20.500.12556/RUL-187094 Magnetno polje aktivnega nematika z enim defektom Magnetic field of an active nematic with a single defect V magistrskem delu obravnavamo aktivni nematik z enim topološkim defektom kot vir magnetnega polja. Aktivni nematiki so sistemi delcev izven termodinamskega ravnovesja, ki s pretvarjanjem energije v gibanje ustvarjajo kompleksne tokove v okoliškem mediju. Če je medij ionska raztopina, ti tokovi predstavljajo električni tok, ki v okolici sistema inducira magnetno polje. Izhajamo iz znanega analitičnega izraza za hitrostno polje aktivnega nematika v dveh dimenzijah. Z ustreznim reskaliranjem koordinat uvedemo anizotropno omejeno domeno, ki bolje odraža realne eksperimentalne razmere. Tako dobljeno hitrostno polje uporabimo za določitev gostote električnega toka, na podlagi katerega z uporabo Biot–Savartovega zakona numerično izračunamo gostoto magnetnega polja v več ravninah nad plastjo aktivnega nematika. Rezultati kažejo, da magnetno polje v prostoru odraža strukturo tokovnic v ionski raztopini ter da njegova jakost z razdaljo od plasti aktivnega nematika pojema. Oblika in simetrija magnetnega polja sta odvisni od topološkega tipa defekta in geometrije domene. Predstavljeni pristop omogoča kvalitativno povezavo med topologijo aktivnega nematika, hidrodinamskimi tokovi in elektromagnetnim odzivom sistema. 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. Aktivni nematik topološki defekti magnetno polje Biot–Savartov zakon aktivna snov. Active nematics topological defects magnetic field Biot–Savart law active matter. true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-09-09 08:15:09 2026-09-09 08:15:14 2026-09-14 14:24:31 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 162966 291040771 22011.pdf 22011.pdf 1 46FA40FFCE90443F0CBB06AB25A6F779 3ec78809d7d61c16a5ff5d4c945df28cce8f9b0f12fdc8f2271e6545c5e43494 cd93a74b-ac15-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=246532 Fakulteta za matematiko in fiziko 0 0 0