  Topological defects are a universal concept across many disciplines, such as
crystallography, liquid-crystalline physics, low-temperature physics,
cosmology, and even biology. In nematic liquid crystals, topological defects
called disclinations have been widely studied. For their three-dimensional (3D)
dynamics, however, only recently have theoretical approaches dealing with fully
3D configurations been reported. Further, recent experiments have observed 3D
disclination line reconnections, a phenomenon characteristic of defect line
dynamics, but detailed discussions were limited to the case of approximately
parallel defects. In this study, we focus on the case of two disclination lines
that approach at finite angles and lie in separate planes, a more fundamentally
3D reconnection configuration. Observing and analyzing such reconnection
events, we find the square-root law of the distance between disclinations and
the decrease of the inter-disclination angle over time. We compare the
experimental results with theory and find qualitative agreement on the scaling
of distance and angle with time, but quantitative disagreement on distance and
angle relative mobilities. To probe this disagreement, we derive the equations
of motion for systems with reduced twist constant and also carry out
simulations for this case. These, together with the experimental results,
suggest that deformations of disclinations may be responsible for the
disagreement.
