Bifurcation diagram for saddle/source bimodal linear dynamical systems

We continue the study of the structural stability and the bifurcations of planar bimodal linear dynamical systems (BLDS) (that is, systems consisting of two linear dynamics acting on each side of a straight line, assuming continuity along the separating line). Here, we enlarge the study of the bifurcation diagram of saddle/spiral BLDS to saddle/source BLDS and in particular we study the position of the homoclinic bifurcation with regard to the new improper node bifurcationPostprint (published version

Jupyter Notebooks for the study of advanced topics in fluid mechanics

In recent years, Jupyter Notebooks have become a very useful free and opensource tool in teaching, as they allow you to combine text, images, mathematical expressions, links and code into a single document. This gives students an interactive document with which they can experiment and learn with the help of high-level mathematical calculus. In Fluid Mechanics, it is very common for students to deal with complex computations that take away attention from the Mechanic, especially in advanced topics such as Rheology, Turbulence, or Boundary Layer. The subject “Advanced Fluid Mechanics” is an elective one of the last year of the Bachelor's degree in Industrial and Aerospace Technology Engineering at the Terrassa School of Industrial, Aerospace and Audiovisual Engineering at the Universitat Politècnica de Catalunya. This subject has three ECTS credits and has been taught since the academic year 2020–2021 This subject complements the compulsory subject Fluid Mechanics and is developed in 6 weeks with 5h of class each week. This work presents Fluid Mechanics modules with Jupyter Notebooks that complement the syllabus given in the compulsory subject. An elective subject is presented where subjects of Fluid Mechanics per week are studied independently, using different Python tools: symbolic calculation, modeling of experimental data, statistical analysis, numerical calculation, and so forth. The main goal is for the student to focus on mechanical concepts and actively learn to use the tools available, especially open source, to do the associated mathematical calculationsPostprint (published version

Structural stability of (C,A)-marked and observable subspaces

Given an observable pair of matrices (C;A) we consider the manifold of (C;A)-invariant and observable subspaces having a fixed Brunovsky- Kronecker structure. Using Arnold’s techniques we obtain the explicit form of a miniversal deformation of a marked and observable (C;A)- invariant subspace with regard to the usual equivalence relation. As an application, we obtain the dimension of the orbit and we characterize the structurally stable subspaces

Gamification tools in the learning of shipbuilding in the undergraduate marine engineering education

This study assesses the implementation of different gamification tools and learning complexity in the of the subject Shipbuilding Principles of the Universitat Politècnica de Catalunya · BarcelonaTech (UPC). This experience has been carried out under a triple new scenario: the virtuality due to the Covid-19 pandemic, added to the gamified training, and the assessment carried out remotely. Both the content and the assessment of the subject have been presented using three gamification web tools (Kahoot!, Mentimeter, and Socrative) and three learning complexity (Lexicon, Comprehension, and Visual & Relationship). The content of the subject has been taught in a dynamic, entertaining, and active way. An important factor that has been taken into account was student diversity when responding to gamified elements, using different gamification tools and different learning complexity. This experience of gamification had a positive impact on student motivation, class attendance, participation, collaborative learning, and classroom climate, which is key in a scenario like the current one, with an adaptation of classes to online learning due to the pandemic. From the results obtained, it can be stated that the gamified experience, even offering a good result compared to previous academic years, did not provide a significant improvement in the overall academic performance of the students. Regarding the gamification tools, the one that presented a slight advantage over the rest was Socrative, which is based on a particular challenge without competition between peers or groups. Regarding the learning complexity, all presented a similar level of success.Objectius de Desenvolupament Sostenible::4 - Educació de QualitatPostprint (published version

Encouraging students’ motivation and Involvement in STEM degrees by the execution of real applications in mathematical subjects: the population migration problem

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining the city population equilibrium point, and making a sociological interpretation of population flows. This practical problem is part of the seminar “Applications of Linear Algebra in Engineering”, which is being held at the Universitat Politècnica de Catalunya-BarcelonaTech (UPC). This seminar consists in the learning of linear algebra by the implementation of real applications where mathematical tools are required to resolve them. This paper presents an application of linear algebra to the population migration problem and analyses students’ appreciation through anonymous surveys and personal interviews. The surveys assessed students’ motivation towards the subject of linear algebra and their learning of mathematical concepts. Personal interviews were conducted for students in order to let them express in detail their opinion about the seminar. The results confirm that the introduction of real applications in the learning of mathematics increases students’ motivation and involvement, which implies an improvement in students’ performance in the first courses of STEM degrees.Peer ReviewedObjectius de Desenvolupament Sostenible::4 - Educació de QualitatPostprint (published version

Improving calculus curriculum in engineering degrees: implementation of technological applications

The teaching of mathematics has always concerned all the professionals involved in engineering degrees. Curently students have less interest in these studies, what has caused an increase of this concern. The lack of awareness of students about the significance of mathematics in their careers, provoke the decrease of undergraduate students’ motivation, which derives in a low interest in engineering degrees. The aim of this work is that engineering students achieve a greater motivation and involvement in first academic courses, through the implementation of real and technological applications related to their degrees in the learning of mathematical concepts. To this end, the 2019/2020 and 2020/2021 academics years, the seminar “Applications of Multivariable Calculus in Engineering” has been held in Universitat Politècnica de Catalunya-BarcelonaTech (UPC), based on the teaching of Multivariable Calculus by the execution of real problems where calculus concepts are necessary to solve them. With the aim of analyzing students’ motivation and assessment of the seminar, anonymous surveys and personal interviews have been conducted. The number of attending students to the sessions in each academic year has been 16 and all of them have been participants in the surveys and interviews. The results show that students’ responses were generally positive and they agree that their motivation to the subject Multivariable Calculus has increased with the use of real applications of mathematics. The execution of practical problems with engineering applications improves the acquirement of mathematical concepts, what could imply an increase of students’ performance and a decrease of the dropout in the first academic courses of engineering degrees.Peer ReviewedObjectius de Desenvolupament Sostenible::4 - Educació de QualitatPostprint (published version

A systematized approach to obtain dependable controller specifications for hybrid plants

This chapter focuses on the problem that a designer of an automation system controller must solve related with the correct synchronization between different parts of the controller specification when this specification obeys a previously defined structure. If this synchronization is not done according to some rules, and taking some aspects into consideration, some dependability aspects concerning the desired behaviour for the system may not be accomplished. More specifically, this chapter will demonstrate a systematized approach that consists of using the GEMMA (Guide d`Etude des Modes de Marches et d`Arrêts) (Agence Nationale pour le Developpement de la Production Automatisée) [ADEPA], 1992) and the SFC (Sequential Function Chart) (International Electrotechnical Commission [IEC], 2002) formalisms for the structure and specification of all the system behaviour, considering all the stop states and functioning modes of the system. The synchronization of the models, corresponding to the controller functioning modes and the controller stop states, is shown in detail and a systematized approach for this synchronization is presented. For this the advantages and disadvantages of the vertical coordination and horizontal coordination proposed by the GEMMA formalism are discussed and a case study is presented to explain the proposed systematic approach. A complete safe controller specification is developed to control a hybrid plant. Also this chapter presents and discusses a case study that applies a global approach for considering all the automation systems emergency stop requirements. The definition of all the functioning modes and all the stop states of the automation system is also presented according the EN 418 (European Standard [EN], 1992) and EN 60204-1 (EN, 1997) standards. All the aspects related to the emergency stop are focused in a particular way. The proposed approach defines and guarantees the safety aspects of an automation system controller related to the emergency stop. For the controller structure the GEMMA methodology is used; for the controller entire specification the SFC is used and for the controller behaviour simulation the Automation Studio software (FAMIC, 2003) is used

Dimension of the orbit of marked subspaces

Given a nilpotent endomorphism, we consider the manifold of invariant subspaces having a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained. Here we obtain the explicit form of this deformation when the invariant subspace is marked, and we use it to calculate the dimension of the orbit and in particular to characterize the stable marked subspaces (those with open orbit).Moreover, we study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal deformation of the giving subspace.Peer Reviewe

Estructura diferenciable de las clases de equivalencia de un par controlable

Dado un par de matrices que representa un sistema lineal controlable, estudiamos las clases de equivalencia por la acción individual o combinada de realimentaciones y cambio de variables de estado y de entrada, así como sus intersecciones. En particular, demostramos que son variedades diferenciables y calculamos sus dimensiones

Perturbations preserving conditioned invariant subspaces

Given the set of matrix pairs M ⊂ Mm,n(C) × Mn(C) keeping a subspace S ⊂ Cn invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset of M. It generalizes the known results when S is a supplementary subspace of the unobservable one.Postprint (published version