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Transient phases in the Vicsek model of flocking

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DOI: 10.23977/jptc.2018.11003 | Downloads: 143 | Views: 5363

Author(s)

Sayantani Kayal 1, Muktish Acharyya 1

Affiliation(s)

1 Department of Physics, Presidency University 86/1 College street, Kolkata-700073, India

Corresponding Author

Sayantani Kayal

ABSTRACT

The Vicsek model of flocking is studied by computer simulation. We confined our studies here to the morphologies and the lifetimes of transient phases. In our simulation, we have identified three distinct transient phases, namely, vortex phase, colliding phase and multi-domain phase. The mapping of Vicsek model to XY model in the v->0 limit prompted us to explore the possibility of finding any vortex kind of phases in the Vicsek model. We have obtained rotating vortex phase and measured the lifetime of this vortex phase. We have also measured the lifetimes of other two transient phases, i.e., colliding phase and multi-domain phase. We have measured the integrated lifetime (Tt) of all these transient phases and studied this as function of density and noise. In the low noise regime, we proposed here a scaling law TtN-a = F(pN-b) where F(x) is a scaling function like F(x)~x-s. By the method of data collapse, we have estimated the exponents as a = -0.110+/-0.010, b = 0.950+/-0.010 and s = 1.027+/-0.008. The integrated lifetime T (defined in the text differently) was observed to decrease as the noise approaches the critical noise from below. This behaviour is quite unusual and contrary to the critical slowing down observed in the case of well-known equilibrium phase transitions. We have provided a possible explanation from the time evolution of the distribution of the directions of velocities.

KEYWORDS

Vicsek model, Transient phases, Lifetime, Data collapse, Scaling, Critical slowing down.

CITE THIS PAPER

Sayantani, K., Muktish, A., Transient phases in the Vicsek model of fl ocking, Journal of Physics Through Computation (2018) 1: 17-30.

REFERENCES

[1] S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Physics 1 (2010) 323-345. doi:10.1146/annurev-conmatphys-070909-104101.
[2] V. Narayan, S. Ramaswamy, N. Menon, Long-lived giant number uctuations in a swarming granular nematic, Science 317 (5834) (2007) 105-108. doi:10.1126/science.1140414.
[3] M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85 (3) (2013) 1143. doi:10.1103/RevModPhys.85.1143.
[4] I. D. Couzin, J. Krause, R. James, G. D. Ruxton, N. R. Franks, Collective memory and spatial sorting in animal groups, J. theor. Biol. 218 (1) (2002) 1{11.
[5] C. K. Hemelrijk, D. A. P. Reid, H. Hildenbrandt, J. T. Padding, The increased efficiency of fish swimming in a school, FISH and FISHERIES 16 (3) (2015) 511-521. doi:10.1111/faf.12072.
[6] E. Mehes, T. Vicsek, Collective motion of cells: from experiments to models, Integr. Biol. 6 (9) (2014) 831-854. doi:10.1039/c4ib00115j.
[7] T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, O. Schochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75 (6) (1995) 1226. doi:10.1103/PhysRevLett.75.1226.
[8] N. D. Mermin, H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17 (22) (1966) 1133. doi:10.1103/PhysRevLett.17.1133.
[9] T. Vicsek, A. Zafeiris, Collective motion, Physics Reports 517 (3{4) (2012) 71-140. doi:10.1016/j.physrep.2012.03.004.
[10] F. Ginelli, The physics of the Vicsek model, Eur. Phys. J. Special Topics 225 (11{12) (2016) 2099-2117. doi:10.1140/epjst/e2016-60066-8.
[11] A. Filella, F. Nadal, C. Sire, E. Kanso, C. Eloy, Model of collective fish behavior with hydrodynamic interactions, Phys. Rev. Lett. 120 (19) (2018) 198101. doi:10.1103/PhysRevLett.120.198101.
[12] B. Bhattacherjee, S. Mishra, S. S. Manna, Topological-distance-dependent transition in ocks with binary interactions, Phys. Rev. E 92 (6) (2015) 062134. doi:10.1103/PhysRevE.92.062134.
[13] B. Bhattacherjee, K. Bhattacharya, S. S. Manna, Cyclic and coherent states in ocks with topological distance, Frontiers in Physics 1 (2014) 35. doi:10.3389/fphy.2013.00035.
[14] M. Durve, A. Saha, A. Sayeed, Active particle condensation by non-reciprocal and time-delayed interactions, Eur. Phys. J. E 41 (4) (2018) 49. doi:10.1140/epje/i2018-11653-4.
[15] A. Choudhary, D. Venkatraman, S. S. Ray, Effect of inertia on model ocks in a turbulent environment, Europhysics Letters 112 (2) (2015) 24005. doi:10.1209/0295-5075/112/24005.
[16] A. P. Solon, H. Chate, J. Tailleur, From phase to microphase separation in ocking models: The essential role of nonequi-librium uctuations, Phys. Rev. Lett. 114 (6) (2015) 068101. doi:10.1103/PhysRevLett.114.068101.
[17] A. P. Solon, J. Tailleur, Revisiting the ocking transition using active spins, Phys. Rev. Lett. 111 (7) (2013) 078101. doi:10.1103/PhysRevLett.111.078101.
[18] A. P. Solon, J.-B. Caussin, D. Bartolo, H. Chate, J. Tailleur, Pattern formation in ocking models: A hydrodynamic description, Phys. Rev. E 92 (6) (2015) 062111. doi:10.1103/PhysRevE.92.062111.
[19] G. Gregoire, H. Chate, Onset of collective and cohesive motion, Phys. Rev. Lett. 92 (2) (2004) 025702. doi:10.1103/PhysRevLett.92.025702.
[20] J. M. Kosterlitz, D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6 (7) (1973) 1181.
[21] D. S. Calovi, U. Lopez, S. Ngo, C. Sire, H. Chate, G. Theraulaz, Swarming, schooling, milling: Phase diagram of a data-driven fish school model, New J. Phys. 16 (2014) 015026. doi:10.1088/1367-2630/16/1/015026.

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