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Urejanje točkastih multipolov na sferi
Gnidovec, Andraž (Author), Čopar, Simon (Mentor) More about this mentor... This link opens in a new window

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Abstract
Razporeditev interagirajočih delcev na sferi je zgodovinsko dobro znan problem, neraziskano pa je ostalo urejanje delcev z anizotropnimi medsebojnimi interakcijami, kamor spadata tudi dipolna in kvadrupolna interakcija. Problema orientacijskega urejanja sistemov točkastih dipolov pri fiksnem pozicijskem redu na sferi se lotimo z numerično minimizacijo energije ter predstavimo ureditvene parametre za kvantitativno klasifikacijo najdenih konfiguracij. Osnovna stanja pri različnih številih gradnikov so vrtinčna, vzbujena stanja pa imajo tudi drugačne ureditve. Raziščemo odziv sistema na zunanje polje in odkrijemo več orientacijskih faznih prehodov. Izvedemo tudi simulacije orientacijskega urejanja kvadrupolnih sistemov na sferi, kjer opazimo pomembne razlike med urejanjem linearnih in planarnih kvadrupolov. Rezultati, pridobljeni v tej nalogi, služijo kot izhodišče za nadaljnje raziskovanje sistemov delcev z anizotropno interakcijo na neevklidskih geometrijah.

Language:Slovenian
Keywords:dipoli, kvadrupoli, parska interakcija, urejanje na sferi, Thomsonov problem, orientacijski fazni prehod
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
COBISS.SI-ID:3351140 This link opens in a new window
Views:338
Downloads:128
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Secondary language

Language:English
Title:Ordering of point multipoles on a sphere
Abstract:
Distribution of interacting particles on a sphere is historically a well known problem, however, ordering of systems with anisotropic interaction, specifically dipole and quadrupole interaction, remains unexplored. We solve orientational ordering of point dipoles on a sphere with fixed positional order with numerical minimization of energy and introduce order parameters needed for quantitative classification of different configurations. We find vortex ground states for different system sizes while excited states also show other configurations. We explore system response in external field where multiple orientational phase transitions emerge. We also perform simulations of orientational ordering of quadrupole systems and notice important differences between linear and planar quadrupoles. Results acquired in this thesis represent a starting point for further research on systems with anisotropic interaction on non-Euclidean geometries.

Keywords:dipoles, quadrupoles, pair interaction, ordering on sphere, Thomson problem, orientational phase transition

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