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Driven Brownian coagulation of polymers
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Krapivsky, Pavel L. and Connaughton, Colm. (2012) Driven Brownian coagulation of polymers. Journal of Chemical Physics, Vol.136 (No.20). Article:204901. ISSN 10897690

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Official URL: http://dx.doi.org/10.1063/1.4718833
Abstract
We present an analysis of the meanfield kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, a, of the aggregates. We find that two types of long time behavior are possible. For 0 <= a < 1/2 the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of a. For 1/2 < a <= 1, the cluster size distribution never reaches a stationary state. Instead a bimodal distribution is formed in which a narrow population of small clusters near the monomer scale is separated by a gap (where the cluster size distribution is effectively zero) from a population of large clusters which continue to grow for all time by absorbing small clusters. The marginal case, a=1/2, is difficult to analyze definitively, but we argue that the cluster size distribution becomes stationary and there is a logarithmic correction to the algebraic tail.
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):  Brownian movements, Coagulation  Mathematical models 
Journal or Publication Title:  Journal of Chemical Physics 
Publisher:  American Institute of Physics 
ISSN:  10897690 
Official Date:  22 May 2012 
Volume:  Vol.136 
Number:  No.20 
Page Range:  Article:204901 
Identification Number:  10.1063/1.4718833 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  Boston University, University of Warwick 
Related URLs:  
References:  [1] S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943). 
URI:  http://wrap.warwick.ac.uk/id/eprint/44640 
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