Análisis y desarrollo de medidas de centralidad aplicadas a la formación de metales vítreos

Abstract

The general objective of this doctoral thesis is to contribute to the understanding of glassy metal formation through the use of complex networks by implementing a new centrality measure. In order to achieve this general objective, the beginning of the present study focuses on the introduction of centrality measures, as well as their implementation, in case studies with a type of application of complex networks, such as urban networks. Then, a new centrality measure is proposed and adapted to be implemented in the particular case of glassy metal formation, which is the main objective of this Doctoral Thesis. The first part of this thesis focuses on the study of classical centrality measures in order to understand them and their use. In this introductory part of the study, these classical centrality measures are applied to urban networks with the aim of elucidating concrete and efficient restoration improvements that provide a substantial increase in accessibility in a historic city. The use of classical centrality measures often proves to be insufficient for the study of specific problems such as glassy metal formation, the main objective of this Doctoral Thesis. For this reason, there are currently different centrality measures adapted to each specific problem, some being more general and others more specific. In this thesis, an adapted centrality measure is proposed, with a certain generality to be applied to different fields, but specially designed to solve the problem of understanding the formation of glassy metals. The centrality measures performed with the classical betweenness measure (CBT) are based on the shortest paths and the random walk, i.e. they measure the global importance of a node as an intermediate node, but they have the common feature of not taking into account the cluster density of each node. To address this shortcoming, a new centrality measure based on betweenness random walks (2RW) has been proposed. From the point of view of dense networks, this measure quantifies the importance of a node through the relationships between four different neighbouring nodes. In the analysis of the implementation of the new network centrality measure, it has been applied from a node ranking perspective, reinforcing dense communities by evaluating graphs and using a transition probability matrix of two possible paths. Therefore, a new 2RW centrality measure has been developed that combines the idea of betweenness centrality of the random walk and the link prediction algorithm Return Random Walk. Specifically, the proposed metric increases the ranking of nodes belonging to dense clusters with a higher average degree than the rest of the clusters, observing that it performs better in dense networks. Moreover, we can detect the weakness of a network by comparing the CBT method with our proposal (2RW). The application of the original proposed centrality measure 2RW was not completely adapted to the problem initially posed, mainly due to the natural directionality of the problem. Therefore, in this Thesis, the Directed Bidirectional Randomised Bidirectional Brokerage Centrality Algorithm (D2RWBT), a new centrality model for directed networks, has been proposed. Using this model, rankings of nodes in directed networks have been obtained to describe their relevance within the network as transition nodes. In more detail, the model describes a node by means of four indices that provide information about the density of its cluster/community (dense or sparse), the strength of its connections, the relative and absolute importance in the network, or the relevance as an intraor inter-cluster node. From the application of the new centrality measure (D2RWBT) for the understanding of the formation of glassy metals through one of the most relevant variables, the reduced glass transition temperature, results have been obtained that have been ratified by a good correlation between these and the real obtaining of metallic glasses in recent research. In particular, it has been possible to extract the relevance of the chemical elements that make up the dense networks and the elements that form dispersed networks, as well as to compare these results with those obtained with the classical measure of classical centrality, Betweenness (BT). In addition, the role of the glassy metal-forming chemical elements within the lattice and which of them play similar functions within the lattice and can therefore be possible substitution elements has been obtained from the study. As a further part of the final study, the elements with relevant functions in the composition of both types of lattices have been analysed. Finally, the results have been collated and a synthesis of the understanding of the glassy metal formation problem has been made, addressing the general objective described above.