Using polyhedral models to automatically sketch idealized geometry for structural analysis

Simplification of polyhedral models, which may incorporate large numbers of faces and nodes, is often required to reduce their amount of data, to allow their efficient manipulation, and to speed up computation. Such a simplification process must be adapted to the use of the resulting polyhedral model. Several applications require simplified shapes which have the same topology as the original model (e.g. reverse engineering, medical applications, etc.). Nevertheless, in the fields of structural analysis and computer visualization, for example, several adaptations and idealizations of the initial geometry are often necessary. To this end, within this paper a new approach is proposed to simplify an initial manifold or non-manifold polyhedral model with respect to bounded errors specified by the user, or set up, for example, from a preliminary F.E. analysis. The topological changes which may occur during a simplification because of the bounded error (or tolerance) values specified are performed using specific curvature and topological criteria and operators. Moreover, topological changes, whether or not they kept the manifold of the object, are managed simultaneously with the geometric operations of the simplification process

On systematic approaches for interpreted information transfer of inspection data from bridge models to structural analysis

In conjunction with the improved methods of monitoring damage and degradation processes, the interest in reliability assessment of reinforced concrete bridges is increasing in recent years. Automated imagebased inspections of the structural surface provide valuable data to extract quantitative information about deteriorations, such as crack patterns. However, the knowledge gain results from processing this information in a structural context, i.e. relating the damage artifacts to building components. This way, transformation to structural analysis is enabled. This approach sets two further requirements: availability of structural bridge information and a standardized storage for interoperability with subsequent analysis tools. Since the involved large datasets are only efficiently processed in an automated manner, the implementation of the complete workflow from damage and building data to structural analysis is targeted in this work. First, domain concepts are derived from the back-end tasks: structural analysis, damage modeling, and life-cycle assessment. The common interoperability format, the Industry Foundation Class (IFC), and processes in these domains are further assessed. The need for usercontrolled interpretation steps is identified and the developed prototype thus allows interaction at subsequent model stages. The latter has the advantage that interpretation steps can be individually separated into either a structural analysis or a damage information model or a combination of both. This approach to damage information processing from the perspective of structural analysis is then validated in different case studies

Randomness in topological models

p. 914-925There are two aspects of randomness in topological models. In the first one, topological idealization of random patterns found in the Nature can be regarded as planar representations of three-dimensional lattices and thus reconstructed in the space. Another aspect of randomness is related to graphs in which some properties are determined in a random way. For example, combinatorial properties of graphs: number of vertices, number of edges, and connections between them can be regarded as events in the defined probability space. Random-graph theory deals with a question: at what connection probability a particular property reveals. Combination of probabilistic description of planar graphs and their spatial reconstruction creates new opportunities in structural form-finding, especially in the inceptive, the most creative, stage.Tarczewski, R.; Bober, W. (2010). Randomness in topological models. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/695

Nonlinear Generalized Functions: their origin, some developments and recent advances

We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally neglected up to now by mathematicians. Then we describe how a "nonlinear theory of generalized functions" was obtained inside the Leopoldo Nachbin group of infinite dimensional holomorphy between 1980 and 1985. This new theory permits to multiply arbitrary distributions and contains the above mathematical objects, which shows that the features of this theory are natural and unavoidable for a mathematical description of the real world. Finally we present direct applications of the theory such as existence-uniqueness for systems of PDEs without classical solutions and calculations of shock waves for systems in non-divergence form done between 1985 and 1995, for which we give three examples of different nature: elasticity, cosmology, multifluid flows.Comment: 42 pages, 4 figure

Understanding as integration of heterogeneous representations

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding

On Locality in Quantum General Relativity and Quantum Gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.Comment: Mac-Word file translated to postscript for submission. The author may be reached at: [email protected] To appear in Found. Phys. vol. 27, 199

Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction