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On particles in equilibrium on the real line
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Georgakopoulos, Agelos and Kolountzakis, M. N. (2017) On particles in equilibrium on the real line. Proceedings of the American Mathematical Society, 145 . pp. 3501-3511. doi:10.1090/proc/13492 ISSN 0002-9939.
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Official URL: https://doi.org/10.1090/proc/13492
Abstract
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question is whether each equilibrium configuration needs to be an arithmetic progression. Under very broad assumptions on the force we show this for the particles on the circle. In the case of infinitely many particles on the line we show the same result under the assumption that the maximal (or the minimal) gap between successive points is finite (positive) and assumed at some pair of successive points. Under the assumption of analyticity for the force field (e.g., the Coulomb force) we deduce some extra rigidity for the configuration: knowing an equilibrium configuration of points in a half-line determines it throughout. Various properties of the equlibrium configuration are proved.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Numbers, Real, Equilibrium, Particles | ||||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||||
| Publisher: | American Mathematical Society | ||||||||
| ISSN: | 0002-9939 | ||||||||
| Official Date: | 2017 | ||||||||
| Dates: |
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| Volume: | 145 | ||||||||
| Page Range: | pp. 3501-3511 | ||||||||
| DOI: | 10.1090/proc/13492 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 9 March 2017 | ||||||||
| Date of first compliant Open Access: | 28 April 2017 | ||||||||
| Funder: | European Research Council (ERC) | ||||||||
| Grant number: | 639046 | ||||||||
| Is Part Of: | The first author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 639046). The second author has been partially supported by the “Aristeia II” action (Project FOURIERDIG) of the operational program Education and Lifelong Learning and is co-funded by the European Social Fund and Greek national resources. |
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