20.500.12556/RUL-154362 Celični avtomat "škatla-žogica", sklopljen z Markovskim rezervoarjem Box Ball System coupled to a Markovian reservoir V magistrskem delu je predstavljen deterministični dinamični sistem Box-Ball (BBS), sklopljen s stohastičnim Markovskim rezervoarjem. Rezervoar predstavlja robni pogoj, kjer stohastično nastajajo žoge v sistemu. Dinamika tega sklopljenega sistema je drugačna od klasičnega BBS in zato potrebujemo definicijo pomožnega prostora. Predstavljene so lastnosti sklopljenega sistema ter numerično dobljeni rezultati za opazljivke. Opazljivke in lastnosti, ki so predstavljene in izračunane v tej nalogi, so: gostota, tok žog, dinamična matrika, parcialne matrike dinamične matrike in njihove rekurzivne zveze, spektri stacionarnih stanj, marginalne vsote stacionarnih stanj, Schmidtovi ranki biparticij neravnovesnega stacionarnega stanja, korelacijske funkcije in porazdelitve pomožnega prostora. Z uporabo dobljenih rezultatov lahko postavimo domneve o BBS, sklopljenem s stohastičnim Markovskim rezervoarjem, ki jih bo nadaljnje raziskovanje morda dokazalo. Ključne domneve v magistrskem delu se nanašajo na spekter stacionarnega stanja, parcialne matrike, Schmidt ranke, kristalno fazo in korelacije. In this master thesis we present the deterministic dynamical model Box-Ball System (BBS) coupled to a stochastic reservoir. This reservoir represents a boundary condition where balls are stochastically created and enter the system. The dynamics of such a system is different from the classical BBS and because of that we will define the auxiliary space. In the thesis we present the properties of this coupled system and numerical results obtained for observables. The properties and observables included in this thesis are: density, ball current, dynamical matrix, partial matrixes of the dynamical matrix and their recursive properties, spectrums of the steady state, marginal sums of the steady state, Schmidt ranks of bipartitions of non-equilibrium steady state, correlation functions and distributions of balls in the auxiliary space. With the results gathered in the thesis we can make conjectures about BBS coupled with a stochastic reservoir that further study might prove. The key conjectures in this thesis are about the spectrum of the steady state, partial matrixes, Schmidt ranks, crystal phase and correlations. Box-Ball Sistem solitoni stacionarno stanje Schmidtovi ranki korelacije pomožni prostor parcialne matrike Box-Ball system solitons steady state Schmidt rank correlations auxiliary space partial matrix true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-02-08 08:15:04 2024-02-08 08:15:09 2024-02-13 13:37:26 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 139712 184121347 12004.pdf 12004.pdf 1 1057FFD8002ACF4C5EC562E833CCC8CB bb21a3e25052c85ac2a9d66079fadcc63378df6b076fb1af1dfcc0077874f029 cc6d0d16-c651-11ee-a2e4-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180743 Fakulteta za matematiko in fiziko 0 0 0