In this thesis, we investigate an active nematic containing a single topological defect
as a source of a magnetic field. Active nematics are systems of particles driven out of
thermodynamic equilibrium, where continuous energy conversion into motion generates
complex flow patterns in the surrounding medium. When the medium is an ionic
solution, these flows correspond to electric currents, which in turn induce a magnetic
field. Starting from an analytically known expression for the two-dimensional
velocity field of an active nematic, we introduce an anisotropically confined domain
by rescaling the spatial coordinates. This approach provides a more realistic description
of experimentally relevant systems. The resulting velocity field is used to
determine the electric current density, and the magnetic field is then computed numerically
in several planes above the active nematic layer using the Biot–Savart law.
The results show that the magnetic field reflects the structure of the flow streamlines
and decreases in magnitude with increasing distance from the active nematic
layer. Both the shape and symmetry of the magnetic field depend on the topological
charge of the defect and on the geometry of the confining domain. The presented
approach offers a qualitative link between topology, hydrodynamic flows, and the
electromagnetic response of active nematic systems.
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