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Mathematical theory of exchange-driven growth
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Esenturk, Emre (2018) Mathematical theory of exchange-driven growth. Nonlinearity, 31 (7). 3460. doi:10.1088/1361-6544/aaba8d
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Official URL: https://doi.org/10.1088/1361-6544/aaba8d
Abstract
Exchange-driven growth is a process in which pairs of clusters interact by exchanging single unit of mass at a time. The rate of exchange is given by an interaction kernel [See full-text] which depends on the masses of the two interacting clusters. In this paper we establish the fundamental mathematical properties of the mean field rate equations of this process for the first time. We find two different classes of behavior depending on whether [See full-text] is symmetric or not. For the non-symmetric case, we prove global existence and uniqueness of solutions for kernels satisfying [See full-text]. This result is optimal in the sense that we show for a large class of initial conditions and kernels satisfying [See full-text] the solutions cannot exist. On the other hand, for symmetric kernels, we prove global existence of solutions for [See full-text] while existence is lost for [See full-text]. In the intermediate regime [See full-text] we can only show local existence. We conjecture that the intermediate regime exhibits finite-time gelation in accordance with the heuristic results obtained for particular kernels.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QH Natural history |
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| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Growth -- Mathematical models, Cluster analysis | ||||||
| Journal or Publication Title: | Nonlinearity | ||||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||||
| ISSN: | 0951-7715 | ||||||
| Official Date: | 8 June 2018 | ||||||
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| Volume: | 31 | ||||||
| Number: | 7 | ||||||
| Article Number: | 3460 | ||||||
| DOI: | 10.1088/1361-6544/aaba8d | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access | ||||||
| RIOXX Funder/Project Grant: |
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