Shape theory and mathematical design of a general geometric kernel through regular stratified objects

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed

Rayleigh-Taylor mixing: confinement by stratification and geometry

Rayleigh-Taylor instability has been an area of active research in fluid dynamics for the last twenty years, but relatively little attention has been paid to the dynamics of problems where Rayleigh-Taylor instability plays a role, but is only one component of a more complex system. Here, Rayleigh-Taylor instability between miscible fluids is examined in situations where it is confined by various means: by geometric restriction, by penetration into a stable linear stratification, and by impingement on a stable density interface. Water-based experiments are modelled using a variety of techniques, ranging from simple hand calculation of energy exchange to full three-dimensional numerical simulation. Since there are well known difficulties in modelling unconfined Rayleigh-Taylor instability, the confined test cases have been sequenced to begin with dynamically simple benchmark systems on which existing modelling approaches perform well, then they progress to more complex systems and explore the limitations of the various models. Some work on the phenomenology of turbulent mixing is also presented, including a new experimental technique that allows mixed fluid to be visualised directly, and an analysis of energy transport and mixing efficiency in variable density flows dominated by mixing

Musical preferences and technologies: Contemporary material and symbolic distinctions criticised

Today how individuals interact with various cultural items is not perfectly consistent with theoretical frameworks of influential scholars on cultural consumption, such as Bourdieu (1984), Gans (1999), and Peterson and Simkus (1992). One such variation is in the ever increasing variety of technological modes to acquire and listen to music (Pinch and Bijsterveld, 2004). However, as a consequence of digital divides (van Dijk, 2006), technological items may not be distributed equally among social groups. At present, the value of status-making through a preference for different genres of music extends itself to different forms of consumption and ways of experiencing music. We are yet to fully understand the power these practices have on generating status. This article is therefore motivated by the need to integrate within quantitative frameworks of taste and cultural consumption, an analysis of individuals’ technological engagement. These two dimensions, integrated as components of musical practices, enhance our understanding of cultural boundaries across different social groups.The objective is to bridge a gap detected in the literature, addressing the following questions: Are technological modes to listen to music related to musical tastes

The reasonable effectiveness of Mathematics and its Cognitive roots 1

“At the beginning, Nature set up matters its own way and, later, it constructed human intelligence in such a way that [this intelligence] could understand it” [Galileo Galilei, 1632 (Opere, p. 298)]. “The applicability of our science [mathematics] seems then as a symptom of its rooting, not as a measure of its value. Mathematics, as a tree which freely develops his top, draws its strength by the thousands roots in a ground of intuitions of real representations; it would be disastrous to cut them off, in view of a short-sided utilitarism, or to uproot them from the ground from which they rose ” [H. Weyl, 1910]. Summary. Mathematics stems out from our ways of making the world intelligible by its peculiar conceptual stability and unity; we invented it and used it to single out key regularities of space and language. This is exemplified and summarised below in references to the main foundational approaches to Mathematics, as proposed in the last 150 years. Its unity is also stressed: in this paper, Mathematics is viewed as a "three dimensiona

The consideration of forestry effects in wind energy resource assessment

Research focused on the reduction of uncertainties when considering the wind resource in the vicinity of forestry. This thesis examined the use of high density laser scanning technology to capture the structure of forest canopies along with the measurement of thermal effects using sonic anemometry. Methodologies were then developed to include these high quality data in Computational Fluid Dynamics software in order to allow the complex nature of forestry flows to be considered analytically

Convection, dissipation, and rotation in simulations of stellar and planetary interiors and atmospheres

A wide range of fluid flows occur within astrophysical bodies such as stars and planets. In particular, convective flows are dominant throughout a significant portion of the structure of these objects, playing a key role in the transport of heat throughout their interiors. In a steady state, this convection must be maintained against any viscous and Ohmic dissipation that is present. Prior numerical studies on the nature of this dissipation have often lacked key physical components of the convection, such as the influence of rotation and stratification. Additionally, in planetary atmospheres the influence of the underlying interior convection zone on the resulting surface circulation has historically been underrepresented. This thesis examines idealised convective systems in an attempt to understand some of these influences. We present the first systematic numerical study of viscous dissipation and convection in a Cartesian layer in the highly stratified, rotating regime, and mixed fixed-entropy and fixed-flux boundary conditions. We find that while the influence of rotation does not affect the total amount of dissipation within the layer, the spatial distribution varies considerably as a result of the change in dynamical structure in the rotationally constrained cases. The obtained heat transport scalings show good agreement with those obtained in prior Boussinesq calculations and we define a new parameter which quantifies the spatial distribution of the dissipation and appears to provide a good indicator for whether a given system follows the rotationally constrained scalings or not. We also use the globally averaged value of dissipative heating to place constraints on the maximum (negative) value of the kinetic energy flux. Lastly, this thesis presents preliminary results on the influence of more physically motivated convective parameterisations on the atmospheric circulation of highly irradiated tidally locked exoplanets. Initial results show a significant weakening of the eastward equatorial jet, with an accompanying acceleration of the westward midlatitude jets. The thesis then concludes with a discussion of future work, along with accompanying proof-of-concept results.Science and Technology Facilities Counci

Spatial ontologies for architectural heritage

Informatics and artificial intelligence have generated new requirements for digital archiving, information, and documentation. Semantic interoperability has become fundamental for the management and sharing of information. The constraints to data interpretation enable both database interoperability, for data and schemas sharing and reuse, and information retrieval in large datasets. Another challenging issue is the exploitation of automated reasoning possibilities. The solution is the use of domain ontologies as a reference for data modelling in information systems. The architectural heritage (AH) domain is considered in this thesis. The documentation in this field, particularly complex and multifaceted, is well-known to be critical for the preservation, knowledge, and promotion of the monuments. For these reasons, digital inventories, also exploiting standards and new semantic technologies, are developed by international organisations (Getty Institute, ONU, European Union). Geometric and geographic information is essential part of a monument. It is composed by a number of aspects (spatial, topological, and mereological relations; accuracy; multi-scale representation; time; etc.). Currently, geomatics permits the obtaining of very accurate and dense 3D models (possibly enriched with textures) and derived products, in both raster and vector format. Many standards were published for the geographic field or in the cultural heritage domain. However, the first ones are limited in the foreseen representation scales (the maximum is achieved by OGC CityGML), and the semantic values do not consider the full semantic richness of AH. The second ones (especially the core ontology CIDOC – CRM, the Conceptual Reference Model of the Documentation Commettee of the International Council of Museums) were employed to document museums’ objects. Even if it was recently extended to standing buildings and a spatial extension was included, the integration of complex 3D models has not yet been achieved. In this thesis, the aspects (especially spatial issues) to consider in the documentation of monuments are analysed. In the light of them, the OGC CityGML is extended for the management of AH complexity. An approach ‘from the landscape to the detail’ is used, for considering the monument in a wider system, which is essential for analysis and reasoning about such complex objects. An implementation test is conducted on a case study, preferring open source applications

A 3D Digital Approach to the Stylistic and Typo-Technological Study of Small Figurines from Ayia Irini, Cyprus

The thesis aims to develop a 3D digital approach to the stylistic and typo-technological study of coroplastic, focusing on small figurines. The case study to test the method is a sample of terracotta statuettes from an assemblage of approximately 2000 statues and figurines found at the beginning of the 20th century in a rural open-air sanctuary at Ayia Irini (Cyprus) by the archaeologists of the Swedish Cyprus Expedition. The excavators identified continuity of worship at the sanctuary from the Late Cypriot III (circa 1200 BC) to the end of the Cypro-Archaic II period (ca. 475 BC). They attributed the small figurines to the Cypro-Archaic I-II. Although the excavation was one of the first performed through the newly established stratigraphic method, the archaeologists studied the site and its material following a traditional, merely qualitative approach. Theanalysis of the published results identified a classification of the material with no-clear-cut criteria, and their overlap between types highlights ambiguities in creating groups and classes. Similarly, stratigraphic arguments and different opinions among archaeologists highlight the need for revising. Moreover, pastlegislation allowed the excavators to export half of the excavated antiquities, creating a dispersion of the assemblage. Today, the assemblage is still partly exhibited at the Cyprus Museum in Nicosia and in four different museums in Sweden. Such a setting prevents to study, analyse and interpret the assemblageholistically. This research proposes a 3D chaîne opératoire methodology to study the collection’s small terracotta figurines, aiming to understand the context’s function and social role as reflected by the classification obtained with the 3D digital approach. The integration proposed in this research of traditional archaeological studies, and computer-assisted investigation based on quantitative criteria, identified and defined with 3D measurements and analytical investigations, is adopted as a solution to the biases of a solely qualitative approach. The 3D geometric analysis of the figurines focuses on the objects’ shape and components, mode of manufacture, level of expertise, specialisation or skills of the craftsman and production techniques. The analysis leads to the creation of classes of artefacts which allow archaeologists to formulate hypotheses on the production process, identify a common production (e.g., same hand, same workshop) and establish a relative chronological sequence. 3D reconstruction of the excavation’s area contributes to the virtual re-unification of the assemblage for its holistic study, the relative chronological dating of the figurines and the interpretation of their social and ritual purposes. The results obtained from the selected sample prove the efficacy of the proposed 3D approach and support the expansion of the analysis to the whole assemblage, and possibly initiate quantitative and systematic studies on Cypriot coroplastic production

Spatial ontologies for architectural heritage

Informatics and artificial intelligence have generated new requirements for digital archiving, information, and documentation. Semantic interoperability has become fundamental for the management and sharing of information. The constraints to data interpretation enable both database interoperability, for data and schemas sharing and reuse, and information retrieval in large datasets. Another challenging issue is the exploitation of automated reasoning possibilities. The solution is the use of domain ontologies as a reference for data modelling in information systems. The architectural heritage (AH) domain is considered in this thesis. The documentation in this field, particularly complex and multifaceted, is well-known to be critical for the preservation, knowledge, and promotion of the monuments. For these reasons, digital inventories, also exploiting standards and new semantic technologies, are developed by international organisations (Getty Institute, ONU, European Union). Geometric and geographic information is essential part of a monument. It is composed by a number of aspects (spatial, topological, and mereological relations; accuracy; multi-scale representation; time; etc.). Currently, geomatics permits the obtaining of very accurate and dense 3D models (possibly enriched with textures) and derived products, in both raster and vector format. Many standards were published for the geographic field or in the cultural heritage domain. However, the first ones are limited in the foreseen representation scales (the maximum is achieved by OGC CityGML), and the semantic values do not consider the full semantic richness of AH. The second ones (especially the core ontology CIDOC – CRM, the Conceptual Reference Model of the Documentation Commettee of the International Council of Museums) were employed to document museums’ objects. Even if it was recently extended to standing buildings and a spatial extension was included, the integration of complex 3D models has not yet been achieved. In this thesis, the aspects (especially spatial issues) to consider in the documentation of monuments are analysed. In the light of them, the OGC CityGML is extended for the management of AH complexity. An approach ‘from the landscape to the detail’ is used, for considering the monument in a wider system, which is essential for analysis and reasoning about such complex objects. An implementation test is conducted on a case study, preferring open source applications