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Transport and Localization in Classical and Quantum Billiards
Črt Lozej, 2020, doktorska disertacija

Opis: In this thesis the classical and quantum dynamics in billiard systems are considered. Extensive numerical studies of the classical transport properties in several examples of billiard families including the ergodic Bunimovich stadium and cut-circle billiards and the mixed-type Robnik and lemon billiards are performed. The analysis of the transport is based on the random model of diffusion which assumes that due the strongly chaotic dynamics the motion of the orbit on the discretized phase space is temporally uncorrelated. The cause of the deviations from the random model dynamics is traced to dynamical trapping due to stickiness. A novel approach to locally quantifying stickiness based on the statistics of the recurrence times is presented and applied to distinguish between exponential decays of recurrence times and other types of decays. This enables the identification of sticky areas in the chaotic components. Detailed maps of their structure for a wide range of parameter values, mapping the evolution of the mixed-phase spaces and revealing some particularly interesting special examples are presented. The recurrence time distributions in sticky areas are found to be well described by a mixture of exponential decays. The transport of particle ensembles in the momentum space of classical billiards is described by using an inhomogeneous diffusion model and the classical transport times are determined. The classical transport times are vital for the analysis of the localization of chaotic eigenstates in quantum billiards. The control parameter that describes the the degree of localization of the chaotic quantum eigenstates is the ratio between the Heisenberg time (Planck's constant divided by the mean level spacing) and the classical transport time. Extensive numerical calculations of the high-lying spectra and eigenstates of the stadium, Robnik and lemon quantum billiards are performed. The spectral statistics are analysed in terms of the standard methods of quantum chaos. The level repulsion exponent of localized eigenstates is found to be a rational function of the control parameter. The degree of localization is determined with respect to localization measures based on the Poincaré-Husimi representation of the eigenstates. The mean localization measure is found to be a rational function of the control parameter and linearly related to the level repulsion exponent. The distributions of the localization measures are analysed and found to be of a universal shape well described by a two parameter empirical distribution in billiards with no apparent stickiness. The nonuniversal system specific features of localization measure distributions are related to the presence of sticky areas in the phase spaces of classical billiards with specific examples shown.
Ključne besede: Transport, localization, chaos, quantum chaos, Hamiltonian systems, level spacing distribution, mixed phase space, billiard, quantum billiard, Husimi functions, stickiness, cantorus, chaotic eigenstates, level repulsion.
Objavljeno: 13.01.2021; Ogledov: 117; Prenosov: 38
.pdf Celotno besedilo (24,93 MB)

The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundery value problems
Leopold Vrankar, Franc Runovc, Goran Turk, 2007, izvirni znanstveni članek

Opis: Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method.
Ključne besede: mesh free methods, radial basis functions, finite difference methods, finite elemnt methods, boundary elements methods, geostatistics, Eulerian method, Lagrangian method, level set method
Objavljeno: 18.05.2018; Ogledov: 446; Prenosov: 40
.pdf Celotno besedilo (214,16 KB)
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Shopping and business centres in Sarajevo
Rahman Nurković, 2012, izvirni znanstveni članek

Opis: In the paper, influence of shopping and business centres: Mercator, Tuš, Obi Robot, Konzum and BBI on development of Sarajevo city is analysed. Results of the survey made among visitors indicate to presence of social functions (walk, leisure, recreation, fun, socialization) in five centres. The mentioned functions are more expressed in new shopping centres, while shopping is the most important motive of visits to commercial centres. Sarajevo city makes, with its surrounding, a functionally connected wholeness – city, respectively an urban region.
Ključne besede: shopping and business centres, central business centre, public space, social functions, Sarajevo
Objavljeno: 10.04.2018; Ogledov: 446; Prenosov: 60
.pdf Celotno besedilo (233,01 KB)
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Representation of Boolean functions with ROBDDs
Aleš Časar, Robert Meolic, samostojni znanstveni sestavek ali poglavje v monografski publikaciji

Opis: This paper describes data structures and algorithms for representation of Boolean functions with reduced ordered binary decision diagrams (ROBDDs). A hash table is used for quick search. Additional information about variables and functions is stored in binary trees. Manipulations on functions are based on a recursive algorithm of ITE operation. The primary goal of this article is describe programming technics needed to realize the idea. For the first time here recursive algorithms for composing functions and garbage collection with a formulae counter are presented. This is better than garbage collection in other known implementations. The results of the tests show that the described representation is very efficient in applications which operate with Boolean functions.
Ključne besede: Reduced Ordered Binary Decision Diagram, Boolean function, logic functions, logic design verification, hash table
Objavljeno: 02.02.2018; Ogledov: 1334; Prenosov: 32
.pdf Celotno besedilo (323,32 KB)

Increased augmentation index and central systolic arterial pressure are associated with lower school and motor performance in young adolescents
Bernarda Vogrin, Marjan Rupnik, Dušanka Mičetić-Turk, 2017, izvirni znanstveni članek

Opis: Objective: In adults, improper arterial function has been linked to cognitive impairment. The pulse wave velocity (PWV), augmentation index (AIx) and other vascular parameters are useful indicators of arterial health. In our study, we monitored arterial properties, body constitution, school success, and motor skills in young adolescents. We hypothesize that reduced cognitive and motor abilities have a vascular origin in children. Methods: We analysed 81 healthy school children aged 11-16 years. Anthropometry central systolic arterial pressure, body mass index (BMI), standard deviation scores (SDS) BMI, general school performance grade, and eight motor tests were assessed. PWV, AIx, and central systolic arterial pressure (SBPao) were measured. Results: AIx and SBPao correlated negatively with school performance grades. Extremely high AIx, PWVand SBPao values were observed in 5% of children and these children had average to low school performance. PWV correlated significantly with weight, height, and waist and hip circumference. AIx, PWV, school success, and BMI correlated strongly with certain motor functions. Conclusions: Increased AIx and SBPao are associated with lower school and motor performance in children. PWV is influenced by the body's constitution.
Ključne besede: augmentation index, pulse wave velocity, school success, motor functions, young adolescents, central systolic arterial pressure, body mass index
Objavljeno: 13.07.2017; Ogledov: 452; Prenosov: 239
.pdf Celotno besedilo (160,29 KB)
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Inverse limits in the category of compact Hausdorff spaces and upper semicontinuous functions
Iztok Banič, Tina Sovič, 2013, izvirni znanstveni članek

Opis: V članku obravnavamo inverzne limite v kategoriji ▫$mathcal{CHU}$▫ kompaktnih Hausdorffovih prostorov in navzgor polzveznih (u.s.c) preslikav. Vpeljemo pojem šibkih inverznih limit in pokažemo, da inverzne limite z navzgor polzveznimi veznimi preslikavami skupaj s projekcijami niso nujno inverzne limite v ▫$mathcal{CHU}$▫, so pa vedno šibke inverzne limite v tej kategoriji. Med drugim gre za realizacijo kategorijalnega pristopa k reševanju problema, ki ga je zastavil W. T. Ingram.
Ključne besede: topologija, kategorije, navzgor polzvezne funkcije, inverzne limite, posplošene inverzne limite, šibke inverzne limite, topology, upper semi-continuous functions, inverse limits, generalized inverse limits, weak inverse limits
Objavljeno: 10.07.2015; Ogledov: 496; Prenosov: 72
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Inverse limits with generalized Markov interval functions
Iztok Banič, Tjaša Lunder, 2013, izvirni znanstveni članek

Opis: V [S. Holte, Inverse limits of Markov interval maps, Topology Appl. 123, 2002,421-427] so bile predstavljene markovske preslikave in dokazano je bilo, da sta inverzni limiti z markovskimi veznimi funkcijami z enakim vzorcem homeomorfni. V tem članku predstavimo posplošene markovske preslikave, ki so posplošitev markovskih preslikav na večlične preslikave in pokažemo, da sta inverzni limiti s posplošenimi markovskimi veznimi preslikavami z enakim vzorcem homeomorfni.
Ključne besede: topologija, inverzne limite, navzgor polzvezne funkcije, posplošene markovske preslikave, topology, inverse limits, upper semi-continuous functions, generalized Markov interval functions
Objavljeno: 10.07.2015; Ogledov: 607; Prenosov: 75
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Inducing functions between inverse limits with upper semicontinuous bonding functions
Iztok Banič, Matevž Črepnjak, Goran Erceg, Matej Merhar, Uroš Milutinović, 2013, izvirni znanstveni članek

Opis: V članku predstavljamo kategorijo ▫$mathcal{CU}$▫, kjer so objekti kompaktni metrični prostori ▫$X$▫ morfizmi med njimi pa navzgor polzvezne preslikave iz ▫$X$▫ v ▫$2^Y$▫. Vpeljemo tudi kategorijo ▫$mathcal{ICU}$▫ inverznih zaporedij v ▫$mathcal{CU}$▫. Proučujemo inducirane funkcije med inverznimi limitami kompaktnih metričnih prostorov z navzgor polzveznimi veznimi funkcijami. Podamo kriterije za njihov obstoj in dokažemo imajo pod določenimi pogoji surjektivne grafe. Pokažemo tudi da predpis, ki objektom iz ▫$mathcal{ICU}$▫ priredi njihove inverzne limite, ki so objekti v ▫$mathcal{CU}$▫, morfizmom pa priredi inducirane preslikave ni funktor iz ▫$mathcal{ICU}$▫ v ▫$mathcal{CU}$▫, (je pa temu zelo blizu). Na koncu podamo še uporabno aplikacijo dokazanih rezultatov.
Ključne besede: topologija, inverzne limite, navzgor polzvezne funkcije, inducirane funkcije, inducirani morfizmi, topology, inverse limits, upper semi-continuous functions, induced functions, induced morphisms
Objavljeno: 10.07.2015; Ogledov: 471; Prenosov: 31
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Ważewski's universal dendrite as an inverse limit with one set-valued bonding function
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, Tina Sovič, 2012, izvirni znanstveni članek

Opis: Konstruirana je družina navzgor polzveznih večličnih funkcij ▫$f:[0,1] rightarrow 2^{[0,1]}$▫, za katere velja, da je inverzna limita inverznega zaporedja intervalov ▫$[0,1]$▫ in ▫$f$▫ kot edine vezne preslikave homeomorfna univerzalnemu dendritu Ważevskega.
Ključne besede: topologija, kontinuum, inverzna limita, večlična funkcija, dendrit, univerzalni dendrit Ważevskega, topology, continua, inverse limits, upper semi-continuous functions, dendrites, Ważewski's universal dendrite
Objavljeno: 10.07.2015; Ogledov: 601; Prenosov: 122
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