Title: Curvature-driven stability of defects in nematic textures over spherical disks,
Abstract: Stabilizing defects in liquid-crystal systems is crucial for many physical
processes and applications ranging from functionalizing liquid-crystal textures
to recently reported command of chaotic behaviors of active matters. In this
work, we perform analytical calculations to study the curvature driven
stability mechanism of defects based on the isotropic nematic disk model that
is free of any topological constraint. We show that in a growing spherical disk
covering a sphere the accumulation of curvature effect can prevent typical +1
and +1/2 defects from forming boojum textures where the defects are repelled to
the boundary of the disk. Our calculations reveal that the movement of the
equilibrium position of the +1 defect from the boundary to the center of the
spherical disk occurs in a very narrow window of the disk area, exhibiting the
first-order phase-transition-like behavior. For the pair of +1/2 defects by
splitting a +1 defect, we find the curvature driven alternating repulsive and
attractive interactions between the two defects. With the growth of the
spherical disk these two defects tend to approach and finally recombine towards
a +1 defect texture. The sensitive response of defects to curvature and the
curvature driven stability mechanism demonstrated in this work in nematic disk
systems may have implications towards versatile control and engineering of
liquid crystal textures in various applications.