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While keeping the discreteness of the reciprocal space, we calculate the spectrum of incoherent electron-hole excitations in the conducting Fermi liquids. The method is illustrated on the well-known jellium model within the random phase approximation. It also leads to the formulation of a sum rule from which we get the details of the dispersion curve for the collective plasmon mode. The notion of time averaging in the discrete approach is briefly recalled., Računamo spektar nekoherentnih uzbuda elektron-šupljina u vodljivim Fermijevim tekućinama zadržavajući diskretnost recipročnog prostora. Pristup se predstavlja pomoću poznatog modela drhtavice i približenja nasumičnih faza. Dobiva se zbrojno pravilo iz kojeg slijede pojedinosti disperzijske krivulje za kolektivan plazmonski mod. Podsjeća se ukratko na pojam vremenskog prosjeka u ovom diskretnom pristupu.

Krajem 19. stoljeća, ultraljubičasta katastrofa bila je jedna od glavnih okidača velikih promjena u poimanju fizike mikrosvijeta. Klasične teorije nisu bile dostatne u rješavanju problema moderne fizike. RayleighJeansov zakon predstavlja klasičnu teoriju zračenja crnog tijela koja u domenama viših frekvencija daje divergentne nefizikalne izraze za izračenu energiju crnog tijela. Velike promjene dolaze s idejama kvantne fizike, odnosno kvantizacijom energije koja dopušta precizni opis zračenja crnog tijela dan Planckovim distribucijskim funkcijama. Cilj ovog rada jest osposobiti aparaturu potrebnu za mjerenje zračenja crnog tijela te eksperimentalno utvrditi da se zračenje crnog tijela odnosno žarulje ponaša prema Planckovom zakonu. U ovom radu pažnju stavljam na praktični dio osposobljavanja uređaja te provedbu i numeričku analizu dobivenih podataka. Iz provedenih mjerenja zračenja crnog tijela pri raznim temperaturama želim interpolacijskim metodama dobiti kontinuirane ovisnosti detektirane struje o valnim duljinama iz kojih bih zaključio slažu li se dobiveni podatci s teorijom., At the end of the 19th century, ultraviolet catastrophe presented one of the most significant indicators of new theories and the physics of the microscopic scale. Classical theories did not yield accurate results. Rayleigh-Jeans law presents the classical theory of black body radiation which gives divergent nonphysical results in the domain of higher frequencies. Significant changes arrive with the ideas of quantum physics and the quantization of energy which allows accurate description of black body radiation given by Planck’s distribution functions. The goal of this thesis is to repair the apparatus needed for black body radiation measurement and to experimentally determine that the measured radiation is consistent with Planck’s law. Most of the attention is on the practical part and the numerical analysis of the obtained data. From black body radiation measurements at various temperatures, I want to obtain the continuous dependence of the detected current on the wavelengths from which I would conclude whether the obtained data agrees with the theory of black body radiation.

U ovom radu primjenjuje se teorija funkcionala gustoće i vremenski ovisna teorija funkcionala gustoće na metalne olovne halidne perovskite. Metalni olovni halidni perovskit materijal je koji se zbog dobrih optičkih i električnih svojstava te relativno niske cijene sve više istražuje za primjenu u solarnim ćelijama. U radu se razmatraju halidni perovskiti s atomima broma, klora, fluora i joda. Od pet promatranih iona PbX6 2−, četiri imaju jednu vrstu halogenog elementa, a jedan ion se sastoji od dva atoma broma, dva atoma klora i dva atoma joda. Odabrane strukture su optimirane te je izračunata energija, duljine veza i kutovi među vezama. Kod optimizacije strukture koristi se teorija funkcionala gustoće. Nakon optimizacije, određen je apsorpcijski spektar i glavni prijelazi u pobuđeno stanje za svaki od pojedinih iona. Prilikom računanja apsorpcijskog spektra i prijelaza koristi se vremenski ovisna teorija funkcionala gustoće i to metoda koja se zove teorija linearnog odziva. Apsorpcijski spektar miješanog iona određuje se kako bi se vidjelo može li se određenom kombinacijom halogenih elemenata dobiti apsorpcijski spektar koji će imati najveći intenzitet u vidljivom dijelu spektra, a što je glavni cilj kod primjene u solarnim ćelijama. Simulacije su rađene u programskim paketima Turbomole i Dalton., In this master thesis, density functional theory and its time – dependent counterpart will be applied to study metal halide lead perovskites. Metal halide lead perovskite materials came in the focus of the research community due to the extraordinary optical and electrical properties and low price for possible application to increase performance of solar cells. Within this thesis, I have studied metal halide perovskites with bromine, chloride, iodine and flourine atoms. There are five distinguish ions PbX6 2− in total of which four of them have one type of halogene element and the last ion has two atoms of bromine, two of chloride and two of iodine. Selected structures are optimized using gradient techniques and their electronic DFT energy has been determined, as well as other structural properties such as bond lenghts and angles between them. All optimizations have been performed using density functional theory. Following structural optimization, UV-Vis absorption spectra have been simulated and main transitions for excited states for every single ion have been analyzed using time – dependent density functional theory. Absorption spectra investigations are interesting because I wanted to find out what combination of halogene elements within metal perovskite materials would give rise to the absorption spectrum with maximum intensity covering whole visible part of EM spectrum. All calculations have been performed using Turbomole and Dalton density functional theory software codes on server cluster.

Grafit i ostale alotropske modifikacije ugljika imaju sve veću primjenu u proizvodnji i industriji. Iz otpada, primjerice automobilskih guma, moguće je pirolitičkim postupkom izdvojiti ugljik te dobiti grafit, odnosno grafen koji je materijal budućnosti. Naš cilj je proučavati uzorke ugljika te analizirati i interpretirati rezultate. U tu svrhu potrebno je staviti rendgenski difraktometar u pogon i proučiti njegov način rada te naučiti rad na njemu. U ovom radu je objašnjena teorija raspršenja x-zraka, a posebno metode raspršenja na praškastim uzorcima. Služili smo se programom PowderCell koji računa kutnu ovisnost o intenzitetu raspršenja i prikazuje sliku kristalne strukture prema unesenim podatcima. Da bismo se mogli služiti programom, upoznajemo se s kristalnim strukturama i njihovom sistematizacijom te kristalnim ravininama kako bismo bolje razumjeli dobivene difraktograme. Na kraju uz pomoć programa analiziramo različite strukture grafita i dobivene rezultate uspoređujemo s uzorcima dobivenim pirolitičkim postupkom.

Substructuring and superelements technique is today one of the most important procedures in large scale stress analysis industry design processes. In this thesis the implementation of substructuring and superelements technique in finite element method is presented, with its application in various types of one, two and three – dimensional problems in stress analysis of thin-walled structures. As a ground basis needed to develop substructuring procedure with FEM, first the programming procedures of the classical FEM in Matlab programming language are presented in the Appendix, alongside with the application of classical FEM in two – dimensional plane stress analysis problems. For the plane stress analysis problems solved in Appendix the programming codes were developed using repository of professor dr. sc. Jack Chessa (University of Texas) called FEMLAB [1], as a basis. Analysis performed in Appendix is serving as an essential foreknowledge needed for the substructuring and superelements approach to be implemented and applied. As for the main part of the thesis, first an overview of FEM implementation in structural analysis is presented. Substructuring and superelements technique is introduced. Physical and mathematical concept of the technique is developed, with the practical aspects emphasized and singled out. Global – local analysis (two levels) is distinguished from multilevel substructuring. The procedure of substructuring is described in detail, with the given data flow diagram in generic multilevel substructuring made of any desired number of levels. Programming concept of the technique is thoroughly described, and the interface between an external mesh generator (Gmsh) and Matlab programming language is developed. The procedure of substructuring was performed with the “top – down” approach, whilst the programming procedure was implemented in both directions, “top – down” and “bottom – up”. The substructuring procedure and its programming are then connected together in application to a set of one, two and three – dimensional problems in stress analysis of thin – walled structures. One – dimensional bar element is solved using this technique by hand, to illustrate the need of programming the procedure for more complex problems. The two – dimensional problems were solved using an automated approach programmed in Matlab, and a thin plate with a non-symmetrical hole subjected to an in-plane bending load is analysed by diving it into a total of ten level two substructures. Programming the technique in 3D is then illustrated through an example of a simple hexahedron case made up of 6 thin plates. Eventually, built on the knowledge collected through working on this thesis, a stress analysis of a 3D ship cover with one bulkhead is performed, according to the drawing made in Catia. Practical aspects of the technique are directly pointed out and emphasized through the analysis of processing and its results, whose visualization, alongside with Matlab, is presented in Paraview Visualization Toolkit. The thesis finishes by describing a concept idea of how to manipulate with large data structures, such as the one obtained and collected through performed analysis of a 3D ship cover.

Prediktivna statistička mehanika je oblik zaključivanja iz dostupnih podataka, bez dodatnih pretpostavki, koje nastoji predvidjeti reproducibilne pojave. Primjenom prediktivne statističke mehanike na sustave s Hamiltonovom dinamikom razmotren je problem predviđanja makroskopske vremenske evolucije sustava u slučaju nepotpune informacije o mikroskopskoj dinamici. Cilj istraživanja je analizom temeljnih načela prediktivne statističke mehanike produbiti razumijevanje njene opće primjenjivosti u relaciji s drugim teorijama koje nastoje objasniti pojavu ireverzibilnosti. Osnovna hipoteza je da se to može postići detaljnim razmatranjem uloge koju informacija o sustavu ima u razjašnjenju problema ireverzibilnosti. Hipoteza je provjerena kroz analizu i daljnu generalizaciju rezultata osnovnog teorijskog modela. U modelu zatvorenog Hamiltonovog sustava koji uz Liouvilleovu jednadžbu koristi pojmove teorije informacije analiziran je gubitak korelacije izmedu početnih putanja u faznom prostoru i konačnih mikrostanja, i s tim povezan gubitak informacije o stanju sustava. Primjena načela najveće informacijske entropije maksimizacijom uvjetne informacijske entropije, uz ograničenje koje je dano Liouvilleovom jednadžbom usrednjenom po faznom prostoru, omogućila je definiciju brzine promjene entropije bez dodatnih pretpostavki. Početni model je generaliziran te je uvođenjem dodatnih ograničenja koja su ekvivalentna hidrodinamičkim jednadžbama kontinuiteta doveden u izravnu vezu s poznatim rezultatima iz neravnotežne statističke mehanike i termodinamike ireverzibilnih procesa. Dobiveni rezultati upućuju na općenitu primjenjivost načela prediktivne statističke mehanike i njihovu važnost za teoriju ireverzibilnosti. Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying predictive statistical mechanics to systems with Hamiltonian dynamics, a problem of predicting the macroscopic time evolution of the system in the case of incomplete information about the microscopic dynamics was considered. The goal of the research is to deepen the understanding, through the analysis of the fundamental principles of predictive statistical mechanics, of its general applicability in relation to other theories that seek to explain the phenomenon of irreversibility. Basic hypothesis is that this can be achieved with the detailed consideration of the role that information about the system has in the clarification of the problem of irreversibility. The hypothesis was tested through the analysis and further generalization of the results of the basic theoretical model. In a model of a closed Hamiltonian system that with the Liouville equation uses the concepts of information theory, analysis was conducted of the loss of correlation between the initial phase space paths and final microstates, and of the related loss of information about the state of the system. Applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, allowed a definition of the rate of change of entropy without additional assumptions. Initial model was generalized, and with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, brought into direct connection with the known results from the nonequilibrium statistical mechanics and thermodynamics of irreversible processes. The results obtained in this work suggest the general applicability of the principles of predictive statistical mechanics and their importance for the theory of irreversibility.