20.500.12556/RUL-185892 Univerzalno skaliranje fronte kaosa v 2+1 dimenzijah Universal Scaling of the Chaos Front in 2+1 Dimensions V nalogi preučujemo širjenje lokalizirane perturbacije v reverzibilnem (2+1)-dimenzionalnem celičnem avtomatu na heksagonalni mreži kot makroskopsko različico učinka metulja v mnogodelčnih sistemih. Domet perturbacije opišemo s fronto kaosa in njene statistične lastnosti analiziramo v okviru formalizma dinamike mejnih plasti. Z numeričnimi simulacijami določimo kritične eksponente, preučimo vpliv končne velikosti sistema in časovne popravke ter rezultate primerjamo z diskretnimi modeli z znano univerzalnostjo. Empirično dokažemo, da morfologija fronte kaosa sodi v (1+1)-dimenzionalni Kardar–Parisi–Zhangov univerzalnostni razred pri ravnem začetnem pogoju --- iz njene dinamike izluščimo balistično hitrost, pokažemo, da imajo fluktuacije ustrezne skalirne lastnosti, za porazdelitev šuma pa ugotovimo, da ta ustreza Tracy–Widomovi porazdelitvi Gaussovega ortogonalnega ansambla. In this thesis, we investigate the spreading of a localized perturbation in a reversible (2+1)-dimensional cellular automaton on a hexagonal lattice as a macroscopic analogue of the butterfly effect in many-body systems. The spatiotemporal extent of the perturbation is characterized by the chaos front, whose statistical properties are analyzed within the framework of interface growth phenomena. Using numerical simulations, we determine the critical exponents, examine finite-size and finite-time corrections, and compare the results with discrete models of known universality. We provide empirical evidence that the morphology of the chaos front belongs to the (1+1)-dimensional Kardar–Parisi–Zhang universality class for flat initial conditions. In particular, we extract the ballistic propagation velocity, demonstrate that the front fluctuations exhibit the expected scaling behavior, and show that the noise distribution is described by the Tracy–Widom distribution of the Gaussian Orthogonal Ensemble. Učinek metulja fronta kaosa KPZ univerzalnost Butterfly effect chaos front KPZ universality true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-08-22 08:15:08 2026-08-22 08:15:14 2026-09-03 08:49:49 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 161796 289840131 23424.pdf 23424.pdf 1 0C692ECF63C369E8FE1A1CA9F60E7E96 253d206e0df9b3b393a3b0d2ea881398f03833f98f23ea2defa9ca3ce93af3c7 72f65f56-9df0-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=244899 Fakulteta za matematiko in fiziko 0 0 0