24 citations · 98 across the 16 of their papers we have counts for
17 papers
Complex singularities for Burgers' equation with piecewise-continuous initial conditions
Jacob C. Gentner, Michael C. Dallaston, Scott W. McCue
There is a body of research devoted to understanding how complex singularities of solutions of nonlinear partial differential equations (pdes) spontaneously emerge at and p…
Self-similar smoothing of a discontinuity by degenerate cross-diffusion
Michael C. Dallaston
We consider the dynamics of an idealised cross-diffusion model of biological invasion in which the diffusion of an invading population is inhibited by a resident population, which…
Self-similar rupture of thin films of power-law fluid
Michael C Dallaston, Steven A Kedda, Scott W McCue
Models that describe Newtonian liquid films evolving due to the competing effects of surface tension and attractive intermolecular or van der Waals forces are known to rupture in f…
Thin filaments in Hele-Shaw cells
Nitay Ben-Shachar, Michael C. Dallaston, Scott W. McCue
Using a recently derived filament model, the stability of fluid filaments in Hele-Shaw cells, driven by a constant pressure gradient, is studied. It is found that thin circular fil…
Wavespeed selection and interstitial gap formation in an acid-mediated cancer invasion model
Yuhui Chen, Michael C. Dallaston
We consider a two-component reaction-diffusion system that has previously been developed to model invasion of cells into a resident cell population. The system is an idealised vers…
Long-time emergent dynamics of liquid films undergoing thermocapillary instability
Steven A Kedda, Michael C Dallaston, Scott W McCue
The study of viscous thin film flow has led to the development of highly nonlinear partial differential equations that model how the evolution of the film height is affected by dif…
Capillary levelling of thin liquid films of power-law rheology
Michael C Dallaston
We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface te…
Two-interface and thin filament approximation in Hele--Shaw channel flow
Michael C Dallaston, Michael J W Jackson, Liam C Morrow +1
When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consid…
Onset of convective instability in an inclined porous medium
Emmanuel E. Luther, Michael C. Dallaston, Seyed M. Shariatipour +1
The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable de…
Stability of similarity solutions of viscous thread pinch-off
Michael C. Dallaston, Chengxi Zhao, James E. Sprittles +1
In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with…
A review of one-phase Hele-Shaw flows and a level-set method for non-standard configurations
Liam C. Morrow, Timothy J. Moroney, Michael C. Dallaston +1
The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-…
Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow
Liam C. Morrow, Michael C. Dallaston, Scott W. McCue
We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving b…
Matched asymptotic analysis of self-similar blow-up profiles of the thin film equation
Michael C. Dallaston
We consider asymptotically self-similar blow-up profiles of the thin film equation consisting of a stabilising fourth order and destabilising second order term. It has previously b…
Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows
Michael C Dallaston, Dmitri Tseluiko, Zhong Zheng +2
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid a…
Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures
Michael C. Dallaston, Marco A. Fontelos, Dmitri Tseluiko +1
The formation of iterated structures, such as satellite and sub-satellite drops, filaments and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a comput…
Saffman-Taylor fingers with kinetic undercooling
Bennett P. J. Gardiner, Scott W. McCue, Michael C. Dallaston +1
The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned…
Corner and finger formation in Hele--Shaw flow with kinetic undercooling regularisation
Michael C. Dallaston, Scott W. McCue
We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and n…