O metrici induciranoj ikosadodekaedrom i trijakontaedrom

The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications. If every points of a line segment that connects any two points of the set are in the set, then it is convex. The more geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra. A polyhedra, when it is convex, is an extremely important special solid in R^n. Some examples of convex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and Archimedean Duals or Catalan Solids. In this study, we give two new metrics to be their spheres an archimedean solid icosidodecahedron and its archimedean dual rhombic triacontahedron.Teorija konveksnih skupova je vitalno i klasično područje moderne matematike s bogatom primjenom. Ako se sve točke dužine, koja spaja bilo koje dvije točke skupa, nalaze u tom skupu, tada je taj skup konveksan. Sve se više geometrijskih aspekata o konveksnim skupovima razvija uvodeći neke pojmove, ponajprije poliedre. Konveksni poliedar je iznimno važno posebno tijelo u R^n. Neki primjeri konveksnih podskupova euklidskog trodimenzionalno prostora su Platonova tijela, Arhimedova tijela, tijela dualna Arhimedovim tijelima i Catalanova tijela. U ovom članku prikazujemo dvije metrike koje su sfere Arhimedovom tijelu ikosadodekaedru i njemu dualnom tijelu, trijakontaedru

O metrici induciranoj ikosadodekaedrom i trijakontaedrom

The theory of convex sets is a vibrant and classical field of modern mathematics with rich applications. If every points of a line segment that connects any two points of the set are in the set, then it is convex. The more geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra. A polyhedra, when it is convex, is an extremely important special solid in R^n. Some examples of convex subsets of Euclidean 3-dimensional space are Platonic Solids, Archimedean Solids and Archimedean Duals or Catalan Solids. In this study, we give two new metrics to be their spheres an archimedean solid icosidodecahedron and its archimedean dual rhombic triacontahedron.Teorija konveksnih skupova je vitalno i klasično područje moderne matematike s bogatom primjenom. Ako se sve točke dužine, koja spaja bilo koje dvije točke skupa, nalaze u tom skupu, tada je taj skup konveksan. Sve se više geometrijskih aspekata o konveksnim skupovima razvija uvodeći neke pojmove, ponajprije poliedre. Konveksni poliedar je iznimno važno posebno tijelo u R^n. Neki primjeri konveksnih podskupova euklidskog trodimenzionalno prostora su Platonova tijela, Arhimedova tijela, tijela dualna Arhimedovim tijelima i Catalanova tijela. U ovom članku prikazujemo dvije metrike koje su sfere Arhimedovom tijelu ikosadodekaedru i njemu dualnom tijelu, trijakontaedru

Computational Fluid Dynamics in Unconsolidated Sediments: Model Generation and Discrete Flow Simulations

Numerical solutions of the Navier-Stokes Equations became more popular in recent decades with increasingly accessible and powerful computational resources. Simulations in reconstructed or artificial pore geometries are often performed to gain insight into microscopic fluid flow structures or are used for upscaling quantities of interest, like hydraulic conductivity. A physically adequate representation of pore-scale flow fields requires analysis of large domains. We solve the incompressible NSE in artificial ordered and random pore-space structures. A simple cubic and face-centred packings of spheres placed in a square duct are analysed. For the fluid flow simulations of random media, packings of spheres, icosahedra, and cubes forming unconsolidated sediments are generated using a rigid body simulation software. The Direct Numerical Simulation method is used for the solution of the NSE implemented in the open-source computational fluid dynamics software OpenFOAM. The influence of the number of spheres in ordered packings, the mesh type, and the mesh resolution is investigated for fluid flow up to Reynolds numbers of 100 based on the spheres' diameter. The random media mesh generation method relies on approximate surface reconstruction. The resulting tetrahedral meshes are then used for steady-state simulations and refined based on an a-posteriori error estimator. The fluid flow simulation results can further be used twofold: 1) They provide homogenized hydro-mechanical properties of the analysed medium for the larger meso and macro groundwater flow simulations. A concept of one-way binding for large-scale simulations is presented. 2) Visualisation: A post-processing image rendering technique was employed in interactive and still image visualisation environments allowing better overview over local fluid flow structures. The ogs FEM code for the solution of large-scale groundwater processes was inspected for computational efficiency. The conclusions drawn from this analysis formed the~basis for the implementation of the~new version of the code---ogs6. The improvements include comparison of linear algebra software realisations and an implementation of optimized memory access patterns in FEM-local assembler part

Palermo as a postmodern carnival: forms of resistance in the cinema of Ciprì and Maresco

This thesis aims to assess the originality, the aesthetic value and the ethical stance of Daniele Ciprì and Franco Maresco’s cinema through an examination of the representation of Palermo in their three feature-length films Lo zio di Brooklyn / The Uncle from Brooklyn (1995), Totò che visse due volte / Totò Who Lived Twice (1998) and Il ritorno di Cagliostro / The Return of Cagliostro (2003) and their works on video. The aim is to demonstrate how their cinema reflects a need to delve deeply into the most unsettling aspects of Sicilian society and acts as a form of resistance against dominant ideologies and sources of power. In addition to areas traditionally related to film studies, the thesis encompasses perspectives ranging from anthropology, ecocriticism, philosophy and psychoanalysis to cultural, social and urban studies. It examines Ciprì and Maresco’s use of humour, drawing on Peter Sloterdijk’s studies on Kynicism, Luigi Pirandello’s concept of humour as ‘the art of the opposite’ and the carnivalesque as discussed by Ella Shohat and Robert Stam in their application of Mikhail Bakhtin’s studies to cinema. Focusing on how representations of spatiality convey meanings and reflect the real city, Chapter 1, ‘Cityscapes’, deals with how urban aspects of contemporary Palermo have inspired Ciprì and Maresco’s vision of an enclosed archaic world of ruins and rubble, assessing the impact that the Second World War bombings and the remains of illegal buildings have had on Palermo and considering the phenomenon of the sprawling city. The investigation draws on Bakhtin’s notion of ‘chronotope’ with reference to studies on the road movie and flânerie. Chapter 2, ‘Bodies’, investigates the most characteristic aspects of Ciprì and Maresco’s representation of the human body. It looks at the carnivalesque and the neo-baroque aspects of their cinema and examines how the conflictual relationships between sons and mothers in their all-male world leads to a constant need for sons to affirm their primacy as macho men. It also examines how their representation of masculinity is strongly identified with the feminine and concludes with a discussion on hunger and its association with death and the sacred. Chapter 3 deals with identity and the concept of the Other seen in relation to a type of Sicilianity claimed by Ciprì and Maresco. It looks at how their representation of Palermo presents an autarchic world controlled by an all-powerful Mafia and a hybrid of Christianity and paganism coupled with an obsessive fear of the hereafter. Finally, it examines their use of mock-documentary, the influence of literary texts and the use of Italian subtitles for the Palermitan dialect spoken in their films, focusing on how dialect predominates relegating Italian to the language of the Other. The conclusion includes a review of the directors’ poetics, focusing on what most characterises their vision of Palermo and evaluating the key findings that emerge from the thesis. It considers how their cinema fits into the context of contemporary art cinema and assesses their impact on Italian cinema, concluding with suggestions for further research

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios