Velocity-jump models with crowding effects

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

Volumn 84, Issue 6, 2011, Pages

  Treloar, Katrina K ^a   Simpson, Matthew J ^a   McCue, Scott W ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

AGENT-TO-AGENT INTERACTION; BACTERIA CELL; CANCER INVASION; CELL BIOLOGY; COLLECTIVE MOTIONS; CONTINUUM DESCRIPTION; CROWDING EFFECTS; DILUTE SYSTEM; HIGH CELL DENSITY; HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION; ONE-DIMENSIONAL MODEL; RANDOM WALK MODELS; SIMULATION DATA; STOCHASTIC SIMULATIONS; VELOCITY-JUMP PROCESS; WOUND HEALING;

CELLS; CYTOLOGY; MARKOV PROCESSES; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC MODELS; TISSUE;

VELOCITY;

EID: 84855372909     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.061920     Document Type: Article

References (43)

1. H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, 1983).
2. E. A. Codling, M. J. Plank, and S. Benhamou, J. R. Soc. Interface 1742-5689 10.1098/rsif.2008.0014 5, 813 (2008). (Pubitemid 351882159)
3. J. D. Murray, Mathematical Biology I: An Introduction, 3rd ed. (Springer-Verlag, Heidelberg, 2002).
4. M. J. Simpson, A. Merrifield, K. A. Landman, and B. D. Hughes, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.021918 76, 021918 (2007). (Pubitemid 47294683)
5. R. E. Baker, C. A. Yates, and R. Erban, Bull. Math. Biol. BMTBAP 0092-8240 10.1007/s11538-009-9467-x 72, 719 (2009).
6. B. H. Berg and D. A. Brown, Nature (London) NATUAS 0028-0836 10.1038/239500a0 239, 500 (1972).
7. P. K. Maini, D. L. S. McElwain, and D. I. Leavesley, Tissue Eng. NATUAS 1076-3279 10.1089/107632704323061834 10, 475 (2004). (Pubitemid 38580268)
8. M. Ward, C. McCann, M. DeWulf, J. Y. Wu, and Y. Rao, J. Neurosci. 23, 5170 (2003).
9. A. Q. Cai, K. A. Landman, and B. D. Hughes, J. Theor Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2006.10.024 245, 576 (2007). (Pubitemid 46365739)
10. N. R. Druckenbrod and M. L. Epstein, Dev. Dyn. JTBIAP 1058-8388 10.1002/dvdy.20974 236, 84 (2007). (Pubitemid 46095081)
11. M. J. Simpson, K. A. Landman, and B. D. Hughes, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.10.038 388, 399 (2009).
12. T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Springer-Verlag, Berlin, 1999).
13. L. M. Sander and T. S. Deisboeck, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.051901 66, 051901 (2002). (Pubitemid 40618504)
14. K. J. Painter and T. Hillen, Can. Appl. Math. Q. 10, 501 (2002).
15. C. Deroulers, M. Aubert, M. Badoual, and B. Grammaticos, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.031917 79, 031917 (2009).
16. E. Khain, M. Katakowski, S. Hopkins, A. Szalad, X. Zheng, F. Jiang, and M. Chopp, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.031920 83, 031920 (2011).
17. T. Callaghan, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-006-9022-1 122, 909 (2006). (Pubitemid 43529088)
18. E. Khain, L. M. Sander, and C. M. Schneider-Mizell, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-006-9194-8 128, 209 (2007).
19. J. M. Bloomfield, J. R. Soc. Interface JSTPBS 1742-5689 10.1098/rsif.2010.0071 7, 1525 (2010).
20. M. J. Simpson and R. E. Baker, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.051922 83, 051922 (2011).
21. R. Erban and H. Othmer, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139903433232 65, 361 (2004).
22. S. Goldstein, Q. J. Mech. Appl. Math. QJMMAV 0033-5614 10.1093/qjmam/4.2.129 4, 129 (1951).
23. M. Kac, Rocky Mount. J. Math. RMJMAE 0035-7596 10.1216/RMJ-1974-4-3-497 4, 497 (1974).
24. C. Patlak, Bull. Math. Biophys. BMBIAO 0007-4985 10.1007/BF02476407 15, 311 (1953).
25. A. Okubo and S. A. Levin, Diffusion and Ecological Problems: Modern Perspectives (Springer, Berlin, 2001).
26. V. V. Tetz, O. V. Rybalchenko, and G. A. Savkova, FEMS Microbiol. Lett. FMLED7 0378-1097 10.1111/j.1574-6968.1993.tb06035.x 107, 231 (1993).
27. T. Surrey, F. Nedelec, S. Leibler, and E. Karsenti, Science 0036-8075 10.1126/science.1059758 292, 1167 (2001). (Pubitemid 32440939)
28. A. Snezhko, K. Barlan, I. S. Aranson, and V. I. Gelfand, Biophys. J. BIOJAU 0006-3495 10.1016/j.bpj.2010.09.065 99, 3216 (2010).
29. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.1226 75, 1226 (1995).
30. I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, Nature (London) NATUAS 0028-0836 10.1038/nature03236 433, 513 (2005). (Pubitemid 40204306)
31. B. D. Hughes, Random Walks and Random Environments, Vol. 1 (Oxford University Press, New York, 1995).
32. M. J. Simpson and K. A. Landman, Adv. Water Resour. AWREDI 0309-1708 10.1016/j.advwatres.2007.04.005 30, 2026 (2007). (Pubitemid 46939651)
33. M. J. Simpson, K. A. Landman, and T. P. Clement, Math. Comput. Simulat. MCSIDR 0378-4754 10.1016/j.matcom.2005.03.019 70, 44 (2005). (Pubitemid 41119025)
34. A. Schadschneider, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02) 01036-1 313, 153 (2002).
35. D. Chowdhury, A. Schadschneider, and K. Nishinari, Phys. Life Rev. PHYADX 1571-0645 10.1016/j.plrev.2005.09.001 2, 318 (2005). (Pubitemid 41762628)
36. M. J. Simpson, K. A. Landman, and B. D. Hughes, Physica A PHYADX 0378-4371 10.1016/j.physa.2010.05.020 389, 3779 (2010).
37. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers (McGraw-Hill, New York, 1998).
38. C. Zheng and G. D. Bennett, Applied Contaminant Transport Modeling, 2nd ed. (Wiley, New York, 2002).
39. T. Hillen and H. Othmer, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139999358167 61, 751 (2000).
40. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
41. M. J. Simpson, K. A. Landman, B. D. Hughes, and A. E. Fernando, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.12.010 389, 1412 (2010).
42. M. J. Simpson, C. Towne, D. L. S. McElwain, and Z. Upton, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.041901 82, 041901 (2010).
43. M. J. Simpson, R. E. Baker, and S. W. McCue, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.021901 83, 021901 (2011).