Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

Chervanyov, A. I.; Gómez, Héctor; Thiele, Uwe

doi:10.1209/0295-5075/115/68001

Cited by 16 publications

(25 citation statements)

References 18 publications

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“…However, in our work we avoid spontaneous polarization and use C 1 > 0 with C 2 = 0 as also done in most of the analyses of Refs. [38,39,65]. With C 1 > 0 diffusion tends to reduce polarization.…”

Section: The Model: Governing Equationsmentioning

confidence: 99%

Two-dimensional localized states in an active phase-field-crystal model

et al. 2021

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The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. The analysis is carried out for the model in two spatial dimensions. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.

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Section: The Model: Governing Equationsmentioning

confidence: 99%

Two-dimensional localized states in an active phase-field-crystal model

et al. 2021

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“…However, in most of our work we will avoid spontaneous polarization using positive C 1 > 0 and C 2 = 0 as also done in most of the analysis of Refs. [27,28,54]. With C 1 > 0 diffusion reduces the polarization.…”

Section: A Governing Equationsmentioning

confidence: 99%

“…Alternatively to Cardano's method, the critical wavenumber can be approximated by k c ≈ 1 as used in Ref. [54]. This approximation gives the red lines in Fig.…”

Section: Liquid State and Its Linear Stabilitymentioning

confidence: 99%

Resting and traveling localized states in an active phase-field-crystal model

2018

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The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Löwen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

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“…Microscopic here means that the description is based and operates on the length scales of the individual agents. Thus, for instance, when classical density functional theory (DFT) or its variants are used to describe the properties of crystalline structures [67][68][69][70][71][72][73][74][75][76][77][78][79][80], individual crystal peaks can be resolved in the statistical density field.…”

Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

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Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

Cited by 16 publications

References 18 publications

Two-dimensional localized states in an active phase-field-crystal model

Two-dimensional localized states in an active phase-field-crystal model

Resting and traveling localized states in an active phase-field-crystal model

Dynamical density functional theory for circle swimmers

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