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F. Ginelli and H. Chaté, Relevance of Metric-Free Interactions in Flocking Phenomena, Physical Review Letters, vol.105, issue.16, pp.168103-168123, 2010.
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F. Ginelli, F. Peruani, M. Bar, and H. Chaté, Large-Scale Collective Properties of Self-Propelled Rods, Physical Review Letters, vol.104, issue.18, pp.184502-184522, 2010.
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L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, Defect Annihilation and Proliferation in Active Nematics, Physical Review Letters, vol.110, issue.22, pp.228101-2013
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A. Gopinath, M. F. Hagan, M. C. Marchetti, and A. Baskaran, Dynamical self-regulation in self-propelled particle flows, Physical Review E, vol.85, issue.6, p.2012
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A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson, Enhanced mixing and spatial instability in concentrated bacterial suspensions, Physical Review E, vol.80, issue.3, p.31903, 2009.
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E. Bertin, M. Droz, and G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles, Physical Review E, vol.74, issue.2, pp.22101-445001, 2006.
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M. Moussa?¨dmoussa?¨d, D. Helbing, and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Sciences, vol.108, issue.17, p.6884, 2011.
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F. Ginelli and H. Chaté, Relevance of Metric-Free Interactions in Flocking Phenomena, Physical Review Letters, vol.105, issue.16, p.168103, 2010.
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¼. For and . Ae=2, one has to resort to higher orders, and then finds s þ % q 2 ðÀð 0 =Þ þ 2 2 À 4 2 þ 0 Þ= ð8 2 Þ. This quantity is always negative for the coefficients of Eq

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I. S. Aranson and L. S. Tsimring, Pattern formation of microtubules and motors: Inelastic interaction of polar rods, Physical Review E, vol.71, issue.5, 2005.
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I. S. Aranson and L. S. Tsimring, Theory of self-assembly of microtubules and motors, Physical Review E, vol.74, issue.3, p.31915, 2006.
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T. Balch and R. C. Arkin, Behavior-based formation control for multirobot teams, IEEE Transactions on Robotics and Automation, vol.14, issue.6, pp.926-939, 1998.
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M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proceedings of the National Academy of Sciences, pp.1232-1237, 2008.
DOI : 10.1073/pnas.0711437105

A. Baskaran and M. C. Marchetti, Hydrodynamics of self-propelled hard rods, Physical Review E, vol.77, issue.1, p.11920, 2008.
DOI : 10.1103/PhysRevE.77.011920

A. Baskaran and M. C. Marchetti, Self-regulation in self-propelled nematic fluids, The European Physical Journal E, vol.306, issue.9, pp.95-2012
DOI : 10.1140/epje/i2012-12095-8

E. Bertin, M. Droz, and G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles, Physical Review E, vol.74, issue.2, 2006.
DOI : 10.1103/PhysRevE.74.022101

URL : https://hal.archives-ouvertes.fr/hal-00910408

E. Bertin, M. Droz, and G. Grégoire, Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.44, p.445001, 2009.
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URL : https://hal.archives-ouvertes.fr/ensl-00434536

D. L. Blair, T. Neicu, and A. Kudrolli, Vortices in vibrated granular rods, Physical Review E, vol.67, issue.3, p.31303, 2003.
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J. P. Boyd, D. Buhl, I. D. Sumpter, J. J. Couzin, E. Hale et al., Chebyshev and Fourier spectral methods From disorder to order in marching locusts, Cited on page 57.) [12], pp.3121402-1406, 2001.

A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati et al., Scale-free correlations in starling flocks, Proceedings of the National Academy of Sciences of the United States of America, pp.11865-11870, 2010.
DOI : 10.1073/pnas.1005766107

L. Chen, N. Goldenfeld, and Y. Oono, Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory, Physical Review E, vol.54, issue.1, pp.376-394, 1996.
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L. H. Cisneros, R. Cortez, C. Dombrowski, R. E. Goldstein, and J. O. Kessler, Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations, Experiments in Fluids, vol.84, issue.5, pp.737-753, 2007.
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D. S. Dean, Langevin equation for the density of a system of interacting Langevin processes, Journal of Physics A: Mathematical and General, vol.29, issue.24, pp.613-617, 1996.
DOI : 10.1088/0305-4470/29/24/001

J. Gautrais, C. Jost, M. Soria, A. Campo, S. Motsch et al., Analyzing fish movement as a persistent turning walker, Journal of Mathematical Biology, vol.206, issue.3, pp.429-445, 2009.
DOI : 10.1007/s00285-008-0198-7

URL : https://hal.archives-ouvertes.fr/hal-00315336

F. Ginelli and H. Chaté, Relevance of Metric-Free Interactions in Flocking Phenomena, Physical Review Letters, vol.105, issue.16, pp.168103-168123, 2010.
DOI : 10.1103/PhysRevLett.105.168103

F. Ginelli, F. Peruani, M. Bar, and H. Chaté, Large-Scale Collective Properties of Self-Propelled Rods, Physical Review Letters, vol.104, issue.18, pp.184502-184522, 2010.
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URL : https://hal.archives-ouvertes.fr/hal-00905223

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, Defect Annihilation and Proliferation in Active Nematics, Physical Review Letters, vol.110, issue.22, pp.228101-2013
DOI : 10.1103/PhysRevLett.110.228101

A. Gopinath, M. F. Hagan, M. C. Marchetti, and A. Baskaran, Dynamical self-regulation in self-propelled particle flows, Physical Review E, vol.85, issue.6, p.2012
DOI : 10.1103/PhysRevE.85.061903

Y. Hatwalne, S. Ramaswamy, M. Rao, and R. A. Simha, Rheology of Active-Particle Suspensions, Physical Review Letters, vol.92, issue.11, p.118101, 2004.
DOI : 10.1103/PhysRevLett.92.118101

T. Ihle, Kinetic theory of flocking: Derivation of hydrodynamic equations, Physical Review E, vol.83, issue.3, p.2011
DOI : 10.1103/PhysRevE.83.030901

T. Ihle, Invasion-wave-induced first-order phase transition in systems of active particles, Physical Review E, vol.88, issue.4, 2013.
DOI : 10.1103/PhysRevE.88.040303

C. Lanczos, Linear differential operators, 1961.

L. D. Landau and L. D. Landau, Edited and with an introduction by D. ter Haar, p.24, 1965.

N. D. Mermin and H. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models, Physical Review Letters, vol.17, issue.22, pp.1133-1136, 1966.
DOI : 10.1103/PhysRevLett.17.1133

S. Mishra, A. Baskaran, and M. C. Marchetti, Fluctuations and pattern formation in self-propelled particles, Physical Review E, vol.81, issue.6, p.61916, 2010.
DOI : 10.1103/PhysRevE.81.061916

M. Moussaid, D. Helbing, and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Sciences, vol.108, issue.17, pp.6884-6888, 2011.
DOI : 10.1073/pnas.1016507108

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3084058

S. Ramaswamy, R. A. Simha, and J. Toner, Active nematics on a substrate: Giant number fluctuations and long-time tails, Europhysics Letters (EPL), vol.62, issue.2, pp.196-202, 2003.
DOI : 10.1209/epl/i2003-00346-7

P. Romanczuk and L. Schimansky-geier, Mean-field theory of collective motion due to velocity alignment, Ecological Complexity, vol.10, pp.83-92
DOI : 10.1016/j.ecocom.2011.07.008

V. Schaller, C. Weber, C. Semmrich, E. Frey, and A. R. Bausch, Polar patterns of driven filaments, Nature, vol.317, issue.7311, pp.73-77, 2010.
DOI : 10.1038/nature09312

A. Sokolov and I. S. Aranson, Reduction of Viscosity in Suspension of Swimming Bacteria, Physical Review Letters, vol.103, issue.14, p.148101, 2009.
DOI : 10.1103/PhysRevLett.103.148101

A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson, Enhanced mixing and spatial instability in concentrated bacterial suspensions, Physical Review E, vol.80, issue.3, p.31903, 2009.
DOI : 10.1103/PhysRevE.80.031903

J. Toner and Y. H. Tu, Model: How Birds Fly Together, Physical Review Letters, vol.75, issue.23, pp.4326-4329, 1995.
DOI : 10.1103/PhysRevLett.75.4326

J. Toner, Y. H. Tu, and S. Ramaswamy, Hydrodynamics and phases of flocks, Annals of Physics, vol.318, issue.1, pp.170-244021305, 2003.
DOI : 10.1016/j.aop.2005.04.011

I. S. Aranson and L. S. Tsimring, Pattern formation of microtubules and motors: Inelastic interaction of polar rods, Physical Review E, vol.71, issue.5, 2005.
DOI : 10.1103/PhysRevE.71.050901

I. S. Aranson and L. S. Tsimring, Theory of self-assembly of microtubules and motors, Physical Review E, vol.74, issue.3, p.31915, 2006.
DOI : 10.1103/PhysRevE.74.031915

T. Balch and R. C. Arkin, Behavior-based formation control for multirobot teams, IEEE Transactions on Robotics and Automation, vol.14, issue.6, pp.926-939, 1998.
DOI : 10.1109/70.736776

M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proceedings of the National Academy of Sciences, pp.1232-1237, 2008.
DOI : 10.1073/pnas.0711437105

A. Baskaran and M. C. Marchetti, Hydrodynamics of self-propelled hard rods, Physical Review E, vol.77, issue.1, p.11920, 2008.
DOI : 10.1103/PhysRevE.77.011920

A. Baskaran and M. C. Marchetti, Self-regulation in self-propelled nematic fluids, The European Physical Journal E, vol.306, issue.9, pp.95-2012
DOI : 10.1140/epje/i2012-12095-8

E. Bertin, M. Droz, and G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles, Physical Review E, vol.74, issue.2, 2006.
DOI : 10.1103/PhysRevE.74.022101

URL : https://hal.archives-ouvertes.fr/hal-00910408

E. Bertin, M. Droz, and G. Grégoire, Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.44, p.445001, 2009.
DOI : 10.1088/1751-8113/42/44/445001

URL : https://hal.archives-ouvertes.fr/ensl-00434536

D. L. Blair, T. Neicu, and A. Kudrolli, Vortices in vibrated granular rods, Physical Review E, vol.67, issue.3, p.31303, 2003.
DOI : 10.1103/PhysRevE.67.031303

J. P. Boyd, D. Buhl, I. D. Sumpter, J. J. Couzin, E. Hale et al., Chebyshev and Fourier spectral methods From disorder to order in marching locusts, Cited on page 57.) [12], pp.3121402-1406, 2001.

A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati et al., Scale-free correlations in starling flocks, Proceedings of the National Academy of Sciences of the United States of America, pp.11865-11870, 2010.
DOI : 10.1073/pnas.1005766107

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2900681

L. Chen, N. Goldenfeld, and Y. Oono, Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory, Physical Review E, vol.54, issue.1, pp.376-394, 1996.
DOI : 10.1103/PhysRevE.54.376

URL : http://arxiv.org/abs/hep-th/9506161

L. H. Cisneros, R. Cortez, C. Dombrowski, R. E. Goldstein, and J. O. Kessler, Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations, Experiments in Fluids, vol.84, issue.5, pp.737-753, 2007.
DOI : 10.1007/s00348-007-0387-y

D. S. Dean, Langevin equation for the density of a system of interacting Langevin processes, Journal of Physics A: Mathematical and General, vol.29, issue.24, pp.613-617, 1996.
DOI : 10.1088/0305-4470/29/24/001

J. Gautrais, C. Jost, M. Soria, A. Campo, S. Motsch et al., Analyzing fish movement as a persistent turning walker, Journal of Mathematical Biology, vol.206, issue.3, pp.429-445, 2009.
DOI : 10.1007/s00285-008-0198-7

URL : https://hal.archives-ouvertes.fr/hal-00315336

F. Ginelli and H. Chaté, Relevance of Metric-Free Interactions in Flocking Phenomena, Physical Review Letters, vol.105, issue.16, pp.168103-168123, 2010.
DOI : 10.1103/PhysRevLett.105.168103

F. Ginelli, F. Peruani, M. Bar, and H. Chaté, Large-Scale Collective Properties of Self-Propelled Rods, Physical Review Letters, vol.104, issue.18, pp.184502-184522, 2010.
DOI : 10.1103/PhysRevLett.104.184502

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