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On the nonequilibrium phase transition in evaporationdeposition models
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Connaughton, Colm, Rajesh, R. and Zaboronski, Oleg V.. (2010) On the nonequilibrium phase transition in evaporationdeposition models. Journal of Statistical Mechanics: Theory and Experiment, Vol.2010 . Article no. P09016 . ISSN 17425468

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Official URL: http://dx.doi.org/10.1088/17425468/2010/09/P09016
Abstract
We study a system of diffusingaggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the nonequilibrium phase transition known to occur in such systems. The transition is between a growing phase in which the total mass increases for all time and a nongrowing phase in which the total mass is bounded. In addition to deriving rigorous bounds on the position of the transition point, we show that the growing phase is in the same universality class as diffusionaggregation models with deposition but no evaporation. In this regime, the flux of mass in mass space becomes asymptotically constant (as a function of mass) at large times. The magnitude of this flux depends on the evaporation rate but the fact that it is asymptotically constant does not. The associated constant flux relation exactly determines the scaling of the twopoint mass correlation function with mass in all dimensions while higher order mass correlation functions exhibit nonlinear multiscaling in dimension less than two. If the deposition rate is below some critical value, a different stationary state is reached at large times characterized by a global balance between evaporation and deposition with a scalebyscale balance between the mass fluxes due to aggregation and evaporation. Both the mass distribution and the flux decay exponentially in this regime. Finally, we develop a scaling theory of the model near the critical point, which yields nontrivial scaling laws for the critical twopoint mass correlation function with mass. These results are well supported by 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):  Evaporation  Mathematical models, Particles  Mathematical models, Diffusion processes, Aggregation (Chemistry), Dynamics of a particle 
Journal or Publication Title:  Journal of Statistical Mechanics: Theory and Experiment 
Publisher:  Institute of Physics Publishing Ltd. 
ISSN:  17425468 
Official Date:  September 2010 
Volume:  Vol.2010 
Number of Pages:  16 
Page Range:  Article no. P09016 
Identification Number:  10.1088/17425468/2010/09/P09016 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Related URLs:  
References:  [1] Meakin P 1992 Rep. Prog. Phys. 55 157 
URI:  http://wrap.warwick.ac.uk/id/eprint/5072 
Data sourced from Thomson Reuters' Web of Knowledge
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