### Abstract

We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow, φ, emerges in this system in a phase-space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise η and the average density of the particles Q is calculated and is found to have the form η_{c}(ρ) ∼ ρ^{1/2}. We also find that φ scales as a function of the external bias h (field or 'wind') according to a power law φ ∼ h^{0.9}. In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.

Original language | English |
---|---|

Pages (from-to) | 1375-1385 |

Number of pages | 11 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 30 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 7 1997 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*30*(5), 1375-1385. https://doi.org/10.1088/0305-4470/30/5/009

**Spontaneously ordered motion of self-propelled particles.** / Czirók, András; Stanley, H. Eugene; Vicsek, Tamás.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 30, no. 5, pp. 1375-1385. https://doi.org/10.1088/0305-4470/30/5/009

}

TY - JOUR

T1 - Spontaneously ordered motion of self-propelled particles

AU - Czirók, András

AU - Stanley, H. Eugene

AU - Vicsek, Tamás

PY - 1997/3/7

Y1 - 1997/3/7

N2 - We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow, φ, emerges in this system in a phase-space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise η and the average density of the particles Q is calculated and is found to have the form ηc(ρ) ∼ ρ1/2. We also find that φ scales as a function of the external bias h (field or 'wind') according to a power law φ ∼ h0.9. In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.

AB - We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow, φ, emerges in this system in a phase-space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise η and the average density of the particles Q is calculated and is found to have the form ηc(ρ) ∼ ρ1/2. We also find that φ scales as a function of the external bias h (field or 'wind') according to a power law φ ∼ h0.9. In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.

UR - http://www.scopus.com/inward/record.url?scp=0031557295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031557295&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/30/5/009

DO - 10.1088/0305-4470/30/5/009

M3 - Article

AN - SCOPUS:0031557295

VL - 30

SP - 1375

EP - 1385

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 5

ER -