Hydrodynamics and phases of flocks

Toner, John; Tu, Yuhai; Ramaswamy, Sriraṁ

doi:10.1016/j.aop.2005.04.011

Cited by 940 publications

(1,110 citation statements)

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“…Most of all the previous theoretical studies on polar active matter have reported the emergence of "giant density fluctuations" in polar liquids. Giant density fluctuations were believed to be a robust and generic feature of active polar liquids [46,48]. Although our model includes classical alignment interactions, it also contains additional repulsive and dipolar couplings: among them, the long-range hydrodynamic interactions destroy the giant density fluctuations, as we show below.…”

Section: Density Fluctuationsmentioning

confidence: 84%

“…Guided by this universal feature, physicists have proposed that solely alignment rules at the individual level could account for the emergence of unidirectional motion at the group level [1][2][3][4] . This hypothesis has been supported by agent-based simulations 1,5,6 .…”

mentioning

confidence: 99%

“…Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic flock at low densities, or in that of a homogenous polar phase at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations, which were hitherto considered as the hallmark of populations of self-propelled particles 2,3,17 . Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion.…”

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confidence: 99%

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Emergence of macroscopic directed motion in populations of motile colloids

Bricard¹,

Caussin²,

Desreumaux³

et al. 2013

Nature

889

1,029

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From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales, populations of motile organisms display coherent collective motion.This consistent behavior strongly contrasts with the difference in communication abilities between the individuals. Guided by this universal feature, physicists have proposed that solely alignment rules at the individual level could account for the emergence of unidirectional motion at the group level [1][2][3][4] . This hypothesis has been supported by agent-based simulations 1,5,6 . However, more complex collective behaviors have been systematically found in experiments including the formation of vortices 7-9 , fluctuating swarms 7, 10 , clustering 11,12 , and swirling [13][14][15][16] . All these (living and man-made) model systems (bacteria 9,10, 16 , biofilaments and molecular motors 7,8,13 , shaken grains 14, 15 and reactive colloids 11,12 ) predominantly rely on actual collisions to display collective motion. As a result, the potential local alignment rules are entangled with more complex, and often unknown, interactions. The large-scale behaviour of the populations therefore strongly depends on these uncontrolled microscopic couplings that are extremely challenging to measure and describe theoretically.Here, we demonstrate a new phase of active matter. We reveal that dilute populations of millions of colloidal rollers self-organize to achieve coherent motion along a unique direction, with very few density and velocity fluctuations. Identifying, quantitatively, the microscopic interactions between the rollers allows a theoretical description of this polar-liquid state. Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic flock at low densities, or in that of a homogenous polar phase at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations, which were hitherto considered as the hallmark of populations of self-propelled particles 2, 3, 17 . Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion.Our system consists of large populations of colloids capable of self-propulsion and of sensing the orientation of their neighbors solely by means of physical mechanisms. We take advantage of an overlooked electrohydrodynamic phenomenon referred to as the Quincke rotation 18,19 (Fig. 1a).When an electric field E 0 is applied to an insulating sphere immersed in a conducting fluid, above a critical field amplitude E Q , the charge distribution at the sphere's surface is unstable to infinitesimal fluctuations. This spontaneous symmetry breaking results in a net electrostatic torque, which causes the sphere to rotate at a constant speed around a random direction transverse to E 0 18 . We 2 exploit this instability to engineer self-propelled colloidal rollers. We use ...

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Section: Density Fluctuationsmentioning

confidence: 84%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Emergence of macroscopic directed motion in populations of motile colloids

Bricard¹,

Caussin²,

Desreumaux³

et al. 2013

Nature

889

1,029

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“…The behaviour of self-propelled objects such as bacteria, algae and synthetic Janus particles has become a dynamic field of research, both for the 'swimming' of individual particles (Lauga & Powers 2009) and for the collective behaviour of active suspensions (Toner, Tu & Ramaswamy 2005). Owing to the particles' self-motion, active matter can spontaneously phase-separate into dense and dilute regions (Cates et al 2010;Fily & Marchetti 2012;Buttinoni et al 2013;Palacci et al 2013;Stenhammar et al 2013Stenhammar et al , 2014Takatori, Yan & Brady 2014;Wysocki, Winkler & Gompper 2014;Yang, Manning & Marchetti 2014;Takatori & Brady 2015) and can move collectively under an orienting field .…”

Section: Introductionmentioning

confidence: 99%

The force on a boundary in active matter

2015

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We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy k B T to the swimmer's activity k s T s = ζ U 2 0 τ R /6, where ζ is the Stokes drag coefficient, U 0 is the swim speed and τ R is the reorientation time of the active particles. The theory, which is valid on all length and time scales, has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behaviour when the boundary size is large compared to the swimmer's run length = U 0 τ R . The theory is used to predict the motion of bodies of all sizes immersed in active matter.

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“…A constant term is not considered in the above expression since the constant contribution can be absorbed by c, the rate of internal dissipation in the energy balance (2). The effects of coefficients a i have been discussed systematically in the previous work [12].…”

Section: Model For Kinesin Motor On Microtubulementioning

confidence: 99%

Walking motion of an overdamped active particle in a ratchet potential

2011

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An active particle can convert its internal energy into mechanical work. We study a generalized energy-depot model of an overdamped active particle in a ratchet potential. Using well-known biological parameters for kinesin-1 and modeling ATP influx as a pulsed energy supply, we apply our model to the molecular motor system. We find that our simple model can capture the essential properties of the kinesin motor such as forward stepping, stalling, backward stepping, dependence on ATP concentration, and stall force. Our model might be quite universal in the sense that it is able to describe dynamics of various types of motors as long as realistic parameters for each motor species are adopted.

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Hydrodynamics and phases of flocks

Abstract: We review the past decadeÕs theoretical and experimental studies of flocking: the collective,

Cited by 940 publications

References 84 publications

Emergence of macroscopic directed motion in populations of motile colloids

Emergence of macroscopic directed motion in populations of motile colloids

The force on a boundary in active matter

Walking motion of an overdamped active particle in a ratchet potential

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