7 citations · 23 across the 10 of their papers we have counts for
10 papers
A new implementation of the geometric method for solving the Eady slice equations
Charlie P. Egan, David P. Bourne, Colin J. Cotter +4
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 an…
Semi-discrete optimal transport methods for the semi-geostrophic equations
David P. Bourne, Charlie P. Egan, Beatrice Pelloni +1
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinate…
A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions
T. D. Hurst, B. D. Goddard, M. Wilkinson
The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when partic…
Local-in-time Physical Solutions of the Incompressible Semi-Geostrophic Equations in Eulerian Coordinates
Mark Wilkinson
We prove the existence of local-in-time smooth solutions of the incompressible semi-geostrophic equations expressed in Eulerian co-ordinates in 3-dimensional smooth bounded simply-…
On Global-in-time Chaotic Weak Solutions of the Liouville Equation for Hard Spheres
Mark Wilkinson
We outline a new method of construction of global-in-time weak solutions of the Liouville equation - and also of the associated BBGKY hierarchy - corresponding to the hard sphere s…
On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles II: Non-uniqueness
Mark Wilkinson
We prove that to each initial datum in a set of positive measure in phase space, there exist uncountably-many associated weak solutions of Newton's equations of motion which govern…
On a paradox in the impact dynamics of smooth rigid bodies
Peter Palffy-Muhoray, Epifanio G. Virga, Mark Wilkinson +1
Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specificc occasions, in the absence of friction, the conserva…
Non-existence of Physical Classical Solutions to Euler's Equations of Rigid Body Dynamics
Mark Wilkinson
We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constitu…
Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential
Mark Wilkinson
We study the existence, regularity and so-called `strict physicality' of weak solutions of a coupled Navier-Stokes Q-tensor system which is proposed as a model for the incompressib…
Dynamic Statistical Scaling in the Landau-de Gennes Theory of Nematic Liquid Crystals
Eduard Kirr, Mark Wilkinson, Arghir Zarnescu
We investigate the asymptotic behaviour of a correlation function associated with a nematic liquid crystal system undergoing an isotropic-nematic phase transition following an inst…