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Fingering in stochastic growth models

Publication ,  Journal Article
Aristotelous, AC; Durrett, R
Published in: Experimental Mathematics
October 2, 2014

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

Duke Scholars

Published In

Experimental Mathematics

DOI

EISSN

1944-950X

ISSN

1058-6458

Publication Date

October 2, 2014

Volume

23

Issue

4

Start / End Page

465 / 474

Related Subject Headings

  • General Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Aristotelous, A. C., & Durrett, R. (2014). Fingering in stochastic growth models. Experimental Mathematics, 23(4), 465–474. https://doi.org/10.1080/10586458.2014.947053
Aristotelous, A. C., and R. Durrett. “Fingering in stochastic growth models.” Experimental Mathematics 23, no. 4 (October 2, 2014): 465–74. https://doi.org/10.1080/10586458.2014.947053.
Aristotelous AC, Durrett R. Fingering in stochastic growth models. Experimental Mathematics. 2014 Oct 2;23(4):465–74.
Aristotelous, A. C., and R. Durrett. “Fingering in stochastic growth models.” Experimental Mathematics, vol. 23, no. 4, Oct. 2014, pp. 465–74. Scopus, doi:10.1080/10586458.2014.947053.
Aristotelous AC, Durrett R. Fingering in stochastic growth models. Experimental Mathematics. 2014 Oct 2;23(4):465–474.

Published In

Experimental Mathematics

DOI

EISSN

1944-950X

ISSN

1058-6458

Publication Date

October 2, 2014

Volume

23

Issue

4

Start / End Page

465 / 474

Related Subject Headings

  • General Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics