Application of statistical mechanics to collective motion in biology

Physica A: Statistical Mechanics and its Applications

Volumn 274, Issue 1, 1999, Pages 182-189

  Vicsek, Tamás ^a   Czirók, András ^a   Farkas, Illés J ^a   Helbing, Dirk ^b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; STATISTICAL MECHANICS;

COLLECTIVE MOTION;

BIOLOGY;

EID: 0033322313     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(99)00317-9     Document Type: Article

References (30)

1. S.-K. Ma, Statistical Mechanics, World Scientific, Singapore, 1985.
2. S.-K. Ma, Modern Theory of Critical Phenomena, Benjamin, New York, 1976.
3. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971.
4. Witten T.A., Sander L.M. Phys. Rev. Lett. 47:1981;1400.
5. T. Vicsek, Fractal Growth Phenomena, 2nd Edition, World Scientific, Singapore, 1992.
6. Bak P., Tang C., Wiesenfeld K. Phys. Rev. Lett. 59:1987;381.
7. A-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.
8. M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow '97, Springer, New York, 1998.
9. See, e.g., D. Helbing, B.A. Huberman, Nature 396 (1998) 738.
10. D. Helbing, A. Hennecke, M. Treiber, Phys. Rev. Lett. 82 (1999) 4360, and references therein.
11. Magnasco M.O. Phys. Rev. Lett. 71:1993;1477.
12. Duparcmeur Y.L., Herrmann H.J., Troadec J.P. J. Phys. (France) I. 5:1995;1119.
13. Hemmingsson J. J. Phys. A 28:1995;4245.
14. Vicsek T., Czirók A., Ben-Jacob E., Cohen I., Shochet O. Phys. Rev. Lett. 75:1995;1226.
15. Reynolds C.W. Computer Graphics. 21:1987;25.
16. Rauch E.M., Millonas M.M., Chialvo D.R. Phys. Lett. A. 207:1995;185.
17. Helbing D., Keitsch J., Molnar P. Nature. 387:1997;47.
18. Helbing D., Schweitzer F., Molnar P. Phys. Rev. E. 56:1997;2527.
19. Czirók A., Barabási A.-L., Vicsek T. Phys. Rev. Lett. 82:1999;209.
20. Czirók A., Stanley H.E., Vicsek T. Spontaneously ordered motion of self-propelled particles. J. Phys. A 30:1997;1375.
21. Czirók A., Vicsek M., Vicsek T. Collective motion of organisms in three dimensions. Physica. A 264:1999;299.
22. Toner J., Tu Y. Phys. Rev. Lett. 75:1995;4326.
23. Toner J., Tu Y. Phys. Rev. E. 58:1998;4828.
24. D. Helbing, I. Farkas, T. Vicsek, preprint cond-mat /9904326 .
25. Schmittmann B., Hwang K., Zia R.K.P. Europhys. Lett. 19:1992;19.
26. Y. Imry, Introduction to Mesoscopic Physics, Oxford University Press, Oxford, 1997.
27. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981.
28. Tan M-L., Goldhirsch I. Phys. Rev. Lett. 81:1998;3022.
29. D. Helbing, T. Vicsek, New J. Phys. 1 (1999) no. 13.
30. Helbing D., Molnár P. Phys. Rev. E. 51:1995;4282.