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The role of zero-clusters in exchange-driven growth with and without
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Esenturk, Emre and Connaughton, Colm (2020) The role of zero-clusters in exchange-driven growth with and without. Physical Review E, 101 . 052134. doi:10.1103/PhysRevE.101.052134 ISSN 1539-3755.
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WRAP-role-zero-clusters-exchange-driven-growth-with-without-Connaughton-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1568Kb) | Preview |
Official URL: http://dx.doi.org/10.1103/PhysRevE.101.052134
Abstract
The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses a constituent unit (monomer) and the other gains this unit. Two variants of the exchange-driven growth model appear in applications. They differ in whether clusters of zero size are considered active or passive. In the active case, clusters of size zero can acquire a monomer from clusters of positive size. In the passive case they cannot, meaning that clusters reaching size zero are effectively removed from the system. The large time behaviour is very different for the two variants of the model. We first consider an isolated system. In the passive case, the cluster size distribution tends towards a self-similar evolution and the typical cluster size grows as a power of time. In the active case, we identify a broad class of kernels for which the the cluster size distribution tends to a non-trivial time-independent equilibrium in which the typical cluster size is finite. We next consider a non-isolated system in which monomers are input at a constant rate. In the passive case, the cluster size distribution again attains a self-similar profile in which the typical cluster size grows as a power of time. In the active case, a surprising new behavior is found: the cluster size distribution asymptotes to the same equilibrium profile found in the isolated case but with an amplitude that grows linearly in time.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Mathematical physics, Nonlinear theories -- Mathematical models, Nonequilibrium statistical mechanics, Statistical physics | ||||||
Journal or Publication Title: | Physical Review E | ||||||
Publisher: | American Physical Society | ||||||
ISSN: | 1539-3755 | ||||||
Official Date: | 22 May 2020 | ||||||
Dates: |
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Volume: | 101 | ||||||
Article Number: | 052134 | ||||||
DOI: | 10.1103/PhysRevE.101.052134 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | © 2020 American Physical Society | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 13 May 2020 | ||||||
Date of first compliant Open Access: | 14 May 2020 | ||||||
RIOXX Funder/Project Grant: |
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