  The interaction between two disks immersed in a 2D nematic is investigated
(i) analitically using the tensor order parameter formalism for the nematic
configuration around isolated disks and (ii) numerically using finite element
methods with adaptive meshing to minimize the corresponding Landau-de Gennes
free energy. For strong homeotropic anchoring, each disk generates a pair of
defects with one-half topological charge responsible for the 2D quadrupolar
interaction between the disks at large distances. At short distance, the
position of the defects may change, leading to unexpected complex interactions
with the quadrupolar repulsive interactions becoming attractive. This short
range attraction in all directions is still anisotropic. As the distance
between the disks decreases their preferred relative orientation with respect
to the far-field nematic director changes from oblique to perpendicular.
