Long-Range Order in a Two-Dimensional Dynamical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>Model: How Birds Fly Together

Toner, John; Tu, Yuhai

doi:10.1103/physrevlett.75.4326

Cited by 1,160 publications

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“…We interpret these results through the well-known Toner and Tu hydrodynamic theory of flocking [26,27], and by making use of a minimal model of self-propelled soft disks, first introduced in [44,45]. Our numerical results show that a simple self-propelled mechanical model with no adhesion forces is able to reproduce qualitatively and even quantitatively the static structure factor and the number fluctuations of both the highly confluent reawakened samples and the near-jammed controls.…”

Section: Introductionmentioning

confidence: 86%

“…However, the experimental observation of GNF in flocking biological systems has been so far quite scarce and limited to systems showing nematic order [30]. Also, while the flocking transition has been thoroughly investigated in low density systems [25,26,27,28,29,31], it is not yet fully understood how it occurs in systems characterised by a large density, such as confluent cellular monolayers. In particular, little is known about how the flocking transition affects the structural, physical properties from the microscopic to the mesoscopic scales.…”

Section: Introductionmentioning

confidence: 99%

“…Hydrodynamic theory results [26,27], and numerical simulations based on the Vicsek model suggest that flocking systems exhibit anomalous fluctuations δN 2 ∼ N 8/5 [28,29]. However, the experimental observation of GNF in flocking biological systems has been so far quite scarce and limited to systems showing nematic order [30].…”

Section: Introductionmentioning

confidence: 99%

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Giant fluctuations and structural effects in a flocking epithelium

Giavazzi¹,

Malinverno²,

Corallino³

et al. 2017

J. Phys. D: Appl. Phys.

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Abstract. Epithelial cells cultured in a monolayer are very motile in isolation but reach a near-jammed state when mitotic division increases their number above a critical threshold. We have recently shown that a monolayer can be reawakened by over-expression of a single protein, RAB5A, a master regulator of endocytosis. This reawakening of motility was explained in term of a flocking transition that promotes the emergence of a large-scale collective migratory pattern. Here we focus on the impact of this reawakening on the structural properties of the monolayer. We find that the unjammed monolayer is characterised by a fluidisation at the single cell level and by enhanced non-equilibrium large-scale number fluctuations at a larger length scale. Also with the help of numerical simulations, we trace back the origin of these fluctuations to the selfpropelled active nature of the constituents and to the existence of a local alignment mechanism, leading to the spontaneous breaking of the orientational symmetry.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Giant fluctuations and structural effects in a flocking epithelium

Giavazzi¹,

Malinverno²,

Corallino³

et al. 2017

J. Phys. D: Appl. Phys.

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“…This model in 2D exhibits a nonequilibrium phase transition: At sufficiently high concentration, all particles spontaneously move in a single direction, thus breaking the rotational symmetry of the system. This phase transition is rationalized within a phenomenological dynamical xy-model [10]. This model further predicts that in 2D, the MSD of a tag particle exhibits superdiffusion at the transition.…”

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confidence: 99%

“…Interestingly, the meansquared displacement (MSD) of these passive beads exhibit superdiffusion at short time and diffusion at long time. It is measured that the crossover time τ c ∼ 2 s and the length ℓ c ≡ [∆x(τ c )] 2 ∼ 10 µm provide a natural time and length scales of these coherent structures, respectively.There have been a few simulation models and theoretical treatments that aim to describe the above and related phenomena [2,10,11,12]. Motivated by the patterns in fish schooling and bird flocking, Vicsek et al numerically studied a model in which each particle (modelled as a point) moves at a constant speed and its direction is determined by averaging over the directions of a large collection of particles in its neighborhood plus a small random perturbation [2].…”

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confidence: 99%

Dynamics of bacterial flow: Emergence of spatiotemporal coherent structures

2007

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We propose a simple model of self-propelled particles to show that coherent structures, such as jets and swirls, can arise from a plausible microscopic mechanisms: (i) the elongated shape of the selfpropelled particles with (ii) the hardcore interactions among them. We demonstrate via computer simulation that these coherent structures, which emerge at sufficiently high densities of particles, have characteristics that are similar to those observed in recent experiments in bacteria baths. PACS numbers: 87.18.Bb, 05.65.+b, 47.54.+r Living systems often exhibit complex spatiotemporal patterns that are characteristic of many systems driven out-of-equilibrium [1]. Examples range from birds flocking [2] to internal organizations inside a cell [3]. A population of live microorganisms, such as bacteria like E. coli, suspended in an aqueous environment can provide a particular interesting model system to study pattern formation and collective motion in biology since the dynamics of the individual bacteria can be directly observed and critical parameters such as density and activity may be brought under experimental control [4]. These microorganisms continuously consume nutrients and dissipate the energy through the process of propelling themselves against the frictional force exerted on them by the fluid [5]. With a typical size of a bacterium of the order of microns and a typical speed of the order of 10 µm/s, the Reynolds number R ≪ 1 is quite small. Yet, a large concentration of these microorganisms constitutes a state that is far from equilibrium, and exhibits self-organized collective motion with spatial and temporal patterns that are both physically fascinating and potentially of great biological significance [6,7,8,9]. As a first step towards understanding of how suspended cells generate coherent motion, we identify, in this Letter, two simple but central ingredients -the elongated shape of the self-propelled particles and the hardcore interactions among them, and demonstrate via computer implementation of these two ingredients that this system exhibits coherent jets and swirls with characteristics strikingly similar to those observed in experiments.Recent experiments [6,7,8,9] show that when concentrated, the crowd of swimming bacteria creates arrays of transient jets and swirls whose size can be orders of magnitude larger than an individual bacterium. These complicated, spatially coherent structures have been observed in Bacillus subtilis colony grown on an agar plate [6], in E. coli confined in a quasi-two-dimensional soap film [7], in Bacillus subtilis at the edge of a pendent drop [9]. It is estimated from direct visualization that these structures have a typical size of about ten times that of a bacterium and persist for a few seconds. More quantitative information about these structures may be extracted from a one-point passive microrheological technique which tracks passive micron-sized beads dispersed in a bacterial bath of E. coli [7]. Interestingly, the meansquared displacement (MSD) of these passive...

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Biologically inspired ant colony simulation

Wei

Ren

Wang

et al. 2018

Computer Animation & Virtual

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We present a unified biologically inspired approach to simulate ant colonies inspired by the key observation of collective behaviors of ants in nature. To generate the trajectories of virtual ants, we construct a motion controller to determine the motion states and the paths of virtual ants, considering dynamic internal and external interactions. The motion controller computes a target position for each ant at every time step according to its motion states. The motion states include four states: basic movement, the stop state, and two dynamic interactions (i.e., internal and external, respectively referring to interaction with neighbors for necessary information transfer about the destination, and interaction with surroundings such as food sources, nests, and obstacles) to represent basic exploration, casual or intentional stop, and purposeful movement, respectively. Based on the motion states, the motion controller plans an optimal path for each virtual ant. Through many simulation experiments, we demonstrate that our method is controllable, scalable, and flexible to simulate hybrid colonies with a large number of ants.

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Long-Range Order in a Two-Dimensional DynamicalXYModel: How Birds Fly Together

Cited by 1,160 publications

References 7 publications

Giant fluctuations and structural effects in a flocking epithelium

Giant fluctuations and structural effects in a flocking epithelium

Dynamics of bacterial flow: Emergence of spatiotemporal coherent structures

Biologically inspired ant colony simulation

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