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* Corresponding author 1 JAD - Laboratoire Jean Alexandre Dieudonné 2 PTB

Abstract : 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 pm, at the critical point Pc, is always a power law such that pm∝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.





Autor: Fernando Peruani - Markus Baer -

Fuente: https://hal.archives-ouvertes.fr/



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