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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Pashaev, Oktay | - |
dc.contributor.author | Yılmaz, Oğuz | - |
dc.date.accessioned | 2016-11-08T09:44:06Z | |
dc.date.available | 2016-11-08T09:44:06Z | |
dc.date.issued | 2008-04 | |
dc.identifier.citation | Pashaev, O., and Yılmaz, O. (2008). Vortex images and q-elementary functions. Journal of Physics A: Mathematical and Theoretical, 41(13). doi:10.1088/1751-8113/41/13/135207 | en_US |
dc.identifier.issn | 1751-8113 | |
dc.identifier.issn | 1751-8113 | - |
dc.identifier.issn | 1751-8121 | - |
dc.identifier.uri | http://doi.org/10.1088/1751-8113/41/13/135207 | |
dc.identifier.uri | http://hdl.handle.net/11147/2392 | |
dc.description.abstract | In the present paper, the problem of vortex images in the annular domain between two coaxial cylinders is solved by the q-elementary functions. We show that all images are determined completely as poles of the q-logarithmic function, and are located at sites of the q-lattice, where a dimensionless parameter q = r 2 2/r 2 1 is given by the square ratio of the cylinder radii. The resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. Our approach in this paper provides an efficient path to rediscover known solutions for the vortex-cylinder pair problem and yields new solutions as well. By composing pairs of q-exponents to the first Jacobi theta function and conformal mapping to a rectangular domain we show that our solution coincides with the known one, obtained before by elliptic functions. The Schottky-Klein prime function for the annular domain is factorized explicitly in terms of q-exponents. The Hamiltonian, the Kirchhoff-Routh and the Green functions are constructed. As a new application of our approach, the uniformly rotating exact N-vortex polygon solutions with the rotation frequency expressed in terms of q-logarithms at Nth roots of unity are found. In particular, we show that a single vortex orbits the cylinders with constant angular velocity, given as the q-harmonic series. Vortex images in two particular geometries with only one cylinder as the q → ∞ limit are studied in detail. | en_US |
dc.language.iso | en | en_US |
dc.publisher | IOP Publishing Ltd. | en_US |
dc.relation.ispartof | Journal of Physics A: Mathematical and Theoretical | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Group theory | en_US |
dc.subject | Special functions | en_US |
dc.subject | Boundary-value problems | en_US |
dc.subject | Electrostatics | en_US |
dc.subject | Vortex dynamics | en_US |
dc.title | Vortex Images and Q-Elementary Functions | en_US |
dc.type | Article | en_US |
dc.authorid | TR57865 | en_US |
dc.authorid | TR1568 | en_US |
dc.institutionauthor | Pashaev, Oktay | - |
dc.institutionauthor | Yılmaz, Oğuz | - |
dc.department | İzmir Institute of Technology. Mathematics | en_US |
dc.identifier.volume | 41 | en_US |
dc.identifier.issue | 13 | en_US |
dc.identifier.wos | WOS:000254153200011 | en_US |
dc.identifier.scopus | 2-s2.0-42649112027 | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.identifier.doi | 10.1088/1751-8113/41/13/135207 | - |
dc.relation.doi | 10.1088/1751-8113/41/13/135207 | en_US |
dc.coverage.doi | 10.1088/1751-8113/41/13/135207 | en_US |
dc.identifier.wosquality | Q1 | - |
dc.identifier.scopusquality | Q2 | - |
item.fulltext | With Fulltext | - |
item.openairetype | Article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.languageiso639-1 | en | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
crisitem.author.dept | 04.02. Department of Mathematics | - |
crisitem.author.dept | 04.02. Department of Mathematics | - |
Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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