| Zugriffsnummer | 29110 |
| Dokumenttyp | Zeitschriftenartikel |
| Peer Review | mit Peer Review |
| Sprache | Englisch |
| Titel | A kinetic model and scaling properties of non-equilibrium clustering of self-propelled particles |
| Autor(in); Institution |
Peruani, Fernando; Université de Nice Sophia Antipolis, Laboratoire J.A. Dieudonné, Nice, FRANCE
Bär, Markus; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
|
| Quelle/Jahr | New Journal of Physics: 15 (2013), 6, 1 - 15 |
| Artikelnummer | 065009 |
| Availability | [online only] |
| ISSN | 1367-2630 |
| DOI | |
| URL | |
| Verlag | IOPscience |
| Klassifikationscode | PACS: 87.10.-e ; PACS: 8716.Qp ; PACS: 8716.Nn ; PACS: 05.70.Fh ; PACS: 87.16.Ka |
| Freie Schlagworte | self organisation ; self-propelled particles ; nonequilibrium clustering |
| Zusammenfassung | Part of Focus on Swarming in Biological and Related Systems We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained by a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with cluster size-described by an exponent α-and the scaling of the cluster perimeter with cluster size-described by an exponent β. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: (i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and (ii) a collective phase characterized by the presence of a non-monotonic CSD with a local maximum at large cluster sizes. Through a finite-size study of the kinetic model, we show that the critical point Pc that separates the two phases scales with the system size N as Pc∝N-ξ, while the CSD p(m), at the critical point Pc, is always a power law such that p(m)∝m−γ, where m is the cluster size. Our analysis shows that the critical exponents ξ and γ are a function of α and β, and even provides the relationship between them. Furthermore, the kinetic approach suggests that in the thermodynamic limit, a genuine clustering phase transition, in two and three dimensions, requires that α = β. Interestingly, the critical exponent γ is found to be in the range 0.8 < γ < 1.5 in line with the observations from experiments and simulations. |
| Kostenfreier Zugang | Open Access Gold |
| Rechteinformation | CC BY 3.0 ; Creative Commons Attribution 3.0 License |