Macroscopic model of self-propelled bacteria swarming with regular reversals

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

Volumn 85, Issue 2, 2012, Pages

  Gejji, Richard ^a,b   Lushnikov, Pavel M ^c   Alber, Mark ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b OHIO STATE UNIVERSITY   (United States)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL APPROXIMATION; BOLTZMANN-MATANO ANALYSIS; CELL POPULATIONS; CELL-BASED; CELLULAR DENSITY; COLLISION TIME; CRITICAL DENSITY; DIRECTION OF MOTION; HIGH DENSITY; LOWER DENSITY; MACROSCOPIC MODEL; NONLINEAR DIFFUSION; NONLINEAR DIFFUSION EQUATIONS; NUMERICAL SOLUTION; PERIODIC REVERSAL; ROD-SHAPED BACTERIA; SEMI-ANALYTICAL; STOCHASTIC DYNAMICS; TRAFFIC JAMS;

CELL CULTURE; CELL PROLIFERATION; DYNAMICS; EMERGENCY TRAFFIC CONTROL; PARTIAL DIFFERENTIAL EQUATIONS; TRAFFIC CONGESTION;

BACTERIA;

EID: 84857567661     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.021903     Document Type: Article

References (38)

1. D. Kaiser, Curr. Bio. CUBLE2 0960-9822 10.1016/j.cub.2007.04.050 17, 561 (2007). (Pubitemid 47043418)
2. Y. Wu, D. Kaiser, Y. Jiang, and M. Alber, PLoS Comput. Biol. 1553-734X 10.1371/journal.pcbi.0030253 3, e253 (2007).
3. A. Kaiser and C. Crosby, Cell Motility CMOTDY 0271-6585 10.1002/cm.970030304 3, 227245 (1983).
4. R. Yu and D. Kaiser, Mol. Microbiol. MOMIEE 0950-382X 10.1111/j.1365-2958.2006.05536.x 63, 454 (2007). (Pubitemid 46058932)
5. Y. Wu, D. Kaiser, Y. Jiang, and M. Alber, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0811662106 106, 1222 (2009).
6. T. Mignot, J. Merlie, and D. Zusman, Science SCIEAS 0036-8075 10.1126/science.1119052 310, 855 (2005). (Pubitemid 41567344)
7. D. E. Whitworth, ed., Myxobacteria Multicellularity and Differentiation (ASM Press, Washington, DC, 2008).
8. Y. Wu, Y. Jiang, D. Kaiser, and M. Alber, Phys. Biol. 1478-3967 10.1088/1478-3975/8/5/055003 8, 055003 (2011).
9. B. D. Blackhart and D. Zusman, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.82.24.8767 82, 8767 (1985).
10. D. Kaiser, in Myxobacteria, Multicellularity, and Differentiation, edited by, D. E. Whitworth, (ASM Press, Washington, DC, 2008), p. 93.
11. E. M. Mauriello, T. Mignot, Z. Yang, and D. R. Zusman, Microbiol. Mol. Biol. Rev. MMBRF7 1092-2172 10.1128/MMBR.00043-09 74, 229 (2010).
12. C. W. Harvey, F. Morcos, C. R. Sweet, D. Kaiser, S. Chatterjee, X. Liu, D. Z. Chen, and M. Alber, Phys. Biol. 1478-3967 10.1088/1478-3975/8/2/026016 8, 026016 (2011).
13. O. A. Igoshin, A. Mogilner, R. D. Welch, D. Kaiser, and G. Oster, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.221579598 98, 14913 (2001). (Pubitemid 34013944)
14. O. A. Igoshin and G. Oster, Math Biosci. MABIAR 0025-5564 10.1016/j.mbs.2003.04.001 188, 221 (2004). (Pubitemid 38180546)
15. O. A. Igoshin, R. D. Welch, D. Kaiser, and G. Oster, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0400704101 101, 4256 (2004). (Pubitemid 38405916)
16. M. S. Alber, Y. Jiang, and M. A. Kiskowski, Physica D PDNPDT 0167-2789 10.1016/j.physd.2003.11.012 191, 343 (2004).
17. B. V. Reddy and S. N. Khanna, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.068301 93, 068301 (2004).
18. M. A. Kiskowski, Y. Jiang, and M. S. Alber, Phys. Biol. 1478-3967 10.1088/1478-3967/1/3/005 1, 173 (2004). (Pubitemid 44362295)
19. D. Kaiser, Curr. Biol. CUBLE2 0960-9822 10.1016/j.cub.2007.04.050 17, R561 (2007). (Pubitemid 47043418)
20. M. R. D'Orsogna, M. A. Suchard, and T. Chou, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.021925 68, 021925 (2003).
21. T. J. Newman and R. Grima, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.051916 70, 051916 (2004). (Pubitemid 40086533)
22. M. Alber, N. Chen, T. Glimm, and P. M. Lushnikov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.051901 73, 051901 (2006). (Pubitemid 43672797)
23. M. Alber, N. Chen, P. M. Lushnikov, and S. A. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.168102 99, 168102 (2007). (Pubitemid 47613326)
24. P. M. Lushnikov, N. Chen, and M. Alber, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.061904 78, 061904 (2008).
25. M. Alber, R. Gejji, and B. Kazmierczak, Appl. Math. Lett. AMLEEL 0893-9659 10.1016/j.aml.2009.05.013 22, 1645 (2009).
26. C. S. Patlak, Bull. Math. Biophys. BMBIAO 0007-4985 10.1007/BF02476407 15, 311 (1953).
27. E. F. Keller and L. A. Segel, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(70)90092-5 26, 399 (1970).
28. M. P. Brenner, P. Constantin, L. P. Kadanoff, A. Schenkel, and S. C. Venkataramani, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/12/4/320 12, 1071 (1999).
29. P. M. Lushnikov, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2010. 01.068 374, 1678 (2010).
30. S. Dejak, P. Lushnikov, Y. Ovchinnikov, and I. Sigal (to be published).
31. P. J. Murray, C. M. Edwards, M. J. Tindall, and P. K. Maini, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.031912 80, 031912 (2009).
32. R. Welch and A. D. Kaiser, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.261574598 98, 14907 (2001). (Pubitemid 34013943)
33. M. E. Glicksman, Diffusion in Solids: Field Theory, Solid-State Principles, and Applications (Wiley, New York, 2000).
34. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Butterworth-Heinemann, London, 1980).
35. M. Nixon and A. Aguado, Feature Extraction and Image Processing (Academic Press, New York, 2008).
36. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences (Springer-Verlag, Berlin, 2004).
37. P. C. Hemmer, Physica PHYSAG 0031-8914 10.1016/0031-8914(61)90022-2 27, 79 (1961).
38. S. Ispolatov and P. L. Krapivsky, Physica A PHYADX 0378-4371 10.1016/S0378-4371(97)00656-0 252, 165 (1998).