On Generation, Motions, and Collisions of Dowsons

Dowsons are +/- 2 pi point singularities of the unitary complex order parameter e(i phi) characterizing the so-called dowser texture in a thin nematic layer with homeotropic boundary conditions. Dowsons are therefore similar to disclinations in freely-standing smectic C films or to vortices in two-dimensional superfluids or superconductors. Using especially tailored setups called dowsons' colliders, pairs of dowsons of opposite signs are generated and set into motion on counter-rotating trajectories leading to collisions. In a first approximation, the velocity of dowsons is orthogonal and proportional to the local phase gradient backward difference phi. The outcome of collisions, i.e., either annihilation or bypass, depends on the distance of trajectories Delta phi in terms of the phase: for Delta phi < pi a collision of a pair of dowsons leads to their annihilation, while for Delta phi > pi the dowsons are passing by. This rule is valid only for quasi-static stationary wound up textures and can be easily broken by application of a Poiseuille flow in an appropriate direction.