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dc.contributor Казанский федеральный университет Yu.V.Obnosov Yurii Viktorovich 2019-06-13T10:30:35Z 2019-06-13T10:30:35Z 2019
dc.identifier.citation Obnosov Yu.V. Regular hexagonal three-phase checkerboard / Yu.V. Obnosov // Journal of Mathematical Analysis and Applications. - 2019. - DOI: 10.1016/j.jmaa.2019.06.007
dc.description.abstract Two-dimensional doubly-periodic, three-phase hexagonal structure is considered. The flow in the structure is generated by three sets of vortexes/sinks/sources, which are the same in each phase and are located in the centers of the hexagons. Complex analyses methods are utilized to reduce the doubly periodic R-linear conjugation problem to the simpler one, Riemann-Hilbert (RH) problem, on a three-sheeted Riemann surface. In turn, the latter problem is reduced to a RH problem involving three joined sectors on the plane, which was previously investigated in \cite{cras_obn2004}. The limiting cases with one non-conducting phase and two phases of the same conductivities are investigated. All solutions derived are verified both numerically and analytically. Examples of relevant flow networks, streamlines and equipotentials, are plotted in the whole structure and separately in each phase.
dc.language.iso en
dc.relation.ispartofseries Journal of Mathematical Analysis and Applications
dc.rights открытый доступ
dc.subject Composite materials
dc.subject doubly periodic structure
dc.subject complex analysis
dc.subject piece-wise meromorphic solution
dc.subject conformal mapping
dc.subject.other Математика
dc.title Regular hexagonal three-phase checkerboard
dc.type Article Институт математики и механики им.Н.И.Лобачевского
dc.description.pages 1-15 203421
dc.identifier.doi 10.1016/j.jmaa.2019.06.007

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