Importance of the Voronoi domain partition for position-jump reaction-diffusion processes on nonuniform rectilinear lattices

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 88, Issue 5, 2013, Pages

  Yates, Christian A ^a   Baker, Ruth E ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL AND BIOLOGICALS; COMPUTATIONAL DOMAINS; DIFFUSION PROCESS; HIGHER DIMENSIONS; MOLECULAR CONCENTRATION; REACTION DIFFUSION SYSTEMS; REACTION-DIFFUSION PROCESS; TRANSITION RATES;

MARKOV PROCESSES; MOLECULES; PARTIAL DIFFERENTIAL EQUATIONS;

BIOLOGICAL SYSTEMS;

ARTICLE; DIFFUSION; THEORETICAL MODEL;

DIFFUSION; MODELS, THEORETICAL;

EID: 84889261868     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.054701     Document Type: Article

References (8)

1. E. E. Holmes, M. A. Lewis, J. E. Banks, and R. R. Veit, Ecology 0012-9658 10.2307/1939378 75, 17 (1994).
2. K. J. Painter, P. K. Maini, and H. G. Othmer, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.96.10.5549 96, 5549 (1999). (Pubitemid 29234655)
3. S. A. Newman, Nat. Rev. Mol. Cell Biol. 8 (2007), doi: 10.1038/nrm1830-c1.
4. T. Miura and K. Shiota, Anat. Rec. ANREAK 0003-276X 10.1002/(SICI)1097- 0185(20000101)258:1<100::AID-AR11>3.0.CO;2-3 258, 100 (2000). (Pubitemid 30030460)
5. S. C. Ferreira, Jr., M. L. Martins, and M. J. Vilela, Phys. Rev. E 1063-651X 10.1103/PhysRevE.65.021907 65, 021907 (2002). (Pubitemid 40619418)
6. T. Biancalani, D. Fanelli, and F. Di Patti, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.046215 81, 046215 (2010).
7. C. A. Yates, R. E. Baker, R. Erban, and P. K. Maini, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.021921 86, 021921 (2012).
8. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevE.88.054701 for an example of the formation of a morphogen gradient on a nonuniform domain, a confirmatory example of the propriety of the Voronoi domain partition for rectilinear lattices, and the consideration of some alternative structured domain partitions.