Self-organization in two-dimensional swarms

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

Volumn 81, Issue 6, 2010, Pages

  Touma, Jihad R ^a   Shreim, Amer ^b   Klushin, Leonid I ^a  

^a AMERICAN UNIVERSITY OF BEIRUT   (Lebanon)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COLLECTIVE MOTIONS; DETERMINISTIC MODELS; FINITE CLUSTERS; GAS LIQUIDS; INTERPARTICLE POTENTIAL; NUMERICAL EXPLORATION; SELF-ORGANIZATIONS; SELF-ORGANIZED; SELF-PROPELLED PARTICLES; TRANSITION LINES; TWO-DIMENSION;

PHASE DIAGRAMS;

PHASE TRANSITIONS;

EID: 77953385964     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.066106     Document Type: Article

References (30)

1. J. Parrish and L. Edelstein-Keshet, Science 284, 99 (1999). 10.1126/science.284.5411.99
2. W.-J. Rappel, A. Nicol, A. Sarkissian, and H. Levine, Phys. Rev. Lett. 83, 1247 (1999). 10.1103/PhysRevLett.83.1247
3. E. Ben-Jacob, I. Cohen, A. Czirók, T. Vicsek, and D. L. Gutnick, Physica A 238, 181 (1997). 10.1016/S0378-4371(96)00457-8
4. A. M. Delprato, A. Samadani, A. Kudrolli, and L. Tsimring, Phys. Rev. Lett. 87, 158102 (2001). 10.1103/PhysRevLett.87.158102
5. A. Ordemann, G. Balazsi, and F. Moss, Physica A 325, 260 (2003). 10.1016/S0378-4371(03)00204-8
6. A. Mogilner and L. Edelstein-Keshet, J. Math. Biol. 38, 534 (1999). 10.1007/s002850050158
7. G. Flierl, D. Grunbaum, S. Levin, and D. Olson, J. Theor. Biol. 196, 397 (1999). 10.1006/jtbi.1998.0842
8. J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995). 10.1103/PhysRevLett.75.4326
9. J. Toner and Y. Tu, Phys. Rev. E 58, 4828 (1998). 10.1103/PhysRevE.58. 4828
10. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995). 10.1103/PhysRevLett.75.1226
11. A. Czirok and T. Vicsek, Physica A 281, 17 (2000). 10.1016/S0378-4371(00) 00013-3
12. H. Levine, W.-J. Rappel, and I. Cohen, Phys. Rev. E 63, 017101 (2000). 10.1103/PhysRevE.63.017101
13. N. Shimoyama, K. Tsuyoshi, Y. Hayakawa, and M. Sano, Phys. Rev. Lett. 76, 3870 (1996). 10.1103/PhysRevLett.76.3870
14. M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi, and L. S. Chayes, Phys. Rev. Lett. 96, 104302 (2006). 10.1103/PhysRevLett.96.104302
15. R. Mach, F. Schweitzer, and F. Schweitzer, Bull. Math. Biol. 69, 5239 (2007). 10.1007/s11538-006-9135-3
16. A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, J. Math. Biol. 47, 353 (2003). 10.1007/s00285-003-0209-7
17. Y. Chuang, M. R. D'Orsogna, D. Marthaler, A. L. Bertozzi, and L. S. Chayes, Physica D 232, 33 (2007). 10.1016/j.physd.2007.05.007
18. Refer to for details.
19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, 2nd ed. (Cambridge University Press, Cambridge, England, 2002).
20. In, a polarized vortex is obtained by forcing polarized initial conditions; here, it arises naturally from random initial conditions.
21. D. Ruelle, Statistical Mechanics: Rigorous Results (World Scientific, Singapore, 1999).
22. All the states referred to here are steady-state solutions reached by starting from random initially conditions, and not by following a relaxed state with slowly changing parameters.
23. The ring state (existence, radius, and stability) is nicely handled in a mean-field approach, through which the dynamics reduces to that of coupled limit cycles (see for further details). These results along with a more elaborate treatment of the dynamics of coupled limit cycles, the organized states that are captured through it, and their stability analysis will constitute the subject of an upcoming work.
24. P. Chaikin and T. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2000).
25. A. M. Skvortsov, L. I. Klushin, and F. A. M. Leermakers, J. Chem. Phys. 126, 024905 (2007). 10.1063/1.2406075
26. D. I. Dimitrov, L. I. Klushin, A. Skvortsov, A. Milchev, and K. Binder, Eur. Phys. J. E 29, 9 (2009). 10.1140/epje/i2008-10442-0
27. G. Grégoire and H. Chate, Phys. Rev. Lett. 92, 025702 (2004). 10.1103/PhysRevLett.92.025702
28. The experiments of in which, interestingly enough, bacterial colonies evolve from a disk into a ring state when exposed to uv radiation offer a promising setting in which the evolution of phases of collective motion with population size, medium resistance, and chemoattractant concentration may be fruitfully studied.
29. A. Shreim, Master 's thesis, American University of Beirut, 2004.
30. J. Touma, L. I. Klushin, and A. Shreim (unpublished).