Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

Author

Eric Bertin 1,2, Michel Droz 2 and Guillaume Grégoire 3

Affiliations

1 Université de Lyon, Laboratoire de Physique, ENS Lyon, CNRS, 46 Allée d'Italie, F-69007 Lyon, France
2 Department of Theoretical Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
3 Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057, CNRS-Université Paris-Diderot, F-75205 Paris Cedex 13, France

E-mail

eric.bertin@ens-lyon.fr

Journal

Journal of Physics A: Mathematical and Theoretical Create an alert RSS this journal

Issue

Volume 42, Number 44

Citation

Eric Bertin et al 2009 J. Phys. A: Math. Theor. 42 445001

doi: 10.1088/1751-8113/42/44/445001


[1]
Toner J, Tu Y and Ramaswamy S 2005 Ann. Phys. 318 170
CrossRef link
[2]
Parrish J K and Hamner W M (ed) 1997 Animal Groups in Three Dimensions (Cambridge: Cambridge University Press)
[3]
Helbing D, Farkas I and Vicsek T 2000 Nature 407 487
CrossRef link PubMed Abstract
[4]
Helbing D, Farkas I J and Vicsek T 2000 Phys. Rev. Lett. 84 1240
PubMed Abstract CrossRef link
[5]
Feare C 1984 The Starlings (Oxford: Oxford University Press)
[6]
Hubbard S, Babak P, Sigurdsson S and Magnusson K 2004 Ecol. Model. 174 359
CrossRef link
[7]
Rauch E, Millonas M and Chialvo D 1995 Phys. Lett. A 207 185
CrossRef link
[8]
Ben-Jacob E, Cohen I, Shochet O, Czirók A and Vicsek T 1995 Phys. Rev. Lett. 75 2899
CrossRef link PubMed Abstract
[9]
Harada Y, Nogushi A, Kishino A and Yanagida T 1987 Nature (Lond.) 326 805
PubMed Abstract CrossRef link
[10]
Badoual M, Jülicher F and Prost J 2002 Proc. Natl Acad. Sci. USA 99 6696
PubMed Abstract CrossRef link
[11]
Sugawara K, Sano M and Watanabe T 2002 Proc. of 2002 FIRA Robot World Congress p 36
[12]
Vicsek T, Czirók A, Ben-Jacob E, Cohen I and Shochet O 1995 Phys. Rev. Lett. 75 1226
PubMed Abstract CrossRef link
[13]
Czirók A, Stanley H E and Vicsek T 1997 J. Phys. A: Math. Gen. 30 1375
CrossRef link IOP Article
[14]
Grégoire G and Chaté H 2004 Phys. Rev. Lett. 92 025702
PubMed Abstract CrossRef link
[15]
Chaté H, Ginelli F, Grégoire G and Raynaud F 2008 Phys. Rev. E 77 046113
CrossRef link
[16]
Csahòk Z and Cziròk A 2002 Physica A 243 304
CrossRef link
[17]
Toner J and Tu Y 1995 Phys. Rev. Lett. 75 4326
CrossRef link PubMed Abstract
[18]
Toner J and Tu Y 1998 Phys. Rev. E 58 4828-58
CrossRef link
[19]
Bertin E, Droz M and Grégoire G 2006 Phys. Rev. E 74 022101
CrossRef link
[20]
Baskaran A and Marchetti M 2008 Phys. Rev. Lett. 101 268101
PubMed Abstract CrossRef link
[21]
Dauxois T and Peyrard M 2006 Physics of Solitons (Cambridge: Cambridge University Press)
[22]
Albano E V 1996 Phys. Rev. Lett. 77 2129
CrossRef link PubMed Abstract
[23]
Aldana M, Dossetti V, Huepe C, Kenkre V M and Larralde H 2007 Phys. Rev. Lett. 98 095702
PubMed Abstract CrossRef link
[24]
Aldana M and Huepe C 2003 J. Stat. Phys. 112 135
CrossRef link
[25]
Couzin I D 2002 J. Theor. Biol. 218 1
CrossRef link PubMed Abstract
[26]
Duparcmeur Y L, Herrman H and Troadec J P 1995 J. Phys. I (France) 5 1119
CrossRef link
[27]
Grégoire G, Chaté H and Tu Y 2001 Phys. Rev. E 64 011902
CrossRef link
[28]
Levine H, Rappel W J and Cohen I 2000 Phys. Rev. E 63 017101
CrossRef link
[29]
Mikhailov A S and Zanette D H 1999 Phys. Rev. E 60 4571
CrossRef link
[30]
Shimoyama N, Sugawara K, Mizuguchi T, Hayakawa Y and Sano M 1996 Phys. Rev. Lett. 76 3870
CrossRef link PubMed Abstract
[31]
Ratushnaya V I, Bedeaux D, Kulinskii V L and Zvelindovsy A V 2007 Physica A 381 39-46
CrossRef link
[32]
Degond P and Motsch S 2007 Comptes-rendus Mathématiques 345 555-60
CrossRef link
[33]
Degond P and Motsch S 2008 J. Stat. Phys. 131 989-1021
CrossRef link
[34]
Binder K 1976 Phase Transitions and Critical Phenomena ed C Domb and M S Green (New York: Academic)
[35]
Müller-Krumbhaar H and Binder K 1973 J. Stat. Phys. 8 1
CrossRef link
[36]
Privman V (ed) 1990 Finite Size Scaling and Numerical Simulations of Statistical Systems (Singapore: World Scientific)
[37]
Borgs C and Kotecký R 1990 J. Stat. Phys. 61 79
CrossRef link
[38]
Lübeck S 2004 Int. J. Mod. Phys. B 18 3977-4118
CrossRef link
[39]
Marcq P, Chaté H and Manneville P 2006 Prog. Theor. Phys. Suppl. 161 244
CrossRef link
[40]
Grégoire G 2002 Mouvement Collectif et Physique hors d'équilibre PhD thesis Université Paris 7-Denis Diderot
[41]
Baglietto G and Albano E V 2008 Phys. Rev. E 78 021125
CrossRef link
crossref member

View by subject


Export