2010
DOI: 10.1103/physreve.81.061916
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Fluctuations and pattern formation in self-propelled particles

Abstract: We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. F… Show more

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Cited by 212 publications
(281 citation statements)
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“…In the uniform polar state (w = w 0x ), instabilities exist even for λ = 0 and α = 0 and these have been studied before [20,21]. The presence of the reactive birth/death term yields new patterns.…”
mentioning
confidence: 99%
See 1 more Smart Citation
“…In the uniform polar state (w = w 0x ), instabilities exist even for λ = 0 and α = 0 and these have been studied before [20,21]. The presence of the reactive birth/death term yields new patterns.…”
mentioning
confidence: 99%
“…Both these longitudinal and transverse instabilities have been discussed extensively. In particular, the longitudinal instability has been argued to signal the onset of high density ordered bands normal to the direction of mean polarization traveling in a disordered low density background [20,21]. The suppression of motility induced by a finite λ yields a host of complex structures, including traveling dots, stripes and lanes that coarsen at long times into anisotropic phase separated states [13].…”
mentioning
confidence: 99%
“…(1,2) are related to the models of Refs. [20][21][22][23], although even in that limit our emphasis here is on the dynamical pathway the system follows, rather than on steady state behaviour. It is also useful to recast Eqs.…”
Section: Pacs Numbersmentioning
confidence: 99%
“…This is mainly because SPP particles are self-driven systems which are out of, and often far from, thermodynamic equilibrium, as they continuously burn energy from their surroundings or from internal sources, typically in order to move. The nonequilibrium nature of SPP greatly enriches their physics with respect to that of their passive counterparts [1][2][3][4][5]. Examples of systems of SPP abound, both in nature and in the lab, and span a wide range of length scales.…”
Section: Introductionmentioning
confidence: 99%