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Scaling properties of onedimensional clustercluster aggregation with Lévy diffusion
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Connaughton, Colm and Harris, Jamie. (2010) Scaling properties of onedimensional clustercluster aggregation with Lévy diffusion. Journal of Statistical Mechanics: Theory and Experiment, Vol.2010 (No.5). P05003 . ISSN 17425468

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Official URL: http://dx.doi.org/10.1088/17425468/2010/05/P05003
Abstract
We present a study of the scaling properties of clustercluster 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 meanfield statistics to fluctuationdominated 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 Levy jump length distribution. We also show that the twopoint mass correlation function, responsible for the flux of mass in the stationary state, is strongly universal: its scaling exponent is given by the meanfield value independent of the spatial dimension and independent of the value of beta. Finally, we study numerically the twopoint spatial correlation function which characterizes the structure of the depletion zone around heavy particles in the diffusionlimited regime. We find that this correlation function vanishes with a nontrivial 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.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Lévy processes, Cluster analysis, Dynamics of a particle, Aggregation (Chemistry) 
Journal or Publication Title:  Journal of Statistical Mechanics: Theory and Experiment 
Publisher:  Institute of Physics Publishing Ltd. 
ISSN:  17425468 
Date:  May 2010 
Volume:  Vol.2010 
Number:  No.5 
Number of Pages:  19 
Page Range:  P05003 
Identification Number:  10.1088/17425468/2010/05/P05003 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  Research Councils UK (RCUK), Engineering and Physical Sciences Research Council (EPSRC) 
Related URLs:  
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URI:  http://wrap.warwick.ac.uk/id/eprint/5819 
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