20.500.12556/RUL-139561 Simulacija holesterika v vijačno simetrični ograditvi Simulation of a cholesteric in a helically symmetric confinement V magistrskem delu numerično modeliramo dvojno vijačno strukturo v vijačno sime- trični ograditvi, ki je bila nedavno eksperimentalno opažena. Zaradi vijačne simetrije tri-dimenzionalni problem omejimo na dve dimenziji. Prosto energijo zapišemo po Landau-de Gennes modelu in jo diskretiziramo po metodi končnih diferenc, mini- miziramo pa z metodo gradientnega spusta. Metodo nato testiramo na fizikalno relevantnem primeru z domeno s koncentričnim in nekoncentričnim krogom. Dvojno vijačno strukturo modeliramo na domeni v obliki prirejene nefroide. Rezultat je dvojni zvoj z istima ročnostima in lokalizirana defektna območja v konicah nefroide, kar v treh dimenzijah pomeni dve linijski zviti disklinaciji. We numerically model a doubly helical structure in a helically symmetric confinement, which was recently experimentally observed. Due to helical symmetry we are able to reduce the three-dimensional problem to two dimensions. Free energy is expanded according to the Landau-de Gennes model and is discretized by the method of finite differences. Minimization is done with gradient descent. We test the method on physically relevant example of concentric and non-concentric domain. The doubly helical structure is modelled on a adapted nephroid domain. The result is a double twist director structure with the same sign and two localized defects in the two trenches of the nephroid. We observe two twist disclinations Landau-de Gennes prosta energija holesterični tekoči kristal topološki defekti dvojni zvoj zvita disklinacija Landau-de Gennes free energy cholesteric liquid crystal topological defects double twist twist disclination true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-09-04 08:15:02 2022-09-04 08:15:03 2022-09-16 04:11:13 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 125465 120454915 5338.pdf 5338.pdf 1 B5DABF1A2A7927E4B9EEEFAFB3208F2E 8e27793e96937116ccd2abef35e683802c4fb46256732ef3517f7fe0f17aef20 df7f8faa-2c18-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160137 Fakulteta za matematiko in fiziko 0 0 0