Scaling properties of one-dimensional cluster-cluster aggregation with Levy diffusion

TL;DR

This paper investigates how Levy flights influence the scaling behavior of one-dimensional cluster-cluster aggregation, revealing universal properties and the impact of Levy jump characteristics on spatial correlations and fluctuation regimes.

Contribution

It demonstrates that Levy flight parameters can mimic higher-dimensional fluctuation effects in one dimension and uncovers universal scaling of the mass correlation function.

Findings

The transition from mean-field to fluctuation-dominated regimes can be controlled by Levy exponent.

The two-point mass correlation function exhibits universal scaling independent of dimension and Levy parameters.

The depletion zone around heavy particles vanishes with a fractional power law, supported by scaling arguments.

Abstract

We present a study of the scaling properties of cluster-cluster aggregation with a source of monomers in the stationary state when the spatial transport of particles occurs by Levy flights. We show that the transition from mean-field statistics to fluctuation-dominated statistics which, for the more commonly considered case of diffusive transport, occurs as the spatial dimension of the system is tuned through two from above, can be mimicked even in one dimension by varying the characteristic exponent, beta, of the the Levy jump length distribution. We also show that the two-point mass correlation function, responsible for the flux of mass in the stationary state, is strongly universal: its scaling exponent is given by the mean field value independent of the spatial dimension and independent of the value of beta. Finally we study numerically the two point spatial correlation function which characterises the structure of the depletion zone around heavy particles in the diffusion limited regime. We find that this correlation function vanishes with a non-trivial fractional power of the separation between particles as this separation goes to zero. We provide a scaling argument for the value of this exponent which is in reasonable agreement with the numerical measurements.