Pattern formation in flocking models: A hydrodynamic description

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Alexandre SolonJulien Tailleur

Abstract

We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.

References

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Citations

Nov 26, 2019·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·N Gorbushin, L Truskinovsky
Oct 3, 2019·Physical Review. E·Nikos KyriakopoulosFrancesco Ginelli
May 14, 2016·Physical Review. E·Yao-Li ChuangMaria R D'Orsogna
Dec 15, 2016·Physical Review. E·Robert GroßmannMarkus Bär
Feb 1, 2020·Physical Review Letters·Ananyo MaitraMartin Lenz
Jan 14, 2017·Physical Review. E·Hamid Seyed-AllaeiMohammad Reza Ejtehadi
Jun 17, 2018·Physical Review. E·Pavel Castro-Villarreal, Francisco J Sevilla
Jul 16, 2017·Physical Review. E·M HubertS Perrard
Jul 14, 2018·Physical Review Letters·Mourtaza Kourbane-HousseneJulien Tailleur
Oct 17, 2019·Soft Matter·Biplab Bhattacherjee, Debasish Chaudhuri
Nov 21, 2020·Physical Review. E·Matthieu MangeatHeiko Rieger
Nov 17, 2020·Physical Review Letters·Rüdiger Kürsten, Thomas Ihle
Apr 24, 2021·Physical Review Letters·David MartinFrédéric Van Wijland
May 20, 2021·Physical Review. E·N Gorbushin, L Truskinovsky
Nov 10, 2021·Soft Matter·C Miguel Barriuso GutiérrezChantal Valeriani

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