AUTHOR=Pieranski Pawel , Godinho Maria Helena 

TITLE=On Generation, Motions, and Collisions of Dowsons

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00238

DOI=10.3389/fphy.2019.00238

ISSN=2296-424X

ABSTRACT=<p>Dowsons are ±2π point singularities of the unitary complex order parameter <italic>e</italic><sup><italic>iφ</italic></sup> 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 <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover class="overrightarrow"><mml:mrow><mml:mo>∇</mml:mo></mml:mrow><mml:mo>⃗</mml:mo></mml:mover><mml:mo>φ</mml:mo></mml:math></inline-formula>. The outcome of collisions, i.e., either annihilation or bypass, depends on the distance of trajectories Δφ in terms of the phase: for Δφ &lt; π a collision of a pair of dowsons leads to their annihilation, while for Δφ &gt; π 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.</p>