Fingering in stochastic growth models


Journal Article

Copyright © Taylor & Francis Group, LLC. Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, we study two simple growth models on the two-dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model, the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one, u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) - θ)+ and die at rate δ(θ - u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and "fingering" at a threshold θc = 0.5, while in the second case, fingering always occurs, i.e., θc = 0. © 2014

Full Text

Duke Authors

Cited Authors

  • Aristotelous, AC; Durrett, R

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 23 / 4

Start / End Page

  • 465 - 474

Electronic International Standard Serial Number (EISSN)

  • 1944-950X

International Standard Serial Number (ISSN)

  • 1058-6458

Digital Object Identifier (DOI)

  • 10.1080/10586458.2014.947053

Citation Source

  • Scopus