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D. Jesenek^1,2, S. Kralj^1,2,3

Author affiliations
¹Jozef Stefan Institute,
Slovenia, 1000, Ljubljana, Jamova, 39
²Jozef Stefan International Postgraduate School,
Slovenia, 1000, Ljubljana, Jamova, 39
³Faculty of Natural Sciences and Mathematics, University of Maribor,
Slovenia, 2000, Koroska, 160
E-mail: samo.kralj@ijs.si

Abstract
We study numerically impact of spatially varying curvature on position and number of topological defects (TDs). A two-dimensional Landau-de Gennes tensorial formalism is used. We focus on TDs in axially symmetric dumb-bell structures, possessing area patches exhibiting both positive and negative Gaussian curvature. These nematic shells exhibit spherical topology, enforcing the total topological charge m_tot=2. We show that on progressively narrowing necks of dumb-bell structures the number of TDs increases via nucleation of topological defect-antidefect pairs. In each surface patch, characterised by a well defined average Gaussian curvature, the sum of TDs and the total smeared Gaussian topological charge tends to be zero. Therefore, in dumb-bell structures TDs tend to spatially redistribute in a way to compensate the smeared Gaussian curvature topological charge.

Keywords: liquid crystals, nematic shells, Gaussian curvature, topological defects