Flocking in one dimension: Asters and reversals

Benvegnen, Brieuc; Chaté, Hugues; Krapivsky, P. L.; Tailleur, Julien; Solon, Alexandre

doi:10.1103/physreve.106.054608

Cited by 6 publications

(7 citation statements)

References 60 publications

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“…We observe that these clusters never coalesce due to the lack of transverse fluctuations and thus never form a band or polar liquid phase. Similar observations are made when the constant transverse diffusion is switched off in the two-dimensional active Ising model (AIM) [33], although the one-dimensional AIM [34] exhibits a flocking state consisting of a single dense ordered aggregate. Unsurprisingly, analogous to q = 2 and q = 4, for small η, we observe a cluster phase also for the q = 3 DVM.…”

Section: Collective Motion and Phase Diagramsupporting

confidence: 55%

Consequence of anisotropy on flocking: the discretized Vicsek model

Karmakar,

Chatterjee,

Paul

et al. 2024

New J. Phys.

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We numerically study a discretized Vicsek model (DVM) with particles orienting in q possibleorientations in two dimensions. The study probes the significance of anisotropic orientation andmicroscopic interaction on the macroscopic behavior. The DVM is an off-lattice flocking model likethe active clock model [ACM; EPL 138, 41001 (2022)] but the dynamical rules of particle alignmentand movement are inspired by the prototypical Vicsek model (VM). The DVM shows qualitativelysimilar properties as the ACM for intermediate noise strength where a transition from macrophaseto microphase separation of the coexistence region is observed as q is increased. But for small qand noise strength, the liquid phase appearing in the ACM at low temperatures is replaced in theDVM by a configuration of multiple clusters with different polarization which does not exhibit anylong-range order. We find that the dynamical rules have a profound influence on the overarchingfeatures of the flocking phase. We further identify the metastability of the ordered liquid phasesubjected to a perturbation.

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Section: Collective Motion and Phase Diagramsupporting

confidence: 55%

Consequence of anisotropy on flocking: the discretized Vicsek model

Karmakar,

Chatterjee,

Paul

et al. 2024

New J. Phys.

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“…Comparing equation (48) with equation ( 46), we remark that F does not depend on ΓD/v 2 nor on Γ/(v ρ) for the fully connected AIM. For this specific kind of alignment, fluctuations leads to a density-independent correction of the linear Landau term and, consistent with the results of [53], the continuous mean-field transition to collective motion resists fluctuations.…”

Section: J Stat Mech (2024) 084003mentioning

confidence: 87%

“…We then extend our analysis to topological AIMs in section 5, and to Vicsek-like models in section 6. Throughout this article, many numerical results are presented and the corresponding numerical simulations are detailed in appendix F. We note that several of our simulations are implemented in one dimension where it is well known that flocks are metastable and ultimately undergo reversals [25,47,48]. All our simulations were carried out using simulation times shorter than the average time between reversals, to focus on the nature of the transition and not on this otherwise interesting phenomenon.…”

Section: J Stat Mech (2024) 084003mentioning

confidence: 99%

Fluctuation-induced first order transition to collective motion

Martin,

Spera,

Chaté

et al. 2024

J. Stat. Mech.

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The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

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“…Note that it was recently found [30] that the flocking transition does not survive in the one-dimensional AIM. Instead it is replaced by either direction-reversing ordered aggregates or static asters composed of opposing clusters of left and right movers that block each other.…”

Section: Microscopic Dynamics Of Aligning Active Spinsmentioning

confidence: 97%

Thermodynamically consistent flocking: from discontinuous to continuous transitions

Agranov,

Jack,

Cates

et al. 2024

New J. Phys.

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We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhibits tricritical behavior. Self-propulsion has a non-perturbative effect on the phase diagram, yielding novel phase behaviors depending on the type of aligning interactions. For aligning interaction that increase monotonically with the density, the tricritical point diverges to infinite density reproducing the standard scenario of a discontinuous flocking transition accompanied by traveling bands. In contrast, for models where the aligning interaction is non-monotonic in density, the system can exhibit either (the nonequilibrium counterpart of) an azeotropic point, associated with a continuous flocking transition, or a state with counterpropagating bands.

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Flocking in one dimension: Asters and reversals

Cited by 6 publications

References 60 publications

Consequence of anisotropy on flocking: the discretized Vicsek model

Consequence of anisotropy on flocking: the discretized Vicsek model

Fluctuation-induced first order transition to collective motion

Thermodynamically consistent flocking: from discontinuous to continuous transitions

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