{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:59:56Z","timestamp":1760237996942,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T00:00:00Z","timestamp":1594857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study the motion of a single point vortex in simply- and multiply-connected polygonal domains. In the case of multiply-connected domains, the polygonal obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First, we utilize conformal mappings to transfer the polygonal domains onto circular domains. Then, we employ the Schottky-Klein prime function to compute the Hamiltonian governing the point vortex motion in circular domains. We compare between the topological structures of the contour lines of the Hamiltonian in symmetric and asymmetric domains. Special attention is paid to the interaction of point vortex trajectories with the polygonal obstacles. In this context, we discuss the effect of symmetry breaking, and obstacle location and shape on the behavior of vortex motion.<\/jats:p>","DOI":"10.3390\/sym12071175","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T05:10:30Z","timestamp":1595394630000},"page":"1175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Motion of a Point Vortex in Multiply-Connected Polygonal Domains"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1434-2541","authenticated-orcid":false,"given":"El Mostafa","family":"Kalmoun","sequence":"first","affiliation":[{"name":"Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed M. S.","family":"Nasser","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalifa A.","family":"Hazaa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,16]]},"reference":[{"key":"ref_1","first-page":"25","article-title":"\u00dcber integrale der hydrodynamischen gleichungen, welche den Wirbelbewegungen entsprechen","volume":"55","author":"Helmholtz","year":"1858","journal-title":"J. Reine Angew. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"065401","DOI":"10.1063\/1.2425103","article-title":"Point vortex dynamics: A classical mathematics playground","volume":"48","author":"Aref","year":"2007","journal-title":"J. Math. 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