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Isingov model je matematički model uveden kao pojednostavljeni prikaz feromagnetizma u statističkoj fizici i kao takav bavi se fizikom faznih prijelaza. Model sadrži varijable diskretnih vrijednosti ±1, koje predstavljaju magnetske dipolne momente atoma – spinove. Osnovna pretpostavka modela je interakcija spina samo s njegovim najbližim susjedima. U jednodimenzionalnom Isingovom modelu pokazuje se nepostojanje faznoga prijelaza, osim pri temperaturi apsolutne nule. Landauova teorija faznih prijelaza dovodi do zaključka da se u dvodimenzionalnom Isingovom modelu javlja fazni prijelaz drugoga reda pri prelasku sistema iz feromagnetske u paramagnetsku fazu. Monte Carlo simulacijom generira se kvadratna rešetka dvodimenzionalnog Isingovog modela te se računaju termodinamičke veličine prosječne energije, magnetizacije i toplinskog kapaciteta, čija interpretacija dovodi do zaključka o pojavi i vrsti faznoga prijelaza. The Ising model is a mathematical model introduced as a simplified representation of ferromagnetism in statistical physics and, as such, is concerned with the physics of phase transitions. The model consists of variables with discrete values ±1 that represent magnetic dipole moments of atoms - spins. The model assumes that each spin has only nearestneighbour interaction. Phase transition in the one-dimensional Ising model does not occur except at absolute zero temperature. Landau’s theory of phase transitions leads to the conclusion that in the two-dimensional Ising model, a phase transition of the second order occurs during the system’s transition from the ferromagnetic to the paramagnetic phase. Monte Carlo simulation generates a square lattice of the two-dimensional Ising model and calculates the thermodynamic quantities of average energy, magnetization and heat capacity, the interpretation of which leads to a conclusion about the occurrence and type of phase transition.

Cilj diplomskog rada je ustvrditi adekvatnost različitih metoda izračuna rizične vrijednosti putem testiranja unatrag odabranim statističkim testovima koji ispituju svojstva bezuvjetne pokrivenosti i neovisnosti dobivenih procjena rizične vrijednosti. Pritom, metode koje su predmet testiranja su parametarska metoda, povijesna simulacija i Monte Carlo simulacija. Fokus će se posvetiti i detaljnoj analizi karakteristika obveznica, načinima modeliranja krivulje prinosa te odrednicama obvezničkih tržišta, kako bi se definirali glavni čimbenici volatilnosti cijene obveznica. Analiza će se provesti nad podacima o spot prinosima Europske središnje banke, koji služe kao diskontna stopa prilikom izračuna teorijske cijene obveznica u portfelju, dok su karakteristike obveznica temeljene na dospijećima i kuponskim kamatnim stopama trenutno aktivnih izdanja obveznica Luksemburga, Nizozemske i Njemačke. Na taj način u obzir se uzima trenutna struktura obveznica koje su dostupne na tržištu, kako bi se njihove značajke ukomponirale u hipotetski portfelj nad kojim se vrši analiza performansi različitih metoda izračuna rizične vrijednosti. Rezultati Kupiecovog i Christoffersenovog testa upućuju na zaključak kako nijedna od tri ispitane metode ne može objektivno procijeniti rizičnu vrijednost portfelja. Razlog takvog ishoda uglavnom je uvjetovan pretpostavkama o distribuciji prinosa portfelja koje su neophodan element sve tri ispitane metode, a nisu u skladu s empirijskim dokazima o karakteristikama financijskih serija.

U doktorskoj disertaciji su prikazani metoda i rezultati vrednovanja točnosti izračuna apsorbirane doze računalnih algoritama koji se primjenjuju u radijacijskoj onkologiji. Metoda se temelji na primjeni Monte Carlo (MC) simulacije i komplementarna je postojećoj eksperimentalnoj metodologiji. MC simulacija je provedena korištenjem programskog paketa Monte Carlo N-Particle (MCNP). Istraživanje je provedeno za računalni algoritam sustava Elekta Monaco (MCTPS) kao jedan od najnaprednijih algoritama koji se trenutno koriste za planiranje jakosno modulirane radioterapije. Taj algoritam izračun apsorbirane doze dijelom temelji na MC simulaciji. On izračunava apsorbiranu dozu u malom volumenu sredstva koji se nalazi u sredstvu (D_m,m) te pruža mogućnost izračuna apsorbirane doze u vodi (D_w,m). Vrednovanje je provedeno za oba načina izračuna. Da bi se pouzdano utvrdila točnost MCNP izračuna apsorbirane doze bilo je potrebno dozimetrijski vrednovati rezultate MCNP modela 6 MV X-zraka u vodenom fantomu. MCNP simulacije provedene su u 13 postava homogenih fantoma različitih gustoća u rasponu od 0,2 g/cm^3 do 2,17 g/cm^3. Dodatno, vrednovanje je provedeno u složenim geometrijama kojima se nastojalo simulirati stvarne situacije. U heterogenoj geometriji istraživanje je bilo ograničeno na tri materijala gustoća usporedivih s gustoćama pojedinih vrsta tkiva. Osmišljena i simulirana su 4 različita scenarija za ispitivanje utjecaja heterogenosti na točnost izračuna apsorbirane doze u MCTPS, za oba načina izračuna, D_m,m i D_w,m. Korišten je fantom istih dimenzija kao kod izračuna u homogenoj geometriji, s razlikom što su na različitim dubinama dodavani umeci različitih gustoća. Odstupanja su izračunata pomoću korijena srednje vrijednosti kvadrata odstupanja (engl. root mean square deviation, RMS) za krivulje ovisnosti doze o dubini (DD). DD krivulje su izračunate pomoću MCNP programskog paketa te uspoređene s MCTPS izračunima. Također, za svih trinaest materijala ispitivana je točnost uračunavanja doprinosa različitih vrsta međudjelovanja u MCTPS izračunu apsorbirane doze. Prema rezultatima istraživanja, MCTPS način izračuna apsorbirane doze u sredstvu pokazuje RMS odstupanja u odnosu na MCNP izračun manji od 3% za sve materijale, osim za materijal najmanje gustoće (RMS=4,8%). Analiza rezultata između izračuna doza u vodi, nastao pretvorbom iz izračuna doze u sredstvu, i MCNP simulacije izračuna doze u vodi, pokazuje znatna odstupanja za većinu korištenih materijala, do najviše vrijednosti RMS = 13,1% za materijal najveće gustoće. Utvrđeno je da se izračun doze u vodi (D_w,m) koji je nastao pretvorbom iz izračuna doze u sredstvu bitno razlikuje od izračuna doze u vodi (D_w,w) i da ih treba razlikovati. Također, utvrđeno je da za različite materijale apsorbirana doza izračunata kao doza u sredstvu pokazuje bolje slaganje s algoritmima koji izračunavaju apsorbiranu dozu primjenom koncepta Dw,w, pri čemu najveće RMS odstupanje iznosi 3,7% za materijal najveće gustoće. U području gustoća manjih od vode potrebna su poboljšanja izračuna doza u sredstvu (D_m,m) te je predložena korekcija HU-RED krivulje i na taj način je RMS odstupanje smanjeno s 4,8% na 2,8%. Nadalje, s porastom atomskog broja materijala (počevši od materijala gustoće 1,66 g/cm3) utvrđeno je odstupanje u uračunavanju doprinosa fotoelektričnog učinka kao i doprinosa tvorbe para elektron-pozitron. Odstupanja u uračunavanju doprinosa fotoelektričnog učinka u izračunu apsorbirane doze od 1,3% do 1,7% utvrđena su za materijale gustoće od 1,66 g/cm^3 do 2,17 g/cm^3 na dubini od 5 cm. Ispitivanje točnosti uračunavanja doprinosa tvorbe para elektronpozitron na dubini od 10 cm pokazuje trend povećanja odstupanja do maksimalnog odstupanja od 2,3% za materijal gustoće 2,0 g/cm^3. Prikazani rezultati upućuju da MCTPS izračun apsorbirane doze kao doza u sredstvu (D_m,m) predstavlja točniji način izračuna apsorbirane doze. The most advanced treatment planning systems (TPSs) in radiation oncology have Monte Carlo (MC) based algorithms which facilitate the most accurate calculation of absorbed dose distributions in (external beam) radiotherapy. Such algorithms inherently calculate absorbed dose as dose to medium in medium (D_m,m), but also provide the ability to calculate absorbed dose as dose to water in medium (D_w,m) by converting the calculation from D_m,m to D_w,m using Spencer-Attix's extension of Brag-Gray small cavity theory. According to published data, differences between these two calculation options are noted, particularly in bony structures. Unlike the generalized MC codes (MCNP, EGS, GEANT...) several approximations and simplifications were introduced in such algorithms to speed up the calculation time. Thus, additional validation of calculation accuracy for both abovementioned calculation options is required. This doctoral dissertation presents the method and the results of a verification, complementary to the existing experimental methodology, for the accuracy validation of such algorithms using MC simulations. It was performed using Monte Carlo N-Particle code® (MCNP) by which the transport of photons and electrons is simulated. Algorithms used in radiation oncology calculate the absorbed dose without knowledge of the material chemical composition. Therefore, the investigation of the impact of material chemical composition on calculation accuracy was performed using MCNP calculations. Furthermore, the majority of clinical experience is based on the dose to water in water (D_w,w) concept provided by analytical algorithms and it has represented the standard for dose calculation during the past several decades. Considering that, additional MCNP calculation was performed to simulate the D_w,w concept of absorbed dose calculation. Hence, the deviation between the D_w,w and both calculation options provided by the MC based algorithms was determined. Additionally, the influence of predefined probabilities for X-ray interaction mechanisms and its respective contributions to absorbed dose calculations was validated using MCNP. Futhermore, in order to improve the accuracy of absorbed dose calculation for the D_m,m MCTPS calculation option, a correction for the HU-RED curve was applied. The impact of the proposed corrections on the accuracy of the absorbed dose calculation was also validated. Materials and methods: The calculation algorithm for intensity modulated radiotherapy (IMRT) built in the Elekta Monaco TPS is based on MC simulation. Its absorbed dose calculation has three components: a virtual source model (VSM), a transmission filter, and a patient model. The MC simulation is applied only in the final part of the calculation using X-Ray Voxel Monte Carlo (XVMC). Absorbed dose is calculated as Dm,m, but the conversion from Dm,m to Dw,m is enabled as well. In order to investigate the MCTPS absorbed dose distribution calculation accuracy for 6MV photon beam in various geometries, MCNP simulation was performed. To determine the accuracy of the MCNP absorbed dose calculation in any geometry, it is necessary to dosimetrically validate the results of the MCNP 6 MV X-ray beam model with the values measured using an ionization chamber in a water phantom. A virtual phantom of the same dimensions, 30×30×30 cm^3, as for MCTPS calculations was used. Percentage depth dose curves and dose profiles for various field sizes were calculated at several depths and compared to the measured data. For all MCNP calculations, cut-off energies of 1 keV for electrons (E_CUT) and 1 keV for photons (P_CUT) were applied. Statistical uncertainty for MCNP calculations was less than 1%. The validation criterion was set on the central part of the beam where deviation between calculated and measured data less than 0.5% was taken as acceptable. Initially, comparisons between dose calculation options built in MCTPS and MCNP in 13 different materials with mass densities ranging from 0.2 g/cm^3 to 2.17 g/cm3^3 was performed. The MCNP calculations were performed by assigning elemental chemical composition and mass density (MCNP_MEDIUM) and the absorbed dose is calculated as D_m,m. Additional MCNP simulation was performed to simulate D_w,w absorbed dose calculation (MCNP_WATER). Thus, MC simulation was performed for non-standard conditions, where different materials were represented as water of different densities. Depth dose curves (DDs) calculated by MCNP were compared to D_m,m and D_w,m calculated data using Root Mean Square (RMS) deviation (further in text: deviation). Additionally, similar validation of accuracy of absorbed dose calculations was performed in heterogeneous phantoms. For that reason, 4 different scenarios were designed and simulated. Heterogeneous geometries were simulated by placing inserts of different densities (ρ=0,205 g/cm^3 and ρ=1,6 g/cm^3) at different positions in the virtual water phantom. In this part, the study is limited to three materials used to mimic soft tissue, lungs and bones, respectively. In addition, the influence of the position of the heterogenity in the calculation geometry on the calculation of the absorbed dose was investigated. Due to differences in determination of materials in the respective calculation systems the influence of the chemical composition on the calculation of the absorbed dose in the semi-anthropomorphic phantom was eximened. Potential reasons for deviations were investigated. An improvement of the MCTPS Dm,m calculation accuracy is proposed. Results and discussion: The absorbed dose calculation accuracy is related to the capability of the algorithm to calculate absorbed dose at any point of interest within the patient and correlate it to the beam calibration point dose considered as the reference absorbed dose. In the MCTPS dose calculation engine, the chemical composition of the materials is not taken into account, thus introducing additional uncertainty into the calculation of absorbed dose. Deviations between DDs, for Dm,m and Dw,m in different materials become largest for material of mass density 2.17 g/cm3, up to 13%. Comparison for Dm,m calculation option to the MCNPMEDIUM shows very good agreement, with the deviation less than 3% for the majority of examined materials except for the lowest mass density in this research (ρ=0,2 g/cm^3), where the deviation is 4.8%. For the D_w,m calculation option results are acceptable only in the mass density range from 0.5 g/cm^3 to 1.06 g/cm^3 with deviations less than 2.5%. For the rest of the examined materials, the deviation increases, with a maximal value of 12.4% for mass density 2.17 g/cm3. Absorbed dose calculation comparison between D_w,m and MCNP_WATER shows large deviations for the majority of used materials, up to 13.1% for mass density 2.17 g/cm^3. Deviations between the D_m,m calculation option and MCNP_WATER are lower than one might expect, e.g. for the largest mass density in this research the deviation is 3.7%. Furthermore, the assumption of small cavity conditions applied through stopping power ratios of water and different materials for D_w,m calculation was also validated. It could be an acceptable approximation when assumptions of the Bragg-Gray cavity theory are fulfilled. The most probable energy of the secondary electrons for a 6 MV photon beam is below 300 keV. Such electrons have a range of 0.0957 g/cm2, and consequently, the conditions for small cavity when the voxel size of 3×3×3 mm^3 is used, mainly cannot be fulfilled due to the secondary electron range for almost all materials used. To verify the results obtained in simplified geometry, additional validation was performed in more complex geometry. The validation of the MCTPS absorbed dose calculation was performed by comparison with MCNP_MEDIUM calculations, when the conditions for charged particles equilibrium are not met due to heterogeneity. Since the validation was performed in complex geometry, a validation criterion was applied according to which a deviation 1.66 g/cm^3) differences in the calculation of the contribution of the photoelectric effect as well as pair production were observed. Differences in the calculation of the contribution of the photoelectric effect in the calculation of the absorbed dose from 1.3% to 1.7% were determined for materials with densities 1.66 g/cm3-2.17 g/cm^3 at a depth of 5 cm. Within MCTPS, equal stopping powers for positron and electron are applied to electron-positron pair production. However, examination of the deviation in the calculation of the contribution of electronpositron pair production at a depth of 10 cm shows increase of the deviation to a maximum value of 2.3% for the material with a density of 2.0 g/cm^3. The mean free path length, which is one of the parameters defined within the MCTPS when the conditions are met for the electron positron pair production is not correctly defined for the positron within the MCTPS. Conclusion: This doctoral dissertation presents the results of the method for validation of the MC based algorithm calculation accuracy which may be complementary to existing experimental verification methodology. The validation was performed for both options, D_m,m and D_w,m, using MCNP simulations. Although, algorithm built in MCTPS do not take into account the chemical composition of the medium, D_m,m calculation option shows very good agreement with standard MCNP calculations except for low density medium. Furthermore, it is demonstrated that the D_w,m calculation option differs substantially from D_w,w. It was also found that for different materials, absorbed dose calculated as D_m,m shows better agreement to the algorithms that calculate absorbed dose using D_w,w approach. The HU-RED correction was proposed in order to improve the accuracy of D_m,m calculation option built in MCTPS in low density medium. The results indicate that the absorbed dose distribution calculation performed with D_m,m could be preferable in order to allow better consistency with clinical data based on D_w,w dose concept as well as reference dosimetry performed in water. Also, this doctoral dissertation provides additional insight regarding the dilemma which calculation option is more accurate for use in radiation oncology. The results obtained indicate that D_m,m could be regarded as the preferable dose calculation option.

V zaključnem delu sem naredila izračune stroškov za energent in elektriko za tri scenarije: če imamo vozilo z notranjih izgorevanjem, če imamo električno vozilo in če imamo sončno elektrarno in električno vozilo. Osredotočila sem se na analizo ekonomske upravičenosti investicije v sončno elektrarno, če že imamo električno vozilo. Izračuni so pokazali, da se stroški pri zamenjavi vozila z notranjih izgorevanjem z električnih vozilom zmanjšajo za več kot 50 %. Če pa dokupimo še ustrezno dimenzionirano sončno elektrarno, letno prihranimo tudi do 600 EUR, kar investicijo povrne v dobrih 13 letih, neto sedanja vrednost investicije pa je dobrih 850 EUR. Scenarijska analiza po mestih dobro prikaže, da se investicija bolj izplača v mestih z večjo osončenostjo. Kar pa še ne pomeni, da se pri manjši osončenosti investicija ne izplača, le velikost elektrarne je treba prilagoditi. Občutljivostna analiza je pokazala, da imata med obravnavanimi parametri na končni rezultat največji vpliv osončenost in cena sončne elektrarne. Glede na rezultate Monte Carlo simulacije lahko sklepamo, da bi se investicija pri danih parametrih in njihovem obsegu vedno izplačala. Ugotovimo torej, da ne glede na lokacijo elektrarne ter karakteristike porabe in voženj elektrarno lahko dimenzioniramo tako, da se investicija ekonomsko izplača. Veliko ne bomo zaslužili, a če električno vozilo in sončno elektrarno kupimo predvsem z namenom razogljičenja družbe, je nakup dobra odločitev. In this master thesis calculations of energy and electricity costs for three scenarios were made: if we have an internal combustion vehicle, if we have an electric vehicle and if we have a solar power plant and an electric vehicle. I focused on analyzing the feasibility study of investing in a solar power plant if we already have an electric vehicle. Calculations have shown that the costs of replacing an internal combustion vehicle with an electric vehicle are reduced by more than 50 %. If we also purchase an appropriately dimensioned solar power plant we save up to 600 EUR per year, which pays for itself in just over 13 years and the net present value of the investment is over 860 EUR. Scenario analysis by cities shows well that the investment pays off more in cities with higher radiation. This does not mean that the investment does not pay off at places with less radiation, only the power of the solar power plant needs to be adjusted. Sensitivity analysis has shown that among the considered parameters, the final result is most influenced by radiation and the price of a solar power plant. Based on the results of the Monte Carlo simulation, we can conclude that the investment would always pays off. We can conclude that regardless of the location of power plants and the characteristics of consumption and driving habits the solar power plant can be dimensioned in a way that the investment pays off economically. We will not earn much, but if we buy an electric vehicle and a solar power plant primarily for the purpose of decarbonisation, purchase is a good decision.

Cilj ovog doktorskog rada je razvoj konvertera za učinkovitu detekciju termalnih neutrona. Kao osnovni, aktivni materijal u poluvodičkom detektoru, koristi se širokopojasni 4H-SiC. S obzirom na to da se termalni neutroni ne mogu detektirati direktno s poluvodičkim, čvrstim, detektorom već preko nabijenih čestica koje nastaju interakcijom s drugim jezgrama, potreban je učinkovit konverter. Fokus istraživanja je na izotopima 6Li te 10B, koji u interakciji s termalnim neutronima emitiraju alfa-čestice (6Li(n,α)3H, 10B(n,α)7Li). U okviru istraživanja primijenjeno je nekoliko različitih metoda pripreme tankih filmova. Optimalna debljina tankog sloja filma određena je na temelju Monte Carlo simulacija, a očekivane vrijednosti su u granicama od 1 do 30 μm. Morfologija i struktura dobivenih filmova proučavane su mikroskopskim metodama. Učinkovitost dobivenih konvertera testirana je na nuklearnom reaktoru TRIGA Mark II Instituta Jožef Stefan u Ljubljani, Slovenija. Osim odziva detektora na termalne neutrone, obrađen je i odziv silicijeva karbida na druge izvore ionizirajućeg zračenja kao što su alfa-čestice i gama-zračenje. This thesis deals with development of a converter for efficient detection of thermal neutrons. A wide gap 4H-SiC is used here as a basic, active material in the semiconductor detector. It is not possible to detect thermal neutrons directly with solid semiconductor detector, but through charged particles generated by interaction with other cores. Thus, an efficient converter is needed. The focus of the research is on the isotopes of 6Li and 10B, which interact with the thermal neutrons emitting alpha particles (6Li(n,α)3H, 10B(n,α)7Li). Within the scope of the research, a range of techniques of thin film preparation was used. Optimal thin film thickness was determined using Monte Carlo simulation. The expected values are within the range of 1 to 30 μm. The morphology and structure of the obtained films was studied by means of microscopy methods. Efficiency of the obtained converters was tested on the TRIGA Mark II nuclear reactor of the Jožef Stefan Institute in Ljubljana, Slovenia. In addition to the detector response to thermal neutrons, this thesis covers the response of silicon carbide to other sources of ionizing radiation such as alpha particles and gamma radiation as well.

Istraživanjem su unaprjeđene konvencionalne metodologije analize elektroenergetskoga razvoja pametnoga (naprednoga) grada obzirom na očekivanu ekonomičnost, učinkovitost i ukupnu održivost uključivanjem neodređenosti relevantnih varijabli. Karakterizirane su stohastičke (aleatorne) i spoznajne (epistemične) neodređenosti relevantnih veličina prema dostupnim podacima i procjeni. Definirani su specifični modeli za karakteriziranje parametara neodređenosti ulaznih varijabli. Karakterizacijom su definirane statističke funkcije gustoće vjerojatnosti relevantnih parametara za proračun sa ili bez vremenske ovisnosti, ovisno o prirodi implementacije projekta i karakteristikama same varijable. Metodologija definira scenarije na temelju pretpostavki o načinu realizacije elektroenergetskih rješenja pametnoga grada glede financiranja, dinamike implementacije te uspješnosti funkcioniranja naprednih rješenja. Unaprijeđenom metodologijom analize koristi i troškova s karakterizacijom neodređenosti varijabli bolje je određena vjerojatnost uspješnosti realizacije planiranih aktivnosti pametnoga grada uz proračun mjera važnosti varijabli te njihov utjecaj na provedbu planiranih aktivnosti, a time i prioritet za smanjivanje rizika neuspješne realizacije naprednih rješenja. Razvijena metodologija primijenjena je na projektu pametnoga grada u gradu Ludbregu (napredna mjerna infrastruktura i komponente napredne mreže). Znanstveni doprinosi su: 1) Unapređenje konvencionalne metodologije elektroenergetskoga planiranja pametnoga grada (pametna distribucijska mreža i električni transport) uključivanjem neodređenosti i osjetljivosti relevantnih varijabli. 2) Karakteriziranje stohastičke i spoznajne neodređenosti varijabli matematičkog modela elektroenergetskoga planiranja pametnoga grada za dinamiku implementacije, ostvarivanje planiranih učinaka i prihvatljivost izvedenih naprednih rješenja. 3) Provjera primjenjivosti razvijene metodologije elektroenergetskoga planiranja pametnoga grada na primjeru konkretnog grada u Hrvatskoj te usporedba s odabranim konvencionalnim pristupom. The research improved conventional methodologies of analysis of power planning and development of a smart city. It takes into account expected cost-effectiveness, efficiency and overall sustainability and uncertainty of relevant variables. The research plan includes characterization of stochastic (aleatory) and knowledge (epistemic) uncertainties of relevant parameters based on available data and assessment. Specific models have been defined to characterize the uncertainty of the parameters of the input variables. Characterization defines statistical probability density functions of the relevant parameters for the calculation ,with or without time-dependent part. It depends on the nature of project implementation and the characteristics of the variable itself. The methodology consists of defining scenarios based on assumptions about the manner of implementation of power solutions of the smart city in terms of financing, implementation dynamics and performance of advanced solutions. The improved methodology of cost-benefit analysis with the characterization of input variables uncertainty better determine the probability success of the planned activities of a smart city. It would allow measuring of the importance of the variables and their impact on the implementation of planned activities, and thus a priority to reduce the risk of unsuccessful implementation of advanced solutions. The developed methodology was applied to the smart city project and the development of energy-efficient solutions in the city of Ludbreg by developing selected units (smart metering infrastructure and smart network components). Scientific contributions are: 1) Improving the conventional methodology of smart city power planning (smart distribution network and electric transport) by including uncertainty and sensitivity of relevant variables. 2) Characterization of stochastic and knowledge uncertainty of variables of the mathematical model of smart city power planning for the dynamics of implementation, realization of planned effects and acceptability of derived advanced solutions. 3) Applicability check of the developed methodology of a smart cities power planning on the example of a city in Croatia and comparison to the conventional approach chosen.

Predmetna disertacija se bavi istraživanjem telekomunikacijske i podatkovne infrastrukture, njezine raspoloživosti i procesima odlučivanja u svrhu optimizacije dediciranih izvora energije. Kao glavni kriteriji za odlučivanje odabira prikladne arhitekture, zasnovane na različitim kombinacijama raznih distribuiranih izvora električne energije i spremnika energije kao i uporabe pojne mreže ističu se kapitalna ulaganja, operativni troškovi, emisija CO2 i rizici vezani za opskrbu energentima, s različitim težinskim faktorima. Predstavljeni su dinamički modeli interakcije pojedinih izvora energije temeljeni na Monte Carlo metodi. U svrhu kvantifikacije (kvalifikacije) rizika vezanih za opskrbu energentima korištena je neizrazita Delphi metoda, a u svrhu predviđanja vremenskih nizova generiranja električne energije iz obnovljivih izvora razvijeni su modeli temeljeni na neuronskim mrežama. Provedena je detaljna analiza troškova i koristi distribuiranih izvora. Analiza je zasnovana na TOPSIS metodi objedinjujući kapitalne i operativne troškove, emisiju CO2 i rizike opskrbe energentima. Uspostavljen je dinamički model izvora energije u pogledu operativnih troškova i emisije CO2. Zasnovan je sinergijski model raspoloživosti distribuiranih izvora energije cijelog postrojenja. Električne arhitekture su u cijelosti modelirane dinamičkim stablom kvara. Prikupljen je jedinstven set podataka sa detaljnim uvidom u raspoloživost napajanja podatkovnog centra u SAD-u. Temeljem istih, sinergijski model je uspješno verificiran. The dissertation deals with the research of telecommunication and data infrastructure, its availability and decision-making processes in order to optimize dedicated energy sources. The main criteria for deciding on the selection of suitable architecture, based on different combinations of various distributed sources of electricity and energy storage as well as the use of the grid are capital investments, operating costs, CO2 emissions and risks related to energy supply, with different weighting factors. Dynamic models of interaction of individual energy sources based on the Monte Carlo method are presented. For the purpose of quantification (qualification) of risks related to energy supply, the fuzzy Delphi method was used, and for the purpose of predicting time series of electricity generation from renewable sources, models based on neural networks were developed. A detailed cost-benefit analysis of distributed sources was conducted. The analysis is based on the TOPSIS method, combining capital and operating costs, CO2 emissions and energy supply risks. A dynamic model of energy sources in terms of operating costs and CO2 emissions has been established. A synergistic model of the availability of distributed energy sources of the entire plant has been established. The electrical architectures are entirely modeled by a dynamic fault tree. A unique data set was collected with a detailed insight into the availability of data center power in the United States. Based on these, the synergy model was successfully verified.

Otkako je Banka za međunarodna poravnavanja definirala zahtjeve na kapitalne rezerve VaR metodologija postajala je sve važnija u bankovnoj praksi. Bankama je dozvoljeno koristiti vlastite interne modele za računanje izloženosti kreditnom riziku. Prvo uvodimo osnovne koncepte VaR-a, a onda gledamo njegovo potencijalno proširenje na neutržive kredite, te njegovu ulogu u računanju kapitalnih pričuva banke. Posebnu pažnju poklanjamo CreditMetrics-u originalno predloženom od strane J.P. Morgana. CreditMetrics predstavlja korisno pomagalo u VaR modeliranju kreditiranja. Primjenjujemo koncepte kao što su Generalizirana Pareto distribucija s teškim repovima i procjena neočekivanih gubitaka primjenom teorije ekstremne vrijednosti. Predstavljamo metodologiju modela koji koristi Monte Carlo simulaciju za procjenu različitih mjera kreditnog rizika. Na kraju iznosimo rezultate simulacije za hipotetski portfelj obveznica. Since the Bank for International Settlements introduced capital requirements for market risk, VAR methodologies have become more and more important in banking. Certain banks were allowed to develop and use internal VAR models for calculating the exposure to credit risk. Firstly, we review basic VAR concept and then look at its potential extension to nontradable loans and its use in calculating the bank's capital requirement. Special attention is paid to J.P.Morgan's CreditMetrics, which is a useful tool in VAR modelling for credit risk. We apply concepts such as Generalized Pareto distribution with heavy tails and estimate unexpected loss using extreme value theory. We introduce the methodology for Monte Carlo simulation used to assess different credit risk measures. Lastly, we carry out the results of the simulation for a hypothetical loan portfolio.

V magistrski nalogi je opisana simulacija distribucijskega omrežja z Monte Carlo metodo, katero smo uporabili zaradi stohastične narave bremen in nepredvidljivosti polnjenja električnih vozil. Moči bremen za vsak posamezen interval smo predstavili z verjetnostnimi funkcijami. Podobno smo storili tudi za čas začetka polnjenja EV in dolžino polnjenja EV. V vsakem koraku Monte Carlo simulacije smo določili čas začetka in dolžino polnjenja vsakega posameznega EV iz verjetnostnih funkcij. Generirali smo naključno število in določili moči bremen v tistem koraku za vsak posamezen interval. Prebrali smo moč polnjenja EV za posamezen časovni interval ter izvedli izračun pretokov moči. Rezultat simulacije sta bili verjetnostni funkciji napetosti in pretok moči. The Master thesis proposes a simulation of the distribution system with Monte Carlo method. We used this method because of the stochastic nature of loads and unpredictability of EV charging. The power of loads of every time interval was presented with probability functions. EV’s charging start time and charging time was also presented with PDF. In every Monte Carlo step, we determined the charging start time and charging time for every EV from PDF. We created a random number and determined the power of loads in that step for every time interval. We read the power of EV charging and ran the power flow calculation. As a result of the simulation, we got probability functions of voltages at the nodes and power flow across the transformer.

Temelj ekonomske analize je procjena. Ekonomska ocjena projekata bavi se procjenom troškova, novčanog toka i profitabilnosti. Dva su osnovna pristupa procjene troškova, "odozdo prema gore" i "odozgo prema dolje". Postoji nekoliko metoda procjene troškova, a u ovom je radu objašnjena metoda faktora koja se koristi za preliminarne procjene troškova procesnih postrojenja. Tokovi novca uključuju prihode i troškove projekta, a grafički se prikazuju dijagramom toka novca. U ekonomske procjene moraju se uključiti inflacija i amortizacija. Inflacija predstavlja opće povećanje cijene robe i usluga, a ima različite izvore, primjerice opskrba novcem i tečajna lista. Amortizacija se defmira kao smanjenje vrijednosti imovine zbog starosti, trošenja ili zastarjelosti. Metode amortizacije imovine su straight line model, declining balance model i MACRS metoda. Predviđena kumulativna krivulja novčanog toka za projekt tijekom cijelog njegovog životnog vijeka predstavlja temelj daljnje procjene. Najbolje metode za procjenu profitabilnosti alternativa su sada!nja vrijednost, diskontirana stopa povrata i diskontirano vrijeme povrata. Svaka procjena ima svoj stupanj nesigurnosti, a za određivanje njihovog utjecaja na profitabilnost projekta se koriste analiza osjetljivosti i analiza rizika. Cilj provedbe navedenih analiza je donošenje pouzdanijih odluka. Analiza osjetljivosti koristi se za određivanje kritičnih varijabli modela kojima se treba pridati najveća pozornost. Najčešće korištene tehnike u analizi osjetljivosti su Tornado dijagram i spider dijagram. Procjena rizika obuhvaća analizu vjerojatnosti i analizu samog rizika. Analiza rizika može se provesti Monte Carlo simulacijom u kojoj je svaka varijabla predstavljena modelom raspodjele vjerojatnosti. Pomoću Monte Carlo simulacije identificiraju se oni pokazatelji koji najviše doprinose riziku projekta.

U ovom radu je istražen utjecaj djelovanja lokalnog vjetra bure na čelični antenski stup uslijed opterećenja slučajnih vremenskih serija zapisa vjetra. Metoda koja je korištena za istražiti utjecaj djelovanja je Monte Carlo metoda. Koristeći program MATLAB napravljen je dovoljan broj realizacija iz kojeg je vidljivo da pri maksimalnoj brzini vjetra (koja je dana Eurokodom) dolazi do gubitka nosivosti pojedinih elemenata ali se i ne pojavljuje globalni slom što nam je glavni uvjet. The paper aims to analyze effects of local bora wind on steel antenna truss tower. The method used to investigate this effect of action is the Monte Carlo method. Using the software MATLAB, a sufficient number of realizations were conducted, from which it can be seen that the maximum wind speed (given by Eurocode), causes loss of individual elements bearing capacity, but there is no global collapse which is our main condition.

Prikupljeni su publicirani podatci iz različitih izvora o proizvodnji iz naftnih i plinskih ležišta. Podatci su poslužili za izradu baze podataka, te programskog koda koji daje grafički prikaz analize krivulje pada proizvodnje. Služeći se dobivenim rezultatima, analiza je provedena deterministički jednom od Arpsovih krivulja za analizu proizvodnje. Osim Arpsovim formulama, za dodatnu točnost, izrađen je i kod za stohastičku analizu Monte Carlo metodom. Dobiveni rezultati analize krivulje pada proizvodnje povezani su s ekonomskim proračunom sadašnje vrijednosti koja omogućava financijski aspekt u investicijske odluke daljnje proizvodnje nekog ležišta. Ekonomska analiza provedena je upotrebom koda izrađenog u svrhu ovog rada, da bi se olakšale procjene i izbjegli veliki proračuni u MS Excel-u., Published data from various sources on the production of oil and gas reservoirs. The data was used to create a database and a program code that gives a graphical representation of the output curve analysis. Using the results, the analysis was performed deterministically with one of Arps's production analysis curves. Apart from Arps' formulas, for better accuracy, a code for stochastic analysis was made using the Monte Carlo method. The results of the decline curve analysis in the output curve can be linked to the present economic value of the budget, which provides the financial aspect in the investment decisions for the further production of a deposit. Economic analysis was carried out using code programmed for the purpose of this paper because of easier estimate and avoid large budgets in MS Excel.

Nosivi kapacitet vodnih resursa (NKVR) predstavlja maksimalni broj osoba (stanovnika) koje mogu neograničeno obitavati na nekom području, koristeći se pritom dostupnim obnovljivim vodnim resursima. NKVR se može primijeniti prilikom procjene održivosti te prilikom radnji vezanih uz gospodarenje i strateško planiranje. Podaci potrebni za procjenu NKVR često su nedovoljno pouzdani ili stohastičke naravi. Primjenom analize osjetljivosti i neodređenosti moguće je na temelju nepouzdanosti ulaznih podataka odrediti pouzdanost dobivene procjene. Ovaj rad sadrži procjenu NKVR otoka Cresa primjenom prethodno spomenute metode., Water resources carrying capacity (WRCC) is defined as the maximum number of persons (inhabitants) that can be sustained without limitation in a given area, using available renewable water resources. WRCC can be used in sustainability assessments and in the management and strategic planning activities. Data needed for WRCC assessment are often imprecise or stochastic in nature. Sensitivity and uncertainty analysis can be used to quantify reliability of assessment based on imprecision of input data. WRCC assessment for the Island of Cress, based on the above mentioned method, is presented in the paper.

U doktorskom radu su prikazani metodologija i rezultati dozimetrijskog vrednovanja sustava za izračun i optimizaciju raspodjele apsorbirane doze Elekta Monaco, koji za izračunavanje apsorbirane doze koristi algoritam koji se temelji na Monte Carlo simulaciji. Sustav pruža mogućnost izračuna apsorbirane doze na dva načina, kao doza u sredstvu i kao doza u vodi. Dozimetrijsko vrednovanje sustava za izračun i optimizaciju raspodjele apsorbirane doze provedeno je u fantomima različitih vrsta, tako da je izmjerena raspodjela apsorbirane doze uspoređivana s izračunatom. Za mjerenje apsorbirane doze korištene su ionizacijske komore različitih efektivnih mjernih volumena i dvodimenzionalni detektor sastavljen od matrice ionizacijskih komora. U sredstvima gustoće veće od gustoće vode uočene su statistički značajne razlike između dvije metode izračuna. Zbog uočenih statistički značajnih razlika u svrhu dodatne analize je osmišljeno više mjernih/računskih geometrija. Na temelju analize rezultata predložena je metoda vrednovanja sustava za izračun i optimizaciju raspodjele apsorbirane doze u sredstvima gustoće veće od gustoće vode. Kao nadopuna vrednovanju računalnog algoritma u točki provedeno je dvodimenzionalno dozimetrijsko vrednovanje raspodjele apsorbirane doze. Osmišljene su različite nehomogene mjerne i računske geometrije kako bi snop X-zraka na putu do ionizacijskih komora prošao kroz sredstva različitih gustoća. Isti trend rezultata koji su dobiveni u semi-antropomorfnom fantomu dobiveni su i analizom razlike izračunate apsorbirane doze koristeći dvije metode izračuna u stvarnim kliničkim situacijama. Naime, iako odstupanja između dvije metode izračuna u mekom tkivu nisu bila statistički značajna, u organima rizika izgrađenih od koštanih struktura (mandibula, kohlea) razlika između dvije metode izračuna je statistički značajna. Purpose: This doctoral dissertation presents the methodology and results for the dosimetric evaluation of absorbed dose distribution calculation and optimization system Monaco, which uses a Monte Carlo simulation based algorithm. Monte Carlo based treatment planning system (TPS) are the most accurate approach for particle transport. They can calculate absorbed dose in terms of dose to media, Dm, as well as in terms of dose to water, Dw, which is retrospectively converted from Dm. The purpose of our study was to analyse differences between dose-tomedium and dose-to-water calculation options for Monaco TPS (Elekta, Sweden) and to propose a supplement to the existing verification methodology to make the verification of Monte Carlo based systems used for radiation oncology unambiguous and straightforward. Methods: Dosimetric evaluation for the two calculation modes was performed using several homogeneous phantoms, a semi-anthropomorphic and an anthropomorphic phantom. Measured absorbed dose distributions were compared to calculated absorbed dose distributions. Ionization chambers with different effective volumes and a two-dimensional detector with an ionization chamber array were used for measuring the absorbed dose. Additionally, measured absorbed dose distributions were compared to absorbed dose distributions calculated with two analytic calculation algorithms. As a supplement to the calculation algorithm evaluation in a point, a two dimensional dosimetric evaluation of absorbed dose distribution was performed. Different inhomogeneous measuring and computing geometries were designed to allow X-ray beams to pass through media of different densities on their path to the array of small volume ionization chambers. Measured absorbed dose distributions were compared to those calculated using gamma method which assesses the difference in dose for low dose gradient regions and spatial component for high dose gradient regions. Furthermore, we investigated the effect of dose-to-water and dose-to-medium calculation options built in Elekta Monaco TPS on intensity modulated radiotherapy (IMRT) dose distributions in clinical situations. Results: For a water equivalent medium and low density medium differences were statistically insignificant and it was confirmed that the most accurate absorbed dose distributions were calculated using an Monte Carlo based calculation algorithm. The statistically significant differences were observed for high density media between measured and calculated absorbed dose values and therefore several measuring/calculation geometries were designed for additional analysis. To overcome potential ambiguity on the correctness of the verification results in high-density media, we proposed a supplement to current comprehensive verification methodology for performance of algorithm built in the Monte Carlo based treatment planning systems. It is based on the physical principles which are ground for the concept of dose measurements of high energy X-ray beams used for radiotherapy. With this addendum Monte Carlo based calculation algorithms can be verified in described geometry for high-density media with higher level of confidence. Considerable difference among dose distributions calculated using respective calculation option obtained in semi-anthropomorphic phantom was also reported in clinical cases. Even though the discrepancies in tissue equivalent media (all target volumes and most of organs at risk) were not statistically significant, in bony structured organs at risk (mandible, cochlea) the discrepancies between two calculation modes was shown to be statistically significant. Conclusions: This dissertation presents the results of the dosimetric evaluation of the calculation algorithm which uses Monte Carlo simulation for absorbed dose calculation, built in a system for calculation and optimization of absorbed dose distribution Elekta Monaco. A supplement to current comprehensive verification methodology for performance of algorithm built in the Monte Carlo based treatment planning systems was proposed. Although proposed addendum to the verification methodology is not the answer to the dilemma which calculation option shall be used for radiotherapy treatment prescription, it provides additional tools for the verification of the TPS calculation algorithms based on the physics behind.

U prvom dijelu ovog rada, opisan je pristup razvoju strategija održavanja vodoopskrbnih sustava sa aspekta upravljanja imovinom. Dan je pregled najčešćih operacija održavanja (općenito i po komponentama) potrebnih za ispunjavanje tri osnovna zahtjeva svih vodoopskrbnih sustava, a to su: fizička, hidraulička i kvalitativna cjelovitost. Kao najčešći novi pristup u održavanju modernih vodoopskrbnih mreža koristi se proaktivno održavanje tj. pripadajuće metode koje podrazumijevaju analizu temeljnih uzroka nastanka kvarova. Kod opisa tih metoda izneseni su konkretni primjeri njihove primjene. Nadalje, drugi dio rada bavi se mogućim primjenama algoritma genetskog programiranja na održavanje vodoopskrbnih sustava s naglaskom na održavanje kvalitativne cjelovitosti. Najprije je razrađen princip rada GP algoritma te je objašnjen način upotrebe GPTIPS skupine alata za MATLAB. Temeljem podatak prikupljenih na lokalitetu rijeke Jadro, pomoću GPTIPS-a, izrađen je model za predviđanje rezidualnog klora u vodoopskrbnoj mreži, kao ključnog pokazatelja zdravstvene ispravnosti vode za piće. Takav model omogućuje djelatnicima vodovoda da optimiziraju doziranje klora, čime se štedi novac i poboljšava razina usluge. First part of this thesis deals with development of maintenance strategies for water distribution systems. An overview of common maintenance procedures (in general and by certain components) needed to fulfill three basic requirements of all water distribution systems: physical, hydraulic and quality integrity, is given. As the most commonly used new approach to maintaining modern water distribution systems, proactive maintenance implies methods for analysis of the root cause of failure. In description of these methods, concrete examples of their applications are also presented. Furthermore, the second part of this thesis deals with possible applications of genetic programming (GP) algorithm for maintaining water supply systems with emphasis on maintaining a qualitative integrity. Firstly, core principles of GP were elaborated and then usage of GPTISP toolbox for MATLAB was explained. Based on the data collected at the site of the Jadro river, a model for prediction of residual chlorine, as a key indicator for water health safety, was developed using GPTIPS. Such model allows water supply workers to optimize chlorine dosing, saving money and improving service levels.

U ovom doktorskom radu ispitana je primjerenost do sada predloženih dozimetrijskih veličina za procjenu efektivne doze pacijenta pri provedbi postupaka računalnom tomografijom stožastim rendgenskim snopom (CBCT, od engl. cone-beam computed tomography) u dentalnoj medicini i ispitan je utjecaj pojedinih parametara kojima je definiran postupak na ozračenje pacijenta. Ispitivanje je provedeno modeliranjem CBCT uređaja Monte Carlo simulacijom i korištenjem računalnog antropomorfnog fantoma te eksperimentalnim mjerenjima. Simulirane doze organa kreću se od 35 μGy (mozak) do 4136 μGy (površina kosti), a efektivne doze od 21 μSv do 218 μSv, ovisno o kliničkom protokolu. Prosječno efektivnoj dozi najviše doprinose štitna žlijezda (31%), žlijezde slinovnice (25%) i ekstratorakalna regija (21%). Temeljem rezultata istraživanja predlaže se prilikom optimizacije CBCT postupka u dentalnoj medicini koristiti što je moguće manji FOV i umnožak struje i vremena ozračivanja te kut rotacije rendgenske cijevi od 180o, a prilikom odabira položaja FOV-a voditi računa o stohastičkim efektima vezanim uz štitnu žlijezdu, imajući na umu potrebnu kvalitetu snimke. Kao najprimjereniju dozimetrijsku veličinu za CBCT postupke predlaže se DAP (od eng. dosearea product) s obzirom na to da predstavlja dozu i veličinu FOV-a. Iako ovo istraživanje pokazuje ograničenja DAP-a kada se FOV nalazi u blizini štitne žlijezde zbog kojeg ga je potrebno modificirati tako da uzima u obzir i udaljenost od štitne žlijezde, zbog jednostavnosti mjerenja se predlaže koristiti DAP, ali definiran za dva položaja (maksilarni i mandibularni). U radu su dani i konverzijski faktori za procjenu efektivne doze i doze organa iz DAP-a. Cone beam computed tomography (CBCT) used in dental medicine results in complex dose distributions owing to different performance of devices and examination procedures. Consensus within scientific and professional community regarding dosimetric quantity has not been reached yet and conversion factors by which effective dose of the patient could be estimated are not given. The aim of this study is to examine the appropriateness of the suggested dose indices (CT dose index, CBCT dose indices and dose-area product (DAP)) and to show their advantages and disadvantages as well as to examine the influence of scanning parameters defining the CBCT procedure to dose indices, organ doses and effective dose of the patient. Investigation was performed by the use of Monte Carlo simulation and experimental measurements. CBCT dental unit was simulated using Monte Carlo N-Particle transport code (MCNP® 6.1.1beta). For the model verification purposes, PMMA head CTDI phantom and radiochromic films were used. For calculation of organ doses and for the assessment of effective doses computational anthropomorphic phantom was used („Zubal“). Most often clinical protocols involving different exposure geometries including sizes and positions of fields of view (FOV), 180o and 360o X-ray tube rotation angles, different tube current-exposure time products (mAs) and photon energies were simulated. Measured (CTDI and DAP) and simulated dose indices (CBCT dose indices) were compared to effective doses for every exposure geometry and analysed.Organ doses in all simulated CBCT protocols ranged from 35 μGy (brain) to 4119 μGy (bone surface) and effective doses from 22 μSv to 218 μSv, depending on scanning parameters. In average, thyroid gland has the highest contribution to the effective dose (31%) followed by salivary glands (25 %) and extra thoracic region (21%). Results of this study indicate importance of careful choice of FOV's size and its position in optimisation of CBCT procedures considering clinical question and anthropometric features of the patient since size and position of FOV have great impact on organ doses and effective dose, especially on thyroid gland and salivary glands. Choosing 180o for the X-ray tube rotation angle instead of 360o would not decrease image quality but may significantly decrease doses of the organs contributing the most to the effective dose. Due to linear dependence of organ doses and effective dose on mAs, whenever possible lowest mAs should be used, considering level of the image quality required. According to the results of this study, change of tube voltage by ±10 kV does not result in significant change neither of organ doses nor effective dose so further investigation employing greater range of tube potentials while considering image quality is needed. Although DAP introduces a large uncertainty in the risk measure in dental CBCT, after thorough investigation of the relationship of the effective dose and aforementioned dose indices, it is suggested as the most appropriate dose index for the optimisation purposes and estimation of effective dose of the patient since it represents the dose and FOV which are the most important scanning parameters affecting the dose. To decrease uncertainty on the risk measure, the effective dose has to be estimated for FOV position and sizes, considering both, tube rotation angle and tube voltage.

Ovaj rad bavi se procjenjivanjem troškova i profitabilnosti te analizama osjetljivosti i rizika prilikom planiranja inženjerskog projekta. Planirane novčane tokove najbolje je prikazati dijagramom toka novca koji predočuje dobitke i isplate vezane za projekt. Nakon njihove procjene, slijedi analiza profitabilnosti, pri čemu su najčešće korištene tehnike ocjene profitabilnosti sadašnja vrijednost, unutarnja stopa povrata i diskontirano vrijeme povrata. S obzirom da u prikupljenim podacima, odnosno predviđenim tokovima novca zasigurno postoje nesigurnosti, potrebno je u analizu unijeti i određenu procjenu rizika. Alati koji se pri tome koriste su analiza osjetljivosti te Monte Carlo analiza. Analizom osjetljivosti se ispituje koliko pojedina nezavisna varijabla utječe na profitabilnost, kako bi se identificirale one varijable kojima treba posvetiti najveću pozornost. Podaci o relativnoj osjetljivosti pojedinog pokazatelja profitabilnosti mogu biti prikazane u tornado ili spider dijagramu. Monte Carlo analiza koristi se kako bi se ispitao simultani utjecaj nezavisnih varijabli na profitabilnost te na taj način analizirao rizik. Kako bi se procijenio i analizirao rizik, potrebno je najprije izračunati vjerojatnost s kojom se pojavljuje neki događaj, vizualno prikazati stablo ekonomskih odluka te Monte Carlo simulacijom izračunati i grafički prikazati raspodjelu vjerojatnosti pojedinih pokazatelja profitabilnosti te identificirati stavke koje najznačajnije doprinose projektnom riziku. This paper deals with cost and profitability estimations, sensitivity analysis and risk analysis during the engineering process planning. Planned cash flows are best shown by cash-flow diagrams which visualizes revenues and expenses in the project. After this estimation, it follows profitability analysis with present worth (PW), internal rate of return (IRR) and discounted payback (DPB) as most commonly-employed profitability evaluation techniques. Considering that there can be found certain insecurities in collected data, it is necessary to introduce risk estimation in the analysis. The tools used during the risk estimation are sensitivity analysis and Monte Carlo analysis. Sensitivity analysis tests the causality of certain independent variable on profitability with the intention of identification of the variable whom the greatest attention should be dedicate. What's more, information about relative sensitivity of the certain profitability indicator can be summed up by a tornado diagram and spiderplots. Monte Carlo analysis is used to test simultaneous influence of all independent variables on profitability with the intention to analyze the risk. When estimating and analyzing the risk, it is necessary first to calculate probability of certain event. After that, visualizing economy decision tree follows, and, in the end, using Monte Carlo simulation, calculate and show graphically probability distribution of each profitability indicator and identifies items which contribute the most to project risk.

Poker je priljubljena in precej razširjena igra s kartami, pri kateri verjetnost igra ključno vlogo pri določanju zmagovalca. Pri klasičnem igranju pokra v živo si igralec lahko pomaga z opazovanjem in branjem telesne govorice nasprotnikov in s tem izboljša svoje možnosti za zmago. V zadnjem desetletju pa se v živo igra vedno manjši odstotek iger, saj jih nadomešča igranje na spletu. Obstajajo številne spletne strani, ki preko aplikacij ponujajo igranje pokra. Te aplikacije pa igralcu omogočajo le vpogled v dogajanje na mizi in poteze nasprotnikov, zato si z opazovanjem telesne govorice nasprotnikov ne more pomagati. Ob pomanjkanju informacij za odločanje pri igranju na spletu pride v poštev predvidevanje nasprotnikovih kart na podlagi iskanja vseh dobitnih kart v določeni situaciji. Na spletu obstaja že veliko različnih t.i. poker kalkulatorjev, ki za različne variante kart izračunajo odstotke za zmago med igralci. Ti kalkulatorji pa temeljijo na vnosu svojih kart, kart na mizi, prav tako pa tudi nasprotnikovih kart. Zato sem se odločil, da izdelam malo drugačen kalkulator, ki od uporabnika ne zahteva vnosa nasprotnikovih kart, ampak pri danih uporabnikovih kartah in kartah na mizi sam predvidi vse možne dobitne situacije, ki bi jih lahko imel nasprotnik, pri tem pa izračuna odstotke za zmago za vsako situacijo. V prvem krogu igre pa zaradi velikega števila možnosti uporabi predvidevanje na podlagi metode Monte Carlo. Rezultat diplomske naloge je delujoča namizna aplikacija, ki deluje na operacijskem sistemu Windows, poimenovana Poker Assistant, napisana v ogrodju .NET (dotNET) v programskem jeziku C# (C Sharp). Uporabnik lahko simulira igro z izborom kart, pri tem pa ima na voljo različne načine nabora nasprotnikovih kombinacij in različna razvrščanja. Analiza rezultatov je pokazala, da metoda Monte Carlo ob visoko nastavljenem parametru števila ponovitev simulacij poda rezultat z napako do 3%. Čas računanja pa je ob visoko nastavljenem parametru števila ponovitev simulacij (več kot 500) in večji množici nasprotnikovih kombinacij kart (več kot 20) lahko tudi predolg za optimalno uporabo programa. Čas računanja v primerih, ko se ne uporabi predvidevanje z metodo Monte Carlo, je v le dveh od 28 različnih možnih situacij višji od 5 sekund. Torej je optimalna uporaba mogoča v 93% primerov. Poker is a popular card game that is based on probability. In a classic game of poker, where players sit at one table, they can increase their rate of winning with observing oponnent's reactions at their moves and opponent's body language. But in the last decade, more and more players are joining online poker communities. There are many websites that offer play of poker through their applications. These applications only show users general information, there are no options for observing the opponent's behavior. In such cases, a helpful source of information can be predicting the opponent's cards based on searching for every possible hand the opponent could have. There are many poker calculators available online that can calculate percentages for winnig a specific game amongst players in different scenarios. Those calculators are based on user's input, which consists of entering their cards, cards on the table and opponent's cards. I have decided to make a different type of calculator that doesn't demand opponent's hands as input, but instead automatically calculates all possible hands opponent could have for any given situation as well as it calculates winning percentage for each of those hands. In Pre-Flop scenarios (no cards on the table) calculator speculates actual results with the Monte Carlo method. A desktop application that runs on the Windows operating systems was produced within the thesis. It was written in .NET (dotNET) framework in C# (C Sharp) programming language. It is called Poker Assistant and it allows user to simulate different scenarios through clicks on card icons. The user can also choose different settings for finding opponent's cards and different sorting orders. The analysis of results has shown that the Monte Carlo method gives results with maximum 3% error when the number of simulations is set to high values. When number of the opponent's hands combinations is large (more than 20) and number of simulations is set to high values (more than 500), the program takes too much time to calculate for optimal use. Elapsed time for calculating results in scenarios where the Monte Carlo method is not used is less than 5 seconds in 26 out of 28 different scenarios. Thus the program allows optimal use in 93% of those cases.

Tema završnog rada je „Primjena Monte Carlo simulacija u procjeni rizika“ . U ovom radu objašnjeno je što je to ISO norma, te koje su njene prednosti i nedostaci. Također je dan pregled ključnih promjena u normi ISO 9001:2015 u odnosu na prethodnu verziju norme iz 2008. godine. Ključna promjena u ISO 9001:2015 je uvođenje kontrole rizika. Nadalje, definirane su metode procjene rizika sukladno normi ISO 31010:2009. Uz pomoć tih metoda želi se poboljšati upravljanje i kontrola sigurnosti rizika u poslovanju. Na kraju je dan primjer analize rizika primjenom Monte Carlo simulacije koja je statistička simulacija povezana sa slučajnim događajima. The theme of the dissertation is "Application of Monte Carlo simulation in risk assessment". In this paper we describe what ISO standard is, and what are its advantages and disadvantages. It also gives an overview of the key changes in ISO 9001: 2015 in relation to the previous standard in 2008. Key change in ISO 9001: 2015 is the introduction of risk control. Furthermore, methods of risk assessment in accordance with ISO 31010: 2009. With the help of these methods aims to improve the management and control of security risks in business. At the end is an example of a risk analysis using Monte Carlo simulation, which is a statistical simulation associated with random events.

U radu je provedena procjena mjerne nesigurnosti rezultata mjerenja korištenih za određivanja krivulje plastičnog tečenja u postupku modificiranog hidrauličnog udubljivanja. Postupak modificiranog hidrauličnog udubljivanja je novo razvijena metoda koja služi za snimanje krivulje plastičnog tečenja materijala, a temelji se na klasičnom postupku hidrauličnog udubljivanja. Na eksperimentalnom postavu pomoću kojeg je moguće provesti oba navedena postupka snimljena je krivulja plastičnog tečenja aluminija. Pretpostavljeno je membransko stanje naprezanja materijala te je izveden uvjet plastičnog tečenja materijala koji je neophodan za snimanje krivulje plastičnog tečenja. Eksperimentalno dobivena krivulja plastičnog tečenja uspoređena je sa standardiziranom krivuljom plastičnog tečenja. Procjena mjerne nesigurnosti provedena je primjenom Monte Carlo simulacije., In this paper an estimation of measurement uncertainty in determining the flow stress curve by modified hydraulic bulging was carried out. Modified hydraulic bulging is a newer method of the stress-strain diagram acquisition. The method has been derived from the hydraulic bulge test. The flow stressstrain curves were established for an aluminium sheet on an experimental apparatus designed for both methods. The assumption of the membrane stress state was used and the flow rule was determined, which was necessary for establishing the flow stress-true strain curve. The comparison between the experimentally obtained curve and standard true stress – true strain curve from literature is showed on a diagram. The estimation of measurement uncertainty was performed using the Monte Carlo simulation.

Tema završnog rada je „Primjena Monte Carlo simulacija u procjeni rizika“ . U ovom radu objašnjeno je što je to ISO norma, te koje su njene prednosti i nedostaci. Također je dan pregled norme ISO 9001:2015. Nadalje, definirano je upravljanje rizikom normom ISO 31000:2009, te definirane su metode procjene rizika sukladno normi ISO 31010:2009, . Uz pomoć tih metoda želi se poboljšati upravljanje i kontrola sigurnosti rizika u poslovanju. Na kraju je dan primjer analize rizika primjenom Monte Carlo simulacije koja je statistička simulacija povezana sa slučajnim događajima. Ključne riječi: rizik, ISO 9001, ISO 31010, metoda, Monte Carlo simulacija The theme of the dissertation is "Application of Monte Carlo simulation in risk assessment". In this paper we describe what ISO standard is, and what are its advantages and disadvantages. It also gives an overview of the ISO 9001: 2015 Furthermore, guidelines on risk management in accordane with ISO 31000:2009, andmethods of risk assessment in accordance with ISO 31010: 2009. With the help of these methods aims to improve the management and control of security risks in business. At the end is an example of a risk analysis using Monte Carlo simulation, which is a statistical simulation associated with random events. Key words: risk, ISO 9001, ISO 31010, method, Monte Carlo simulation

V magistrskem delu obravnavamo tri pomembne lastnosti nepremičninskih naložbenih projektov, in sicer nepovratnost nastalih stroškov, možnosti prilagodljivega pristopa k načrtovanju in upravljanje negotovosti skozi sposobnosti prepoznavanja naložbenih priložnosti oziroma prilagajanja spremembam na trgu. Dinamične metode vrednotenja ne upoštevajo dejstva, da se vzorec tveganja naložbenega projekta spreminja s časom, prav tako ne upoštevajo fleksibilnosti, ki nam jih tržišče ponuja s svojimi nihanji. Med začetkom in koncem naložbenega projekta je zato možnih veliko različnih izidov, ki jih s tradicionalnimi metodami ne zajamemo. Kot odgovor na pomanjkljivo vedenje o odločanju v razmerah negotove prihodnosti in s tem povezanega tveganja smo proučili teorijo realnih opcij, ki izhaja iz dobro poznanih finančnih opcij na finančnih trgih. Dinamični model vrednotenja smo v magistrskem delu nadgradili z različnimi modeli vrednotenja realnih opcij in pri vseh dobili dodatno opcijsko premijo, ki dokazuje, da ima naložbeni projekt ob danih predpostavkah potencial in možnosti za maksimizacijo koristi. Ugotovili smo, da ni dovolj, da je sedanja vrednost prihodnjih denarnih tokov pozitivna, ampak mora presegati stroške projekta za znesek, ki je enak vrednosti odprte naložbene opcije. Ugotovili smo, da metodološke osnove, ki jih podajajo realne opcije v osnovi spreminjajo temeljni pogled na tveganje in vrednotenje. In this thesis we deal with three important characteristics of real estate investment projects: the irreversibility of the incurred costs, the possibility of a flexible approach to planning and managing uncertainty through the ability of identifying investment opportunities and adapting to changes in the market. Dynamic evaluation methods do not take into account the fact that the pattern of risk in the investment project will change over time, nor it takes into account the flexibility provided by the market with its fluctuations. Between the beginning and the end of the investment project there is so many different possible outcomes, which traditional methods do not capture. In response to the lack of knowledge about decision making under conditions of uncertainty of the future and the associated risks, we examined the theory of real options, which derives from the well-known financial options on the financial markets. Dynamic evaluation model was in this thesis upgraded with different models of real options and by each we got the additional option premium, which proves that the investment project has under the current assumptions the potential and opportunity to maximize benefits. We have found that it is not enough that the present value of future cash flows is positive, but it should exceed the cost of the project for an amount equal to the value of open-ended investment options. We found out that the methodological bases that provide real options basically alter our fundamental views on risk and evaluation.

Procesi liberalizacije tržišta el. energije elektroprivrednim kompanijama uvjetuju sve teže donošenje odluka u vidu srednjoročnog i dugoročnog planiranja; kao što je planiranje proizvodnje, održavanja, izgradnje novih objekata i sl. U svrhu razmatranja složenijih pitanja i donošenja strateških ciljeva vrše se simulacije elektroenergetskog sustava različitim metodama. Simulacijama se, na temelju ograničenog broja ulaznih podataka, pokušava predvidjeti stanje na tržištu u određenom vremenskom razdoblju. U radu su obrađene dvije takve metode simulacije: grafoanalitička metoda simulacije vjerojatnih troškova proizvodnje i Monte Carlo simulacija načinjena u DIgSILENT softveru. Grafoanalitičkom metodom prikazano je modeliranje termoelektrana, vjetroelektrana, računanje vrijednosti vode kod hidroelektrana s raspodjeljivom proizvodnjom te proračun relevantnih indeksa kvalitete tržišta putem izrade krivulje trajanja ekvivalentnog opterećenja. DIgSILENT simulator, za razliku od grafoanalitičke metode, uzima u obzir stvarnu strukturu sustava, prije svega prijenosne kapacitete s njihovim tehničkim ograničenjima. U svrhu Monte Carlo simulacije odabrana je testna mreža pouzdanosti na kojoj su se izmjenjivali parametri scenarija, poput povećanja opterećenja i ulaza novih proizvodnih kapaciteta, te su načinjene ukupno 3 simulacije. Izlaznim varijablama simulacija prikazani su važni tehnički aspekti elektroenergetskog sustava kao što su dostatnost kapaciteta i sigurnost opskrbe s posebnim naglaskom na uvođenje kogeneracijskih elektrana na biomasu manjeg instaliranog proizvodnog kapaciteta u proizvodni miks. Usporedbom simulacija prikazano je da grafoanalitička metoda u praksi ima limitiranu uporabu ukoliko se razmatraju složeniji sustavi, dok računalna simulacija predstavlja odgovarajuć izbor prilikom definiranja strateškog ponašanja sudionika tržišne utakmice. Jedini nedostatak računalne simulacije je što korišteni softver trenutno ne može prikazati sve referentne indekse tržišne kvalitete Monte Carlo metodom. The processes of liberalization of electricity markets are having effect on power companies by making their decision process even more difficult in medium-term and long-term planning; such as production planning, maintenance, construction of new facilities etc. Various simulation methods of power system are available to deal with complex issues and also for consideration of strategic objectives. The aim is to predict behaviour of electricity market in a given time period with simulations based on a limited number of input data. Two such simulation methods are demonstrated in this paper: graphoanalytical probabilistic production cost simulation and Monte Carlo simulation made in DIgSILENT software. Model of thermal power plants, wind power model, calculation of water value of dispatchable hydro power and calculation of relevant electric market system indices, by creating equivalent load duration curve, is shown using graphoanalytical method. Unlike the graphoanalytical method DIgSILENT simulator considers the real structure of system, primarily transmission capacity with its technical constraints. Reliability test system was selected for Monte Carlo simulation with different scenario parameters, such as load increase and input of new generating capacities, making a total of 3 simulations. Important technical aspects of the power system, such as the adequacy of capacity and security of supply, are output variables of these simulations - with particular emphasis on the introduction of cogeneration biomass power plants with smaller installed generation capacity that are added into the generation mix. Comparison of simulations shows that graphoanalytical method has limited use in practice if more complex systems are considered, while computer simulation represents an appropriate choice in defining the strategic behaviour of participants in electricity market. Used software in its current version is unable to display all of the key indices of market quality using Monte Carlo method, which represents the only disadvantage of computer simulation.

Cilj rada je prikazati jedan model za kvantifikaciju rizika i tri metode za izračun rizične vrijednosti, kvantitativne mjere rizika. Metode izračuna rizične vrijednosti (eng. Value at Risk, skraćeno VaR) su statističke metode pomoću kojih se mjeri i upravlja razinom financijskog rizika investicijskog portfelja kroz određeni vremenski period. U radu ukratko opisujemo povijest kvantitativnog modeliranja rizika i pojam rizične vrijednosti. U nastavku prikazujemo tri metode kvantificiranja rizične vrijednosti: povijesnu metodu, parametarsku metodu (metoda varijance i kovarijance) i pojednostavljenu Monte Carlo simulaciju. Izračuni su prikazani na primjerima. Izračuni rizika gubitka vrijednosti su provedeni na portfelju od pet hrvatskih dionica na dnevnoj osnovi uz razinu vjerojatnosti od 95%. Rezultati triju metoda daju slične rezultate, ali svaki od pristupa ima prednosti i mane.

In order to solve the shortcomings of classical convergence analysis and spatial econometric analysis, this paper proposes a delta statistics method to assess economic growth convergence of central China cities. The result shows to be more close to the reality by analyzing the drawbacks of the classical relative beta convergence, combining the advantages of gams convergence, reference panel data, co-integration theory with the time factor into model. Then, Monte Carlo simulation method is used to analyze its distribution, which shows that it obeys to the normal distribution assumption in large samples. At last, our method is applied to the analysis of economic convergence of central China., Kako bi se otklonili nedostaci klasične analize konvergencije i prostorne ekonometrijske analize, ovaj rad predlaže delta statističku metodu za potrebe procjene konvergencije ekonomskog rasta u gradovima centralne Kine. Rezultati pokazuju da se dolazi bliže stvarnosti analizirajući loše strane klasične relativne beta konvergencije kombinirajući prednosti gama konvergencije, referentnih panelnih podataka, kointegracijske teorije s vremenskim faktorom u modelu. Zatim, Monte Carlo model simulacije se koristi za analizu distribucije što pokazuje da odgovara pretpostavci normalne distribucije u velikim uzorcima. Naposljetku, naša se metoda primjenjuje na analizu ekonomske konvergencije u centralnoj Kini.

V diplomskem delu smo teoretično študirali možnost uporabe zunanjega polja za preklapljanje med perkolirano in neperkolirano konfiguracijo nanodelcev v binarnem sistemu mehke snovi, npr. v mešanici nematičnega tekočega kristala in podolgovatih nanodelcev. Za direktni vpliv na orientacijski red nematične komponente lahko uporabimo zunanje magnetno polje. To polje ne vpliva nujno direktno na smeri dolgih osi nanodelcev (kot so npr. ogljikove nanocevke). Namesto direktne reorientacije lahko vpliva na smeri nanodelcev prek sterične interakcije med molekulami tekočega kristala in nanodelci. Ena od mogočih aplikacij tega sestavljenega sistema je uporaba magnetnega polja za preklapljanje med električno prevodno (perkolirano) in neprevodno (neperkolirano) strukturo prevodnih nanodelcev. Za izračun termično ravnovesne strukture binarnega sistema smo uporabili Lebwohl-Lasherjev model, za preverjanje perkolacije (npr. električne prevodne poti) pa smo si pomagali s kontinuumskim perkolacijskim modelom za prevodno komponento iz podolgovatih nanodelcev. We studied theoretically the possibility of using external field for switching between percolated and non-percolated configuration of nanoparticles in the soft matter binary system, e.g., in the mixture of nematic liquid crystal and elongated nanoparticles. External magnetic field can be used to enhance directly the orientational order of nematic liquid crystal component. Magnetic field need not directly affect the direction of long axes of nanoparticles (such as carbon nanotubes). It may do so indirectly through the steric interaction between liquid crystal molecules and nanoparticles. One possible application of this composed system is to use the magnetic field to switch between electrically conducting (percolated) and insulating (non-percolated) structure of conducting nanoparticles. The Lebwohl-Lasher model is used to calculate the thermal equilibrium structure of the binary system, while the continuous percolation model is used to verify the percolation (e.g., electrical connectivity) of the conducting component made of elongated nanoparticles.

Oblast nauke i tehnike koja se bavi fotonaponskim poluprovodničkim detektorima je oblast koja je doživela izuzetno brz razvoj u poslednjih 20 godina. Razlog tome jesu, s jedne strane praktično neograničene mogućnosti primene ovih detektora (optički komunikacioni sistemi, medicinski uređaji, vojni uređaji, automatski upravljački sistemi, razni elektronski uređaji za široku upotrebu), a sa druge strane minijaturizacija elektronskih komponenti i usavršavanje serijske proizvodnje ovih uređaja što je omogućilo da im cena bude relativno niska i da budu dostupni širokoj populaciji. Posebno interesantne primene poluprovodničkih fotonaponskih detektora jesu u vojnim sistemima, u medicinskim aparatima i uređajima i kosmičkim sistemima. Ovo su oblasti primene gde je verovatnoća da se fotonaponski detektori nađu u polju povećane radijacije jako velika. Oblast fotonaponskih detektora i vrsta zračenja kojima oni mogu biti izloženi je jako velika. Ovaj rad se ograničio na posmatranje fotodioda, fototranzistora i solarnih ćelija i njihovo ponašanje u uslovima gama i neutronskog zračenja s obzirom da prilikom čestične emisije iz jezgra, po pravilu, dolazi i do istovremene deeksitacije jezgra potomka emisijom diskretnog gama zračenja. Poluprovodničke komponente, stoga, bivaju izložene superponirajućem dejstvu neutronskog i gama zračenja. Cilj rada jeste istraživanje uticaja pojačanog gama i neutronskog zračenja na PIN fotodiode, fototranzistore i solarne ćelije i na njihove izlazne karakteristike. Posebna pažnja je poklonjena sukcesivnom delovanju gama i neutronskog zračenja i to u dva slučaja. U prvom kada se komponente nalaze u polju gama zračenja a nakon toga u polju neutronskog zračenja, i u drugom kada je neutronsko ozračivanje prvo a gama drugo. Tokom posmatranja uticaja ove dve vrste zračenja na fotodetektore pre i nakon svakog pojedinačnog koraka ozračivanja, snimane su izlazne karakteristike, i to:... Science and technology that deals with photovoltaic semiconductor detectors is an area with an extremely rapid development in the last 20 years. The reason for this are, on the one hand, practically countless possibilities of application of these detectors(optical communication systems, medical devices, military equipment, automatic control systems, various electronic devices), and, on the other hand, miniaturization of electronic components and development of these devices mass production allowed them to have relatively low cost and to be accessible to the wide population. Particularly interesting applications of semiconductor photovoltaic detectors are in military systems, medical devices and equipment and cosmic systems. These are areas where the probability for photovoltaic detectors to be in increased radiation field is very large. The area of photovoltaic detectors and radiation type which they can be exposed is very large. This work is limited to the observation of the photodiodes, phototransistors and solar cells and their behavior in terms of gamma and neutron radiation considering that with particle emission from the core, as a rule, there have been a simultaneous deexcitations descendant core by a discrete gamma-ray emission. Semiconductor devices, therefore, are exposed to summary effect of neutron and gamma radiation. The aim of this paper is to explore the impact of increased gamma and neutron radiation on the PIN photodiodes, phototransistors and solar cells and their output characteristics. Special attention was paid to the successive impact of gamma and neutron radiation in two cases. One, when the components are in the field of gamma radiation and after that in the field of neutron radiation, and two, when neutron irradiation is the first and gamma is the second. During the observation of effects of these two types of radiation on the photodetectors, before and after each step of irradiation, output characteristics have been measured, namely: current-voltage characteristics and spectral response of PIN photodiodes and phototransistors and current-voltage characteristics, serial and parallel...

Kao dio upravljanja kvalitetom postrojenja i sustava često se provodi ultrazvučno mjerenje debljine (Ultrasonic Thickness Measurement, UTM) za čiju je primjenu dovoljan pristup s jedne strane mjerene komponente. Ova široko primjenjiva ultrazvučna tehnika daje kvantitativnu informaciju o debljini stijenke i kao takva pripada području mjeriteljske djelatnosti. U radu je provedeno istraživanje i karakterizacija utjecajnih faktora i značajki elemenata ultrazvučnog mjernog sustava na rezultat ultrazvučnog mjerenja debljine stijenke. Teorijskim razmatranjem i provedbom eksperimenata analizirana je značajnost utjecaja pojedinih parametara i njihovih interakcija. Primjenom planova pokusa i odgovarajuće metodologije za analizu rezultata eksperimenata stvoreni su preduvjeti za procjenu mjerne nesigurnosti rezultata ultrazvučnog mjerenja debljine stijenke. Da bi se procijenila mjerna nesigurnost, analizirani su utjecajni faktori na točnost i preciznost ultrazvučnog mjerenja debljine stijenke. Razvijen je i matematički model za procjenu mjerne nesigurnosti te je kvantificiran doprinos karakterističnih članova regresijskog modela. Temeljem provedenih istraživanja iskazana je mjerna nesigurnost rezultata mjerenja kod primjene odabranog ultrazvučnog mjernog sustava. Procjena mjerne nesigurnosti u postupku ultrazvučnog mjerenja debljine stijenke provedena je primjenom Monte Carlo simulacija (MCS). Ultrasonic thickness measurement (UTM) is used as a part of structure and component integrity assessment. UTM requires access from one side of measured component. This widely used ultrasonic technique provides quantitative information about the material thickness so consequently, UTM belongs to a field of measurements activities. The work presents an experimental research and characterization of influential factors and characteristics of ultrasonic measurements system on ultrasonic thickness measurement results. Using theoretical and experimental analysis, a significance of influential factors and their interactions was examined. With the goal to estimate the measurement uncertainty of the ultrasonic thickness measurement, design of experiments is applied and methodology for experiment results analysis is created. In order to estimate the measurement uncertainty of ultrasonic thickness measurements, all factors that influence accuracy and precision were analysed. The mathematical model for ultrasonic thickness measurement uncertainty estimation was developed and contribution of particular parameters of regression models was quantified. The measurement uncertainty of specific ultrasonic measurement system was presented in accordance to the research. Monte Carlo simulation was used for ultrasonic thickness measurement uncertainty estimation.

Jata tj. skupovi galaksija su veliki virializirani skupovi galaksija. Galaksije doprinose oko 5% mase jata, unutar-klasterski medij oko 10% mase i tamna tvar do 85% mase. Te strukture su nastale iz protojata galaksija. Protojato je rani oblik jata sa manje galaksija i sa uočenom većom gustoćom broja galaksija u odnosu na ostale dijelove promatranog neba. Cilj ovog rada jest simuliranje protojata galaksija na različitim crvenim pomacima (z=2, 3, 4 i 5), pomoću Monte Carlo simulacije, prateći unaprijed definirane površinske profile protojata i uzimajući u obzir pogreške fotometrijskih crvenih pomaka (naspram spektroskopskih crvenih pomaka) specifičnih za COSMOS pregled neba. Simuliranjem 1,000 protojata različitih tipova (prema jatima potomcima ukupnih masa ≥ 10^15M , 3 - 10 x 10^14M⊙ i 1:37 - 3 x 10^14M⊙), kvantificirali smo karakteristike metode traženja protojata u COSMOS pregledu neba, poput kompletnosti (broj koji definira udio galaksija nakon izvedene metode traženja, naspram cijelog broja galaksija protojata), kontaminacije (broj koji definira udio galaksija na nebu koji ne pripada protojatu), gustoće broja (broj galaksija na povr šini neba) i efektivnog radijusa (radijus unutar kojeg se nalazi 68% mase protojata), te njihovo ponašanje za različite tipove protojata i crvene pomake. Također smo izveli metodu traženja protojata pomoću Voronoi dijagrama i metode određivanja ponašanja diferencijalnog viška gustoće (kojem je mjera δ_g) u ovisnosti o udaljenosti od središta protojata. Rezultati pokazuju da se kompletnost protojata ne mjenja u odnosu na crveni pomak, dok kontaminacija očekivano raste sa udaljenosti od središta protojata. Izračunati efektivni radijusi naših simuliranih protojata se slažu do na faktor 2 sa početnim efektivnim radijusima protojata, izračunatim u Chiang et al. (2013). Unatoč tom nepodudaranju, unutar naših efektivnih radijusa nalazi se 55-65% galaksija u protojatu, što je sukladno rezultatima Chiang et al. (2013). Objašnjenje za razlike među radijusima nalazimo u tome što u našim simulacijama nismo uzeli u obzir raspodjelu mase u protojatima. Pretpostavili smo da sve galaksije imaju istu masu, što može značajno utjecati na izračun efektivnog radijusa. Na kraju smo primijenili metode traženja protojata i metodu računanja efektivnog radijusa na postojeća protojata u COSMOS polju, na različitim crvenim pomacima. Galaxy clusters are large virialized collections of galaxies. Galaxies contribute about 5% to the mass of the cluster, the intracluster medium about 10% and the dark matter up to 85%. These structures are formed from galaxy protoclusters. A protocluster is an early type of cluster with fewer galaxies and an observed higher number density of galaxies, compared to other parts of the observed sky. The goal of this paper is to simulate galaxy protoclusters at different redshifts (z = 2, 3, 4 and 5), using Monte Carlo simulations, following the predefined surface profiles of the protoclusters and taking into account the errors of photometric redshifts (versus spectroscopic redshifts) specifically for the COSMOS survey. By simulating 1,000 different types of protoclusters (by the descendant clusters of the total masses ≥ 10^15M , 3 - 10 x 10^14M⊙ i 1:37 - 3 x 10^14M⊙), we quantified the characteristics of the search methods of protoclusters in the COSMOS sky survey, such as completeness (a number that defines the share of galaxies derived after search methods, compared to the total number of galaxies in the protocluster), contamination (a number that defines the share of galaxies in the sky that does not belong to the protocluster), number density (number of galaxies on the surface of the sky) and effective radius (radius within which there is 68% of the protocluster mass), and their behavior for different types of protoclusters and different redshifts. The results show that completeness of the protoclusters does not change compared to the redshift, while the contamination expectedly increases with distance from the centre of protoclusters. The calculated effective radii of our simulated protoclusters agree within a factor of 2 with the initial effective radii of protoclusters, calculated in Chiang et al. (2013). Despite this discrepancy within our effective radii, 55-65% of galaxies are in protoclusters, which is consistent with the results of Chiang et al. (2013). We believe that the differences between the radii are caused by the fact that our simulations do not take into account the distribution of the mass in the protoclusters. We assumed that all galaxies have the same mass, which can significantly affect the calculation of the effective radius. In the end we applied the search methods of protoclusters and the method of calculating the effective radius to existing protoclusters in COSMOS field, at different redshifts.

Diplomski rad podijeljen je na teorijski i praktični dio. U teorijskom dijelu obrađeni su pojmovi vezani uz biomasu i kogeneracijaska postrojena, kao i osnove teorije pouzdanosti. Praktični dio obuhvaća procjenu pouzdanosti distribucijske mreže u koju je uključena elektrana na biomasu Strizivojna Hrast. Procjena pouzdanosti mreže provedena je pomoću analitičke metode pobrojavanja stanja, a zatim i procjena dostatnosti proizvodnje pomoću Monte Carlo simulacije u programu DIgSILENT. Promatrala se promjena indeksa pouzdanosti metodom pobrojavanja stanja u više slučajeva napajanja izvoda na koji je priključena elektrana Strizivojna Hrast. Rezultati su pokazali da je pouzdanost mreže bolja ukoliko se elektrana napaja samo iz jednog izvoda. Rezultati Monte Carlo simulacije ukazuju na povećanje dostatnosti proizvodnje sa smanjenjem ukupnog opterećenja u mreži. This research is divided into theory and practical parts. Terms related to biomas and cogeneration plants, as the ones related to theory of reliability are described in theory part. Practical part encorporates the distribution network reliability assesment of biomas plant Strizivojna Hrast. Network reliability assesment was conducted by analytical method of state estimation, and then by Monte Carlo simulation in the DIgSILENT PowerFactory software. Focus was on the reliability indices changes which were observed by state estimation method in many cases of powerplant feed. The results indicate that network reliabilty is better if powerplant is fed through only one feeder. Monte Carlo simulation results indicate asscending generation adequacy with reduction of total load of the network.

Programski paket Groza 2.0 omogućava programsku podršku projektiranju optimalnog sustava gromobranske zaštite (vanjski sustav hvataljki LPS-a) visokonaponskih rasklopnih postrojenja na otvorenom prostoru, korištenjem GUI sučelja te povezivanjem s AutoCAD platformom za razmjenu informacija o geometriji postrojenja i sustava LPS. Analiza učinkovitosti štićenja sustava LPS postrojenja temelji se na primjeni Monte Carlo simulacije, uz korištenje elektrogeometrijskog modela (EGM) razvoja udara groma.

Kao dio upravljanja kvalitetom postrojenja i sustava često se provodi ultrazvučno mjerenje debljine (Ultrasonic Thickness Measurement, UTM) za čiju je primjenu dovoljan pristup s jedne strane mjerene komponente. Ova široko primjenjiva ultrazvučna tehnika daje kvantitativnu informaciju o debljini stijenke i kao takva pripada području mjeriteljske djelatnosti. U radu je provedeno istraživanje i karakterizacija utjecajnih faktora i značajki elemenata ultrazvučnog mjernog sustava na rezultat ultrazvučnog mjerenja debljine stijenke. Teorijskim razmatranjem i provedbom eksperimenata analizirana je značajnost utjecaja pojedinih parametara i njihovih interakcija. Primjenom planova pokusa i odgovarajuće metodologije za analizu rezultata eksperimenata stvoreni su preduvjeti za procjenu mjerne nesigurnosti rezultata ultrazvučnog mjerenja debljine stijenke. Da bi se procijenila mjerna nesigurnost, analizirani su utjecajni faktori na točnost i preciznost ultrazvučnog mjerenja debljine stijenke. Razvijen je i matematički model za procjenu mjerne nesigurnosti te je kvantificiran doprinos karakterističnih članova regresijskog modela. Temeljem provedenih istraživanja iskazana je mjerna nesigurnost rezultata mjerenja kod primjene odabranog ultrazvučnog mjernog sustava. Procjena mjerne nesigurnosti u postupku ultrazvučnog mjerenja debljine stijenke provedena je primjenom Monte Carlo simulacija (MCS).

U radu je analizirana vremenska kompleksnost Monte Carlo simulacije kvarova i popravaka komponenata optičke mreže. Analizirane su razlike u vremenu obrade i pretraživanja kod primjene lista i vektora. Predloženo je da se uvede nova varijabla koja u primjeni može drastično smanjiti broj poziva funkcija i tako skratiti vrijeme simulacije. Razmotren je utjecaj tipova spremnika i načina pretraživanja spremnika na vrijeme izvođenja simulacije. Značajna ušteda vremena izvođenja simulacije dobivena je promjenom orijentacije niza u spremniku. Prikazani su rezultati optimizacije vremena simulacije za različite vrste spremnika i pretraživanja. Optimalni način pretraživanja i optimalna struktura podataka može se primijeniti i u drugim tipovima simulacije koji koriste veliki broj ponavljanja. In this Master thesis Monte Carlo simulation of failures and component repairs in optical networks is explained. Introduction of one well-planned variable drastically can reduce function calls, and shorten simulation time. With different containers used, search time can be reduced. Differences in processing and search time of vectors and lists are explained. The change of vector orientation can provide decreasing simulation time complexity. Different steps of simulation optimization are explained in detail and they could be used on similar simulations that use large number of repetitions.

U današnje vrijeme zbog povećanih prometnih zahtjeva dolazi do potrebe za unaprjeđenjem prospojnih čvorova. Arhitektura na zahtjev je tehnologija koja omogućuje efikasno i fleksibilno prospajanje. Ovaj rad bavi se mehanizmima zaštite u mreži čiji su čvorovi izvedeni pomoću arhitekture na zahtjev. Implementirani algoritmi pronalaze radne i zaštitne valne puteve te pokušavaju ostvariti zaštitu na razini čvora pomoću prospajanja na razini niti, što je jedna od karakteristika arhitekture na zahtjev. Za simuliranje rada mreže korištena je Monte Carlo simulacija. Nowadays, due to the increase of traffic demands there is need for improvement of optical cross-connect nodes. Architecture on Demand is technology that can provide efficient and flexible cross-connecting. This paper focuses on protection mechanisms in network with nodes implemented by Architecture on Demand. Implemented algorithms are designed to find both working and backup lightpaths, which enable protection on the network level. On the other hand, implented algorithms are trying to enable fibre switching, which is one of the main characteristics of Architecture on Demand. Fibre switching provides protection on the node level. Simulations were conducted by Monte Carlo procedure.

Multigranularni optički prospojnik podupire finu granulaciju prijenosnog pojasa (od optičke komutacije kanala, preko optičke komutacije snopova pa sve do optičke komutacije paketa) i različite razine kvalitete usluge. Arhitektura na zahtjev omogućuje dinamičko povezivanje optičkih komponenata unutar prospojnika, čime pruža mogućnost prilagodbe optičkog prospojnika trenutnim prometnim i prospojnim zahtjevima. Razvijeno programsko pomagalo služi kao pomoć pri shvaćanju principa rada multigranularnog optičkog prospojnika i njegovih algoritama za izračunavanje arhitekture na osnovu zadanog skupa ulaznih signala. Multi-Granular Optical Cross-Connect (MG-OXC) supports multiple bandwidth granularities (optical circuit switching, optical burst switching and optical packet switching) and different quality of service levels. Architecture on demand (AoD) enables dynamic linking of optical components inside MG-OXC and provides the possibility of adaption to new traffic demands. The application is developed as a tool for understanding the principles of MG-OXC and its algorithms for architecture computing based on input parameters.

U ovoj disertaciji opisan je unaprijeđeni simulacijski model pouzdanosti i predviđanja proizvodnje električne energije vjetrolelektrane. Unaprijeđeni simulacijski model vjetroelektrane uzima u obzir zastoje pojedinih komponenti vjetroelektrane kao i trajanje zastoja pojedinih komponenti. Brzina vjetra modelirana je vremenskim nizom, odnosno ARMA modelom. Unaprijđeni model vjetroelektrane razvijen je primjenom sekvencijalne Monte Carlo simulacije. Unaprijđeni model daje utjecaj zastoja pojedinih komponenti vjetroelektrane na očekivanu proizvedenu energiju, očekivanu neisporučenu energiju, razdiobu očekivane neisporučene energije kao i razdiobu očekivane neisporučene energije zbog zastoja pojedinih komponenti. Unaprijeđeni model vjetroelektrane primjenjen je na vjetroelektrane različitih konfiguracijskih koncepta. Primjenom modela dobiveni su pokazatelji pouzdanosti za vjetroelektrane pojedinih konfiguracijskih koncepta. Na kraju je napravljena verifikacija unaprijeđenog modela vjetroelektrane usporedbom s analitičkim modelom s dvama stanjima. This dissertation describes an enhanced simulation prediction and reliability model for wind power plant power generation. The enhanced wind power plant simulation model takes into account failures ad downtimes of partcular wind power plant components. Wind speed is modelled with time series analysis (ARMA). The enhanced wind power plant simulation model use sequential Monte Carlo simualtion. The enhanced model provides impact of particular wind turbine component failures on expected power generation, loss of energy expectation, distributon of loss of energy exepectation due to faillures and downtimes of particular compoets. The enhanced wind power plant simulation model is applied on different wind power plant configuration concepts. The model is applied for the purpose of obtaining reliability indices for different wind power plant configuration concepts reliability, Finaly, the enhanced wind power plant simulation model is verified by way of comparison with analytical model with two states.

Bolje razumijevanje kako unutarnje strukturne promjene utječu na optička svojstva papira zahtijeva modeliranje kompozitne strukture njegovih slojeva. Predložena je simulacija u okviru Monte Carlo platforme, koja omogućuje različite geometrijske reprezentacije unutarnje strukture papira. Monte Carlo simulacija je metoda koja se može koristiti za simulaciju interakcije fotona s podlogom (u našem slučaju papirom). Model se može graditi tako da se povećanje složenosti može dodati kako se model razvija. Dakle, model se razvija od jednostavnog koncepta generacije slučajnih brojeva u vrlo točno tumačenje širenja fotona u papiru. Navedeni model primijenjen je na analizu učinka prirasta rastertonske vrijednosti otisnutih linija raznih debljina. Rezultati simulacije dobro se slažu s mjerenjima refleksije nakon što je dodatno uvedena funkcija "filtar" koja trajno uklanja fotone čime smo prilagodili simulirane vrijednosti mjerenim. U okviru simulacije, možemo procijeniti broj fotona koji završava ispod rasterskog elementa i uzrokuje mogući optički prirast rastertonske vrijednosti., Better understanding of how internal structural changes affect the optical properties requires modelling the composite structure of a paper layer. We propose a Monte Carlo simulation platform, which allows different geometrical representations of the inner paper structure. Monte Carlo Modelling is a method that can be used to simulate photon interaction with substrate (in our case paper). The model can be built such that increasing complexity can be added as the model is being developed. Thus, the model is developed from a simple concept of random number generation to a very accurate interpretation of photon propagation in paper. We applied the model to the analysis of the effect of dot gain. The above model was used to analyse the effect of weight gain dot gain of printed lines of different thicknesses. The simulation results are in good agreement with measurements of reflection after having additionally introduced a "filter" function that permanently removes photons thereby adapting simulated values to the measured ones. Within the framework of the simulation, we can estimate the number of photons that ends below the screen element causing a possible increase of the optical dot gain.

Na površinama zrnaca kozmičke prašine odvijaju se fizički i kemijski procesi značajni za formiranje zvijezda i evoluciju galaksija. Poznato je da veliki broj H2 molekula u difuznim i gustim područjima međuzvjezdanog prostora nije mogao nastati u plinskoj fazi te da su površine zrnaca kozmičke prašine katalizatori u stvaranju H2. U ovom diplomskom radu je napisan program Monte Carlo simulacije površina amorfnog ugljika i olivina, procesa adsorpcije i desorpcije atoma vodika te stvaranja molekula vodika na tim površinama i to na nižim temperaturama i pod uvjetima koji postoje u međuzvjezdanom prostoru. Napisani su i programi vizualizacije površina i procesa koji vode do stvaranja molekula vodika.

Potpovršinsko raspršenje svjetlosti u papiru (tekstilu ili drugim transparentnim materijalima) ovdje je izračunato u okviru Monte Carlo simulacije, što je kao rezultat dalo funkciju razmazivanja točke (PSF) Lorentzove forme. Papir je bio modeliran s obzirom na različite parametre opisa papira: premazanost, sastav i komponente papira te valne duljine svjetlosti kojom je papir obasjavan. S obzirom na to da je Lorentzova raspodjela parametarska, izračunate su ovisnosti parametra w Lorentzove raspodjele o debljini premaza papira o faktoru asimetrije celuloznih vlakana kao sastavnica papira, te o valnoj duljini svjetlosti koja pada na papir. Pokazalo se da osim celuloznih vlakana ostale komponente papira nemaju utjecaj na parametar w. Rezultati su pokazali da je parametar w manji za premazani papir, za manje asimetrične sastavnice papira i za manju valnu duljinu svjetlosti, što je u ovisnosti koeficijenata apsorpcije, odnosno raspršenja svjetlosti u papiru, i valne duljine svjetlosti., Subsurface scattering of light in paper (fabric or other transparent material) has been calculated in the framework of Monte Carlo simulation, which has given the Lorentz shaped point spread function (PSF) as the result. The paper was modelled with respect to various parameters of the paper description: coating, the composition of paper, and a dependence on the wavelength of the light by which the paper was illuminated. Given the fact that the Lorentz distribution is parametric, the following was calculated: the dependence of the Lorentz distribution parameter w on the thickness of paper coating, on the asymmetry factor of cellulose fibres as a component of paper, and on the wavelength of the light that falls onto the paper. It has been shown that in addition to cellulose fibres, other components of paper have no influence on the parameter w. The results have shown that the parameter w is smaller for coated paper, for less asymmetric components of paper and a smaller wavelength of light, which depends on the absorption coefficients and scattering of light in a paper and on the wavelength of light.

Otvaranjem tržišta i ulaskom stranih banaka znatno se povećao broj bankovnih institucija što je rezultiralo oštrom konkurencijom, stoga je za svaku od njih zadržavanje i privlačenje svakog novog klijenata bitno. Iz navedenih razloga ponovno postaje aktualan u svakoj proizvodnoj i uslužnoj organizaciji poslovni koncept kod kojeg je klijent na prvom mjestu, a ne proizvod ili usluga. Privlačenje većeg broja klijenata i postizanje boljih poslovnih rezultata zahtjeva poboljšanje postojećih proizvoda i usluga što ne mora nužno značiti angažiranje dodatnih resursa već je moguće napraviti učinkovitiju preraspodjelu postojećih. Poseban problem u bankovnim institucijama izazivaju redovi čekanja koji kod većine klijenata izazivaju nervozu što u konačnici rezultira njihovim nezadovoljstvom. Cilj ovog rada je prikazati korištenje simulacijskog modeliranja u upravljanju odnosima s klijentima u rješavanju problema redova čekanja.