Abstract
Swarming behaviour is abundant in nature. Over many different length scales, in for example herds, flocking birds and swimming bacteria, roughly identical individuals interact locally to achieve group behaviour. The similarities between these examples suggests the existence of a general underlying principle. We propose here a local interaction model for self-propelling, elliptical particles that results in collective motion. Any particle interacts with its neighbours only, experiences noise on its orientation and pushes inwards if it is in the outer layer of the group. Initially, alignment between particles is the result of steric repulsion. We observe two types of group behaviour. The first type is a migrating group, where particles in the bulk are aligned over large length scales, but do not rearrange. The second type has very little net motion. The elliptical particles form smaller regions of aligned and antialigned particles, effectively cancelling the net motion of the group. Finally, we compare the group behaviour of elliptical particles to circular ones and investigate the importance of polar alignment. We conclude that polar alignment is a requirement for large-scale collective dynamics, like collective migration and rotation.
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References
Calovi, D.S., Lopez, U., Ngo, S., Sire, C., Chaté, H., Theraulaz, G.: Swarming, schooling, milling: phase diagram of a data-driven fish school model. New J. Phys. 16(1), 015026 (2014)
Cavagna, A., Del Castello, L., Dey, S., Giardina, I., Melillo, S., Parisi, L., Viale, M.: Short-range interactions versus long-range correlations in bird flocks. Phys. Rev. E 92(1), 012705 (2015)
Collett, M., Despland, E., Simpson, S.J., Krakauer, D.C.: Spatial scales of desert locust gregarization. Proc. Natl. Acad. Sci. 95(22), 13052–13055 (1998)
Czirók, A., Ben-Jacob, E., Cohen, I., Vicsek, T.: Formation of complex bacterial colonies via self-generated vortices. Phys. Rev. E 54(2), 1791 (1996)
Czirók, A., Vicsek, T.: Collective behavior of interacting self-propelled particles. Phys. A Stat. Mech. Appl. 281(1), 17–29 (2000)
van Drongelen, R., Pal, A., Goodrich, C.P., Idema, T.: Collective dynamics of soft active particles. Phys. Rev. E 91(3), 032706 (2015)
Henkes, S., Fily, Y., Marchetti, M.C.: Active jamming: self-propelled soft particles at high density. Phys. Rev. E 84(4), 040301 (2011)
Landau, L., Lifshitz, E.: Fluid Mechanics, vol. 6 (1987). Course of Theoretical Physics, pp. 227–229
Rappel, W.J., Nicol, A., Sarkissian, A., Levine, H., Loomis, W.F.: Self-organized vortex state in two-dimensional dictyostelium dynamics. Phys. Rev. Lett. 83(6), 1247 (1999)
Thutupalli, S., Sun, M., Bunyak, F., Palaniappan, K., Shaevitz, J.W.: Directional reversals enable myxococcus xanthus cells to produce collective one-dimensional streams during fruiting-body formation. J. R. Soc. Interface 12(109), 20150049 (2015)
Tunstrøm, K., Katz, Y., Ioannou, C.C., Huepe, C., Lutz, M.J., Couzin, I.D.: Collective states, multistability and transitional behavior in schooling fish. PLoS Comput. Biol. 9(2), e1002915 (2013)
Vasiev, B., Siegert, F., Weller, C.J.: A hydrodynamic model fordictyostelium discoideummound formation. J. Theor. Biol. 184(4), 441–450 (1997)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226 (1995)
Vicsek, T., Zafeiris, A.: Collective motion. Phys. Rep. 517(3), 71–140 (2012)
Weijer, C.J.: Dictyostelium morphogenesis. Curr. Opin. Genet. Dev. 14(4), 392–398 (2004)
Wu, Y., Kaiser, A.D., Jiang, Y., Alber, M.S.: Periodic reversal of direction allows myxobacteria to swarm. Proc. Natl. Acad. Sci. 106(4), 1222–1227 (2009)
Zeravcic, Z., Xu, N., Liu, A., Nagel, S., van Saarloos, W.: Excitations of ellipsoid packings near jamming. EPL (Europhys. Lett.) 87(2), 26001 (2009)
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van Drongelen, R., Idema, T. (2016). Collective Dynamics and Motility of Soft Elliptical Particles. In: Knoop, V., Daamen, W. (eds) Traffic and Granular Flow '15. Springer, Cham. https://doi.org/10.1007/978-3-319-33482-0_76
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DOI: https://doi.org/10.1007/978-3-319-33482-0_76
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