Nonlinear diffusion and exclusion processes with contact interactions

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

Volumn 81, Issue 1, 2010, Pages

  Fernando, Anthony E ^a   Landman, Kerry A ^a   Simpson, Matthew J ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CELL MOTILITY; CELL MOTILITY ASSAY; CELL-CELL INTERACTION; CONTACT INTERACTION; CONTINUOUS MODELS; CONTINUUM DESCRIPTION; CONTINUUM MODEL; DIFFUSION FUNCTIONS; DISCRETE LEVELS; EXCLUSION PROCESS; GENERAL CLASS; GLOBAL MEASURES; GOODNESS OF FIT; INTERACTING POPULATION; NEGATIVE VALUES; NONLINEAR DIFFUSION; NONLINEAR DIFFUSION EQUATIONS; PHYSICAL SYSTEMS; REGULAR LATTICE; STRONG INTERACTION;

CONTINUUM MECHANICS; DIFFUSION; PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 75349088750     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.011903     Document Type: Article

References (21)

1. T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Springer-Verlag, Berlin, 1999).
2. F. Spitzer, Adv. Math. 5, 246 (1970). 10.1016/0001-8708(70)90034-4
3. A. Schadschneider, Physica A 313, 153 (2002). 10.1016/S0378-4371(02) 01036-1
4. L. M. Sander and T. S. Deisboeck, Phys. Rev. E 66, 051901 (2002). 10.1103/PhysRevE.66.051901
5. A. John, A. Schadschneider, D. Chowdhury, and K. Nishinari, J. Theor. Biol. 231, 279 (2004). 10.1016/j.jtbi.2004.06.022
6. C. Deroulers, M. Aubert, M. Badoual, and B. Grammaticos, Phys. Rev. E 79, 031917 (2009). 10.1103/PhysRevE.79.031917
7. M. J. Simpson, A. Merrifield, K. A. Landman, and B. D. Hughes, Phys. Rev. E 76, 021918 (2007). 10.1103/PhysRevE.76.021918
8. M. J. Simpson, K. A. Landman, and B. D. Hughes, Bull. Math. Biol. 71, 781 (2009). 10.1007/s11538-008-9381-7
9. M. J. Simpson, K. A. Landman, and B. D. Hughes, Physica A 388, 399 (2009). 10.1016/j.physa.2008.10.038
10. M. J. Simpson, K. A. Landman, and B. D. Hughes, Phys. Rev. E 79, 031920 (2009). 10.1103/PhysRevE.79.031920
11. T. P. Witelski, Appl. Math. Lett. 8, 27 (1995). 10.1016/0893-9659(95) 00062-U
12. Modeling Chemical Systems using Cellular Automata, edited by, L. B. Kier, P. G. Seybold, and, C.-K. Cheng, (Springer-Verlag, Amsterdam, 2005).
13. D. Chowdhury, A. Schadschneider, and K. Nishinari, Phys. Life Rev. 2, 318 (2005). 10.1016/j.plrev.2005.09.001
14. B. D. Hughes, Random Walks and Random Environments (Oxford University Press, Oxford, UK, 1995), Vol. 1.
15. E. A. Codling, M. J. Plank, and S. Benhamou, J. R. Soc., Interface 5, 813 (2008). 10.1098/rsif.2008.0014
16. K. Anguige and C. Schmeiser, J. Math. Biol. 58, 395 (2009). 10.1007/s00285-008-0197-8
17. M. J. Simpson, K. A. Landman, B. D. Hughes, A. E. Fernando, Physica A 389, 1412 (2010). 10.1016/j.physa.2009.12.010
18. V. Y. Kotlyar, Cybern. Syst. Anal. 35, 653 (1999). 10.1007/BF02835861
19. J. A. Sherratt, Proc. R. Soc. London, Ser. A 456, 2365 (2000). 10.1098/rspa.2000.0616
20. B. G. Sengers, C. P. Please, and R. O. C. Oreffo, J. R. Soc., Interface 4, 1107 (2007). 10.1098/rsif.2007.0233
21. B. C. Thorne, A. M. Bailey, D. W. DeSimone, and S. M. Peirce, Birth Defects Res. C 81, 344 (2007). 10.1002/bdrc.20106