experience (SURE) Showcase | University of Sheffield | Poster |
Public outreach
Date | Meeting | Venue | Contribution |
17/05/17 | Pint of Science | The Holt Cafe, Sheffield | Talk (large file: 40.5MB) |
Teaching
At the Univerisity of Sheffield I am involved with teaching for the following undergraduate courses:
- MAS115 Mathematical Investigational Skills (Python, R, Latex, and html) - assistant tutor Mar 2016-present,
- MAS153/159 Mathematics for Chemistry (sets, calculus, limits, differential equations, etc.) - assistant tutor Sep 2015-Dec 2015.