Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2392
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dc.contributor.authorPashaev, Oktay-
dc.contributor.authorYılmaz, Oğuz-
dc.date.accessioned2016-11-08T09:44:06Z
dc.date.available2016-11-08T09:44:06Z
dc.date.issued2008-04
dc.identifier.citationPashaev, O., and Yılmaz, O. (2008). Vortex images and q-elementary functions. Journal of Physics A: Mathematical and Theoretical, 41(13). doi:10.1088/1751-8113/41/13/135207en_US
dc.identifier.issn1751-8113
dc.identifier.issn1751-8113-
dc.identifier.issn1751-8121-
dc.identifier.urihttp://doi.org/10.1088/1751-8113/41/13/135207
dc.identifier.urihttp://hdl.handle.net/11147/2392
dc.description.abstractIn 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.isoenen_US
dc.publisherIOP Publishing Ltd.en_US
dc.relation.ispartofJournal of Physics A: Mathematical and Theoreticalen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectGroup theoryen_US
dc.subjectSpecial functionsen_US
dc.subjectBoundary-value problemsen_US
dc.subjectElectrostaticsen_US
dc.subjectVortex dynamicsen_US
dc.titleVortex Images and Q-Elementary Functionsen_US
dc.typeArticleen_US
dc.authoridTR57865en_US
dc.authoridTR1568en_US
dc.institutionauthorPashaev, Oktay-
dc.institutionauthorYılmaz, Oğuz-
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume41en_US
dc.identifier.issue13en_US
dc.identifier.wosWOS:000254153200011en_US
dc.identifier.scopus2-s2.0-42649112027en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1088/1751-8113/41/13/135207-
dc.relation.doi10.1088/1751-8113/41/13/135207en_US
dc.coverage.doi10.1088/1751-8113/41/13/135207en_US
dc.identifier.wosqualityQ1-
dc.identifier.scopusqualityQ2-
item.fulltextWith Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.languageiso639-1en-
item.cerifentitytypePublications-
item.grantfulltextopen-
crisitem.author.dept04.02. Department of Mathematics-
crisitem.author.dept04.02. 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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