• Compactification for asymptotically autonomous dynamical systems: Theory, applications and invariant manifolds 

  Wieczorek, Sebastian; Xie, Chun; Jones, Chris K.R.T. (IOP Publishing, 2021-05-13)

  We develop a general compactification framework to facilitate analysis of nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a ...
• On nonlinearity in three-dimensional equatorial flows 

  Henry, David (Atlantis and Taylor & Francis, 2018-07)

  We examine an aspect of the modelling of the underlying fluid motion in the equatorial region of the ocean. In particular, we assess whether nonlinearity is inherently vital in capturing the three-dimensional upwelling and ...
• Stratified equatorial flows in cylindrical coordinates 

  Henry, David; Martin, Calin I. (IOP Publishing, 2020-06-05)

  We construct an exact solution modelling the geophysical dynamics of an inviscid and incompressible fluid which possesses a variable density stratification, where the fluid density may vary with both the depth and latitude. ...
• Nonlinear features of equatorial ocean flows 

  Henry, David (The Oceanography Society, 2018-10-21)

  We examine whether certain oceanographic features of equatorial flows can be modeled using a linear theoretical framework. In particular, we show, using elementary mathematical considerations, that linearization fails to ...
• Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces 

  Gilmore, Clifford; Le Masson, Etienne; Sahlsten, Tuomas; Thomas, Joe (Springer Nature Switzerland AG, 2021-04-05)

  We give upper bounds for Lp norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short geodesic loops passing through a point. When ...

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