A vector equilibrium problem for symmetrically located point charges on a sphere
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by r+1 equal point charges that are symmetrically located around the north pole. The support of the equilibrium measure is known as the droplet. The droplet has a motherbody which we charact...
| Main Authors: | , |
|---|---|
| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
arXiv
2020
|
| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2008.01017 https://arxiv.org/abs/2008.01017 |
| id |
ftdatacite:10.48550/arxiv.2008.01017 |
|---|---|
| record_format |
openpolar |
| spelling |
ftdatacite:10.48550/arxiv.2008.01017 2023-05-15T17:39:50+02:00 A vector equilibrium problem for symmetrically located point charges on a sphere del Rey, Juan G. Criado Kuijlaars, Arno B. J. 2020 https://dx.doi.org/10.48550/arxiv.2008.01017 https://arxiv.org/abs/2008.01017 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Classical Analysis and ODEs math.CA Mathematical Physics math-ph Complex Variables math.CV FOS Mathematics FOS Physical sciences 31A15 Article CreativeWork article Preprint 2020 ftdatacite https://doi.org/10.48550/arxiv.2008.01017 2022-03-10T15:35:53Z We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by r+1 equal point charges that are symmetrically located around the north pole. The support of the equilibrium measure is known as the droplet. The droplet has a motherbody which we characterize by means of a vector equilibrium problem (VEP) for r measures in the complex plane. The model undergoes two transitions which is reflected in the support of the first component of the minimizer of the VEP, namely the support can be a finite interval containing 0, the union of two intervals, or the full half-line. The two interval case corresponds to a droplet with two disjoint components, and it is analyzed by means of a genus one Riemann surface. : 61 pages, 7 figures Article in Journal/Newspaper North Pole DataCite Metadata Store (German National Library of Science and Technology) North Pole |
| institution |
Open Polar |
| collection |
DataCite Metadata Store (German National Library of Science and Technology) |
| op_collection_id |
ftdatacite |
| language |
unknown |
| topic |
Classical Analysis and ODEs math.CA Mathematical Physics math-ph Complex Variables math.CV FOS Mathematics FOS Physical sciences 31A15 |
| spellingShingle |
Classical Analysis and ODEs math.CA Mathematical Physics math-ph Complex Variables math.CV FOS Mathematics FOS Physical sciences 31A15 del Rey, Juan G. Criado Kuijlaars, Arno B. J. A vector equilibrium problem for symmetrically located point charges on a sphere |
| topic_facet |
Classical Analysis and ODEs math.CA Mathematical Physics math-ph Complex Variables math.CV FOS Mathematics FOS Physical sciences 31A15 |
| description |
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by r+1 equal point charges that are symmetrically located around the north pole. The support of the equilibrium measure is known as the droplet. The droplet has a motherbody which we characterize by means of a vector equilibrium problem (VEP) for r measures in the complex plane. The model undergoes two transitions which is reflected in the support of the first component of the minimizer of the VEP, namely the support can be a finite interval containing 0, the union of two intervals, or the full half-line. The two interval case corresponds to a droplet with two disjoint components, and it is analyzed by means of a genus one Riemann surface. : 61 pages, 7 figures |
| format |
Article in Journal/Newspaper |
| author |
del Rey, Juan G. Criado Kuijlaars, Arno B. J. |
| author_facet |
del Rey, Juan G. Criado Kuijlaars, Arno B. J. |
| author_sort |
del Rey, Juan G. Criado |
| title |
A vector equilibrium problem for symmetrically located point charges on a sphere |
| title_short |
A vector equilibrium problem for symmetrically located point charges on a sphere |
| title_full |
A vector equilibrium problem for symmetrically located point charges on a sphere |
| title_fullStr |
A vector equilibrium problem for symmetrically located point charges on a sphere |
| title_full_unstemmed |
A vector equilibrium problem for symmetrically located point charges on a sphere |
| title_sort |
vector equilibrium problem for symmetrically located point charges on a sphere |
| publisher |
arXiv |
| publishDate |
2020 |
| url |
https://dx.doi.org/10.48550/arxiv.2008.01017 https://arxiv.org/abs/2008.01017 |
| geographic |
North Pole |
| geographic_facet |
North Pole |
| genre |
North Pole |
| genre_facet |
North Pole |
| op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
| op_doi |
https://doi.org/10.48550/arxiv.2008.01017 |
| _version_ |
1766140607897534464 |