Charlie Egan
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View article: Semi-discrete optimal transport techniques for the compressible semi-geostrophic equations
Semi-discrete optimal transport techniques for the compressible semi-geostrophic equations Open
We prove existence of weak solutions of the 3D compressible semi-geostrophic (SG) equations with compactly supported measure-valued initial data. These equations model large-scale atmospheric flows. Our proof uses a particle discretisation…
A definition of the background state of the atmosphere using optimal transport Open
The dynamics of atmospheric disturbances are often described in terms of displacements of air parcels relative to their locations in a notional background state. Modified Lagrangian Mean (MLM) states have been proposed by M. E. McIntyre us…
Mathematical modelling of a silicon carbide (SiC) pilot furnace Open
This report proposes a one-dimensional mathematical model of a novel silicon carbide furnace designed by Elkem ASA. The model consists of balance equations for volume fractions of three solids -- silicon dioxide, carbon, and silicon carbid…
View article: A new implementation of the geometric method for solving the Eady slice equations
A new implementation of the geometric method for solving the Eady slice equations Open
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The geometric method is a Lagrangian discr…
View article: Existence for the Semi-Geostrophic Equations in Geostrophic Coordinates via Semi-Discrete Optimal Transport
Existence for the Semi-Geostrophic Equations in Geostrophic Coordinates via Semi-Discrete Optimal Transport Open
Using semi-discrete optimal transport, we construct global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates for arbitrary initial measures with compact support. This new …
Summarising the points made in online political debates Open
Online communities host growing numbers of discussions amongst large groups of participants on all manner of topics.This user-generated content contains millions of statements of opinions and ideas.We propose an abstractive approach to sum…