Connaughton, Colm, Rajesh, R. and Zaboronski, Oleg V.. (2010) On the non-equilibrium phase transition in evaporation-deposition models. Journal of Statistical Mechanics: Theory and Experiment, Vol.2010 . Article no. P09016 . ISSN 1742-5468

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Abstract

We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium 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 non-growing 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 diffusion-aggregation 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 two-point mass correlation function with mass in all dimensions while higher order mass correlation functions exhibit nonlinear multi-scaling 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 scale-by-scale 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 non-trivial scaling laws for the critical two-point 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:	1742-5468
Date:	September 2010
Volume:	Vol.2010
Number of Pages:	16
Page Range:	Article no. P09016
Identification Number:	10.1088/1742-5468/2010/09/P09016
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Other Repository
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URI:	http://wrap.warwick.ac.uk/id/eprint/5072

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