Simulacija holesterika v vijačno simetrični ograditvi

Marinko, Peter (author), Čopar, Simon (mentor)

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
• COBISS.SI-ID: 120454915
• Publication date in RUL: 04.09.2022

MARINKO, Peter, 2022, Simulacija holesterika v vijačno simetrični ograditvi [online]. Master’s thesis. [Accessed 11 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=139561

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