# 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 spatial 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 that arises 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 global climate models for inproved climate predictions in the future. See publications section.

### 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

Also see ResearchGate and OrcID.

## Conferences, workshops, and seminars

I have given talks about my research in solar physics at several national and interenational conferences. I have find that conference and seminar presenters jump straight into threir research without context or motivation, so I try to include a discussion of the context of my research within the broader field. As a visual learner, I also try to make my talks visual with videos and images to most effectively portray an idea.

#### Highlights:

• Nervously presenting some results from my Masters research project at the National Astronomy Meeting in 2016.
• Illustrating at the European Solar Physics Meeting in 2017 how my theoretical work on asymmetric MHD waves can be used to approximate the strength of the magnetic field in structures in the solar atmosphere - something that is traditionally very difficult to do!

Below is a list of the conferences, workshops, and significant seminars I have attended and/or contributed to.

Date Meeting Venue Contribution
4-8/09/17 15th European Solar Physics Meeting Eötvös Loránd University, Hungary Talk (large file: 18.4MB)
28-1/08/17 STFC Advanced Summer School in Solar System Physics 2017 University of Central Lancashire Talk (large file: 21.6MB)
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.