20.500.12556/RUL-158594 Structural order in anisotropically interacting systems on spherical surfaces Strukturni red v anizotropno interagirajočih sistemih na sferičnih površinah Interaction anisotropy and substrate curvature both influence the structural order in many physical and biological systems. In this thesis, the interplay between the two effects is investigated in various systems in spherical confinement. Quadrupolar systems with fixed positional order show that both the local particle arrangement and the global lattice symmetries play a role in the emergence of long-range orientational order. Dipolar hard sphere systems where particles are free to move on the spherical surface, are demonstrated to display similar regime behavior to the Euclidean cases. In active nematic shells, the propagation of topological defects is modeled under the influence of external drag forces which are shown to cause collective reorientations of defect trajectories. Furthermore, systems of geodesic spherical ellipses are investigated where a contact function is first constructed and later used to generate dense monodispersed random packing configurations. The dependence of packing density and contact number on ellipse aspect ratio is shown to be non-monontonic, similar to cases of 3D packing of ellipsoidal particles. The packing results are contrasted with other similar studies, both on the sphere and in flat spaces. Finally, inverse design of model patchy interactions is considered, using an automatic differentiation-based optimization scheme to target self-assembly into structures with a desired Gaussian curvature. The model requirements and hyperparameter choices for successful optimization are discussed, and the results of self-assembly into vesicle-like shapes are presented. Tako interakcijska anizotropija kot ukrivljenost substrata vplivata na strukturni red v številnih fizikalnih in bioloških sistemih. V tej disertaciji preučim medsebojne učinke med obema vplivoma v različnih sistemih, omejenih na sferične površine. V kvadrupolnih sistemi s fiksnim pozicijskim redom na pojav daljnosežnega reda vplivata tako lokalni pozicijski red kot globalna simetrija rešetke. Sistemi dipolnih trdnih sfer, kjer se delci lahko prosto gibljejo po sferični površini, se obnašajo podobno kot sistemi v Evklidskem prostoru. V aktivnih nematskih lupinah modeliram učinke zunanjih uporov na propagacijo topoloških defektov, ki povzročijo reorientacijo trajektorij defektov. Nadalje preučim sisteme geodezičnih sferičnih elips, kjer najprej sestavim kontaktno funkcijo, ki jo nato uporabim za generacijo naključjih gostih zlaganj sferičnih elips. Odvisnost gostote zlaganja od razmerja stranic elips je nemonotono, podobno kot v primerih zlaganja 3D elipsoidov. Rezultate primerjam s podobnimi študijami tako v Evklidskem prostoru, kot na sferi. Nazadnje obravnavam obratno načrtovanje interakcij v sistemih delcev z interakcijskimi pikami, kjer uporabim avtomatsko odvajanje za optimizacijo zlaganja delcev v strukture s ciljno Gaussovo ukrivljenostjo. Analiziram lastnosti modela ter izbiro hiperparametrov, ki vodijo do uspešne optimizacije, ter pokažem rezultate samo-sestavljanja delcev v vezikle. anisotropic interactions spherical confinement curved substrate self-assembly anizotropne interakcije omejitev na sferične površine ukrivljen substrat samo-sestavljanje true false false Angleški jezik Slovenski jezik Doktorsko delo/naloga 2024-06-16 08:15:04 2024-06-16 08:15:09 2024-07-22 11:41:21 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 139821 202428163 12090.pdf 12090.pdf 1 47C22DC90EC7FA56A056B884DD02A84B db3560bf9ced1ba890942c59ff4284cd0c10f1d45a9d62cfa4326675b270dae8 cbee57bb-2ba7-11ef-9bcc-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186270 Fakulteta za matematiko in fiziko 0 0 0