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The dynamics of localized spot patterns for reaction-diffusion systems on the sphere
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producingExpand
Do waveless ships exist? Results for single-cornered hulls
Abstract Consider low-speed potential flow past a ship modelled as a semi-infinite two-dimensional body with constant draught. Is it possible to design the hull in such a way as to eliminate theExpand
New gravity–capillary waves at low speeds. Part 1. Linear geometries
Abstract When traditional linearized theory is used to study gravity–capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of itsExpand
Bending of elastic fibres in viscous flows: the influence of confinement ‡
Abstract We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre’sExpand
Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves
In another paper of this volume, Grimshaw has demonstrated how techniques of Borel summation can be used to elucidate the exponentially small terms that lie hidden beyond all orders of a divergentExpand
Curvature suppresses the Rayleigh-Taylor instability
The dynamics of a thin liquid film on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the film thickness and the radius of curvatureExpand
The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls
Abstract In the Dagan & Tulin (J. Fluid Mech., vol. 51, 1972, pp. 529–543) model of ship waves, a blunt ship moving at low speeds can be modelled as a two-dimensional semi-infinite body. A centralExpand
On the distinguished limits of the Navier slip model of the moving contact line problem
When a droplet spreads on a solid substrate, it is unclear what the correct boundary conditions are to impose at the moving contact line. The classical no-slip condition is generally acknowledged toExpand
New gravity–capillary waves at low speeds. Part 2. Nonlinear geometries
Abstract When traditional linearized theory is used to study gravity–capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of itsExpand
New singularities for Stokes waves
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^{\circ }$ . Here, theExpand
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