PGR Practise Talks (Dec, 2021)

The SIAM & IMA Student Chapter is organising a PGR Practice Talk, giving PGR students the opportunity to present their work and ask for input from other PGR students. The event will be held on Thursday the 2nd of December, from 13:00-15:50 in Room E04, Monica Patridge Building (formerly known as Teaching and Learning building).

We will also live stream any in person and any online talk via Teams. The link will become available on the day itself.

Programme

13:50 Adam Blakey: FEMs for Placental Haemodynamics  

The placenta provides nutrients and oxygenated blood to developing foetuses, and is therefore vital to a foetus’ survival. I will talk about the outlook of my PhD project and present some basic computational simulations of maternal blood flow in human placentas using DG FEMs in representative 2D geometries. 

14:15 Alexander Lewis: Stein’s Method on Manifold with Boundary 

Since its inception, Stein’s method has been found to provide powerful, easy-to-construct bounds on probability metrics. At first, Stein applied this framework for comparisons with the normal distribution, however the field has now grown to encompass many classes of distributions on many different spaces. In this talk I will be presenting my current research on how to extend the theory of Stein’s method from Riemannian manifold to manifold with boundary. 

14:40 Thomas Hall: Markov-type Diophantine Equations and their Underlying Geometry and Combinatorics 

It turns out that the Diophantine equation dxyz = ax^2 + by^2 + cz^2 is intimately linked to the behaviour of certain lattice triangles under an operation called “mutation”. In this talk, we will explore this connection and show how to solve such an equation. 

15:10 Robert Barnet: Pore-scale open-source multi-domain solvers for ionic transport and electrochemistry in electrolyte solutions 

In this work we present open-source solvers, built upon the finite volume library OpenFOAM, solving the Stokes-Poisson-Nernst-Planck (SPNP) model for multi-domain ionic transfer in dilute electrolyte solutions. Many real-world applications of SPNP, such as electrochemical energy storage, reinforced concrete  and oil extraction, also include heterogeneous reactions exchanging mass between ionic species. As such, alongside our solvers, we present our formulated set of boundary conditions to model this reactive mass exchange between species, constrained by mass and charge conservation. After outlining the governing equations we perform some dimensional analysis, giving a qualitative description of the different possible transport regimes, quantified by the ratios between the forces inducing ionic transport. Later we give a brief description of the numerical algorithms, based upon the PIMPLE algorithm, underpinning our pore-scale solvers (pnpFoam and pnpMultiFoam) and semi-Newton iterative algorithm used to solve our heterogeneous reactive conditions (mappedChemicalKinetics). We later verify, using one-dimensional test cases, the accuracy of our solvers and conditions. Results are compared against high-order spectral results obtained with the MatLab toolbox Chebfun. Since a large number of applications of SPNP involve complex porous geometries (e.g., batteries involve a porous solid electrode flooded with fluid electrolyte), we later consider a three-dimensional randomly generated porous domain of solid and fluid. Finally, we present preliminary results on applying our work towards a real-world commercial battery cell (LGM50), with hopes to give a comparison with experimental data found in. 

15:30 Niren Bhoja: Spin(10), Octonions and the Standard Model.  

In this talk I explore the spinor representation of Octonions on Cliff_{10} to construct the Lie algebra of the Lie group Spin(10), the usually agreed upon GUT of the standard model.