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
APA
Chicago
ICMJE
MLA
NLM
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