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A new approach to model the motion of floating bushings in external gear pumps is presented in this article, where lubrication conditions have been introduced using dimensional analysis. This model is based on Bond Graph diagrams and has been experimentally validated in lab tests measuring the movement of the floating bushing inside the gear pump by means of laser micrometers. The novelty of this research is the creation of a simple and experimentally validated tool for the behaviour study of these types of pumps, which allows the simulation of a dynamic rigid solid in a fluid boundary with clearances of the order of microns, without using powerful CFD tools, with very short execution times, and using conventional computational tools. The qualitative behaviour of the model with respect to the experimental results is very similar, adjusting the numerical values with very acceptable accuracies by taking into account the precision of the experimental measurements, and allows us to use the model to interpret the volumetric and mechanical efficiency variations according the operating conditions, Postprint (published version)

Dimension reduction is a common strategy to study nonlinear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of the key dynamical features of the original system. Finding such a reduced representation for complex systems is, however, a difficult task. We address this problem for dynamics on weighted directed networks, with special emphasis on modular and heterogeneous networks. We propose a two-step dimension-reduction method that takes into account the properties of the adjacency matrix. First, units are partitioned into groups of similar connectivity profiles. Each group is associated to an observable that is a weighted average of the nodes’ activities within the group. Second, we derive a set of equations that must be fulfilled for these observables to properly represent the original system’s behavior, together with a method for approximately solving them. The result is a reduced adjacency matrix and an approximate system of ODEs for the observables’ evolution. We show that the reduced system can be used to predict some characteristic features of the complete dynamics for different types of connectivity structures, both synthetic and derived from real data, including neuronal, ecological, and social networks. Our formalism opens a way to a systematic comparison of the effect of various structural properties on the overall network dynamics. It can thus help to identify the main structural driving forces guiding the evolution of dynamical processes on networks., Peer Reviewed, Postprint (published version)

En el món actual on cada vegada tenim més tendència a quantificar-ho tot amb números, gràfics i demés, es fa molt necessari que els alumnes se'ls eduqui i ensenyi en els conceptes d'ordres de magnitud i anàlisi dimensional. En aquest TFM s'intentarà donar unes eines didàctiques als alumnes per a que puguin realitzar, el més acuradament possible, la resolució d'aquells problemes que donen poca informació i així saber realitzar les aproximacions correctes. S'analitzaran detalladament tots els passos tant des del punt de vista teòric com pràctic, donant exemples detallats que demostrin el potencial didàctic d'aquesta metodologia de resolució de problemes.

L'objecte d'aprenentatge comença recapitulant alguns conceptes fonamentals de l'anàlisi dimensional, a continuació recorda les regles d'escriptura de les equacions dimensionals i, finalment, mostra com pot aplicar-se aquesta anàlisi a la comprovació de resultats i ho il·lustra amb un parell d'exemples.