Nonlinear Field Equations for Aligning Self-Propelled Rods

Peshkov, Anton; Aranson, Igor S.; Bertin, Éric; Chaté, Hugues; Ginelli, Francesco

doi:10.1103/physrevlett.109.268701

Cited by 146 publications

(282 citation statements)

References 34 publications

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“…For weakly-polarized phases, two possible closure schemes have been used in the context of active fluids. Bertin et al [43,44] introduced a scaling ansatz for the amplitude of the angular Fourier components of the one-point function. This ansatz is expected to be relevant for nearly-isotropic states with small and slow variations of the hydrodynamic field.…”

Section: Transition To Collective Motionmentioning

confidence: 99%

Emergence of macroscopic directed motion in populations of motile colloids

Bricard¹,

Caussin²,

Desreumaux³

et al. 2013

Nature

871

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: Transition To Collective Motionmentioning

confidence: 99%

Emergence of macroscopic directed motion in populations of motile colloids

Bricard¹,

Caussin²,

Desreumaux³

et al. 2013

Nature

871

1,029

View full text Add to dashboard Cite

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“…The connection between the Vicsek model and the Toner-Tu continuum equations was missing until the equations were derived from a microscopic model of particles with binary collisions using a Boltzmann approach [45][46][47][48]. The method was generalized later by considering multiple collisions using an Enskog-type kinetic theory [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Gaussian theory for spatially distributed self-propelled particles

2016

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Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting selfpropelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

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“…In recent years, a variety of efforts have been devoted to modeling the dynamic properties of swarms [15][16][17][18][19][20][21][22][23][24][25][26][27]. In 1995, Vicsek et al proposed a particularly simple but rich model [28].…”

Section: Introductionmentioning

confidence: 99%

Promoting collective motion of self-propelled agents by distance-based influence

2014

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We propose a dynamic model for a system consisting of self-propelled agents in which the influence of an agent on another agent is weighted by geographical distance. A parameter α is introduced to adjust the influence: the smaller value of α means that the closer neighbors have stronger influence on the moving direction. We find that there exists an optimal value of α, leading to the highest degree of direction consensus. The value of optimal α increases as the system size increases, while it decreases as the absolute velocity, the sensing radius and the noise amplitude increase.

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Nonlinear Field Equations for Aligning Self-Propelled Rods

Cited by 146 publications

References 34 publications

Emergence of macroscopic directed motion in populations of motile colloids

Emergence of macroscopic directed motion in populations of motile colloids

Gaussian theory for spatially distributed self-propelled particles

Promoting collective motion of self-propelled agents by distance-based influence

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