Susceptibility of Orientationally Ordered Active Matter to Chirality Disorder

Bruno Ventejou, Hugues Chaté, Raul Montagne, and Xia-qing Shi

Phys. Rev. Lett. 127, 238001 – Published 30 November 2021

Abstract

We investigate the susceptibility of long-range ordered phases of two-dimensional dry aligning active matter to population disorder, taken in the form of a distribution of intrinsic individual chiralities. Using a combination of particle-level models and hydrodynamic theories derived from them, we show that while in finite systems all ordered phases resist a finite amount of such chirality disorder, the homogeneous ones (polar flocks and active nematics) are unstable to any amount of disorder in the infinite-size limit. On the other hand, we find that the inhomogeneous solutions of the coexistence phase (bands) may resist a finite amount of chirality disorder even asymptotically.

Received 29 July 2021
Accepted 27 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.238001

Physics Subject Headings (PhySH)

Collective behavior

Active nematics Dry active matter Living matter & active matter

Collective dynamics Theories of collective dynamics & active matter Vicsek model

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Bruno Ventejou¹, Hugues Chaté ^1,2,3, Raul Montagne ⁴, and Xia-qing Shi ⁵

¹Service de Physique de l’Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
²Computational Science Research Center, Beijing 100193, China
³Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, 75005 Paris, France
⁴Departamento de Fisica, Universidade Federal Rural de Pernambuco (UFRPE), 52171-900 Recife, Pernambuco, Brazil
⁵Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China

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Issue

Vol. 127, Iss. 23 — 3 December 2021

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Images

Figure 1
Phase diagrams in the $(ω_{0}, D_{r})$ plane ( $ρ_{0} = κ = v_{0} = 1$ , $L = 256$ ). (a),(c) (left column) ferromagnetic alignment. (b),(d) (right column) nematic alignment. Top row (a),(b) Gaussian distribution; bottom row (c),(d) bimodal distribution. (Details about the numerical protocol used to build these diagrams are given in Supplemental Material [37].).
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Figure 2
Typical snapshots of phases reported in Fig. 1 taken after transients following random initial conditions. These images were obtained in the Gaussian case, except the polar rotating packets [panels (d),(h)], which are only observed in the bimodal case. For each phase, two subpanels are shown: particles’ orientation (left) and intrinsic chirality (right) are represented as small colored segments [color maps are in panel (g)]. For (e)–(g), which have local nematic order, $2 θ$ is represented in the left subpanel. For the other phases, the polar angle $θ$ is shown. In the right subpanels, chirality-segregated structures appear red (CW) or blue (CCW), while mixed chirality regions appear purple. The chirality color map goes from $- ω_{\max}$ to $+ ω_{\max}$ , with $ω_{\max}$ adapted for each panel for better legibility. (a) polar liquid ( $ω_{0} = 0.004$ , $D_{r} = 0.03$ , $ω_{\max} = 0.005$ ). (b) polar (Vicsek) bands ( $ω_{0} = 0.004$ , $D_{r} = 0.06$ , $ω_{\max} = 0.005$ ). (c) polar vortices ( $ω_{0} = 0.054$ , $D_{r} = 0.03$ , $ω_{\max} = 0.05$ ). (d) rotating polar packets ( $ω_{0} = 0.167$ , $D_{r} = 0.03$ , $ω_{\max} = 0.5$ ). (e) nematic liquid ( $ω_{0} = 0.004$ , $D_{r} = 0.008$ , $ω_{\max} = 0.005$ ). (f) active foam ( $ω_{0} = 0.03$ , $D_{r} = 0.016$ , $ω_{\max} = 0.02$ ). (g) nematic vortices ( $ω_{0} = 0.118$ , $D_{r} = 0.012$ , $ω_{\max} = 0.05$ ). (h) rotating polar packets ( $ω_{0} = 0.05$ , $D_{r} = 0.002$ , $ω_{\max} = 0.1$ ).
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Figure 3
(a) Variation of the $[0, ω_{0}^{*} (L)]$ domain of existence of the homogeneous ordered phases with system size $L$ (ferromagnetic cases $D_{r} = 0.03$ , nematic cases $D_{r} = 0.004$ ). (b) Snapshot taken in the region of coexistence between Vicsek bands and polar vortices [ferromagnetic alignment, Gaussian distribution of chiralities, $ω_{0} = 0.06$ , $D_{r} = 0.054$ , $L = 256$ , colors indicate particles’ orientation as in Figs. 2 and 2, left subpanels].
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Figure 4
Linear stability analysis of the homogeneous ordered solution of the hydrodynamic theory ( $ρ^{+} = ρ^{-} = 1$ ). (a) Direction of most unstable mode in $(ω_{0}, D_{r})$ plane (in the gray area, the solution does not exist; the homogeneous disordered solution is linearly unstable below the dashed line). (b) Variation of $L^{†}$ (size of largest stable system) with $ω_{0}$ at fixed $D_{r} = 0.4$ .
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