4 papers
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…
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…
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…