Active particles in heterogeneous media display new physics
1 Laboratoire J.A. Dieudonné, Université de Nice Sophia Antipolis, UMR 7351 CNRS, Parc Valrose, 06108 Nice Cedex 02, France
2 Department for Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65026 Odessa, UKraine
Received: 24 March 2015
Revised: 18 May 2015
Published online: 24 July 2015
We present a detailed study of the large-scale collective properties of self-propelled particles (SPPs) moving in two-dimensional heterogeneous space. The impact of spatial heterogeneities on the ordered, collectively moving phase is investigated. We show that for strong enough spatial heterogeneity, the well-documented high-density, high-ordered propagating bands that emerge in homogeneous space disappear. Moreover, the ordered phase does not exhibit long-range order, as occurs in homogeneous systems, but rather quasi-long range order: i.e. the SPP system becomes disordered in the thermodynamical limit. For finite size systems, we find that there is an optimal noise value that maximizes order. Interestingly, the system becomes disordered in two limits, for high noise values as well as for vanishing noise. This remarkable finding strongly suggests the existence of two critical points, instead of only one, associated to the collective motion transition. Density fluctuations are consistent with these observations, being higher and anomalously strong at the optimal noise, and decreasing and crossing over to normal for high and low noise values. Collective properties are investigated in static as well as dynamic heterogeneous environments, and by changing the symmetry of the velocity alignment mechanism of the SPPs.
© EDP Sciences, Springer-Verlag, 2015