Kazan (Volga region) Federal University, KFU
KAZAN
FEDERAL UNIVERSITY
 
REGULAR HEXAGONAL THREE-PHASE CHECKERBOARD
Form of presentationArticles in international journals and collections
Year of publication2019
Языканглийский
  • Obnosov Yuriy Viktorovich, author
  • Bibliographic description in the original language 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
    Annotation 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.
    Keywords Composite materials, doubly periodic structure, complex analysis, piece-wise meromorphic solution, conformal mapping
    The name of the journal Journal of Mathematical Analysis and Applications
    On-line resource for training course http://dspace.kpfu.ru/xmlui/bitstream/handle/net/150897/F__exagon.pdf?sequence=1&isAllowed=y
    URL https://doi.org/10.1016/j.jmaa.2019.06.007
    Please use this ID to quote from or refer to the card https://repository.kpfu.ru/eng/?p_id=203421&p_lang=2
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