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Simulacija holesterika v vijačno simetrični ograditvi
ID Marinko, Peter (Author), ID Čopar, Simon (Mentor) More about this mentor... This link opens in a new window

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Abstract
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.

Language:Slovenian
Keywords:Landau-de Gennes prosta energija, holesterični tekoči kristal, topološki defekti, dvojni zvoj, zvita disklinacija
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2022
PID:20.500.12556/RUL-139561 This link opens in a new window
COBISS.SI-ID:120454915 This link opens in a new window
Publication date in RUL:04.09.2022
Views:1133
Downloads:92
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Secondary language

Language:English
Title:Simulation of a cholesteric in a helically symmetric confinement
Abstract:
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

Keywords:Landau-de Gennes free energy, cholesteric liquid crystal, topological defects, double twist, twist disclination

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