Modelling in Science Education and Learning - Vol. 06, Núm. 3 (2013)
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- El concepto de métrica fuzzy a través del filtrado de imágenes digitales
- Modelos compartimentales para el cálculo de dosis interna
- Estudio de la eliminación de arritmias cardíacas mediante el uso de la modelización matemática
- Análisis del comportamiento de procesos térmicos en materiales plásticos. Uso de modelos matemáticos en prácticas de laboratorio de una ingeniería
- Encriptación óptica empleando llaves Weierstrass-Mandelbrot
- Demostració pràctica de la validesa dels models matemàtics en elements finits. Aplicació al model de Cross
- Modeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues
- Integración de investigación y docencia de posgrado a través del diseño eficiente de estructuras
- Poincaré: el método, lo inconsciente y el caso Dreyfus
- Mathematical modelling applied to LiDAR data
- Aplicación de modelos matemáticos para el estudio de degradación térmica de polímeros
- Simulación numérica de una cerámica piezoeléctrica
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- PublicationAnálisis del comportamiento de procesos térmicos en materiales plásticos. Uso de modelos matemáticos en prácticas de laboratorio de una ingeniería(Universitat Politècnica de València, 2013-04-02) Ferrándiz, Santiago; Arrieta, Marina Patricia; López, Juan[EN] Newton has been considered as one of the most important scientist in the history. Associated firstly with the mechanics, also he contributed with all areas of physics, such as viscosity, energy etc. Furthermore, he developed the differential and integral calculus with Leibniz, allowing him to advance in their discoveries. From a teaching point of view, the Law of cooling states is an excellent tool since it allows to the students apply their knowledge in mathematics, by a simple way. They could apply their knowledge?s in terms of integrals, graphical lines, potential, etc. to a series of real experimental values obtained by themselves. In the same way, it is intended that the student will be able to fitting the linear curves obtained and determine which is the equation governing the phenomenon. Newton's Law of cooling shows that the rate of change of the temperature of a body is proportional to the difference in temperatures between its own temperature and the ambient temperature. The most widely used experimentation is monitoring a liquid cooling. But in the second cycle's subject of Materials Engineering and its subsequent conversion to Master Degree, the experience have been adapted to the heating of plastic material in a furnace and the cooling of sheet, so that in addition to its importance in the ”electronic and thermal behavior of materials”, can be accommodated to more applied subjects related to the processing of plastics.
- PublicationAplicación de modelos matemáticos para el estudio de degradación térmica de polímeros(Universitat Politècnica de València, 2013-06-02) Arrieta, Marina P.; López, Juan; Ferrándiz, Santiago; Parres, Francisco; Ministerio de Ciencia e Innovación[EN] The use of mathematical models in the field of education and training is becoming increasingly common. Specifically, in Materials Engineering area, where thermal analysis techniques widely contributes to study the materials thermal decomposition. The application of kinetic methods allows obtaining some parameters that are useful for predicting the behavior of polymers under certain temperature conditions. Polymeric materials are constantly subjected to degradation processes due to its processing, reuse and/or disposal, so that studies associated with thermal degradation of these materials are of particular interest. In this sense, the application of mathematical models for understanding the phenomena of thermal degradation of polymeric materials is useful for undergraduate and research students, MSc. and PhD respectively. Mathematical models can be based on the conversion degree (Friedman, Horowitz and Metzger, Van Krevelen, Coats and Redfern) or, based on the rate of heating measurement (Flynn y Wall). Thermogravimetric analysis (TGA) is an analytical technique which determines the weight loss as a function of temperature or time, allowing to associate specific changes such degradation processes. In this work, we applied different mathematical models to study the thermal degradation of polymeric materials with the main objective that students be able to understand the differences and similarities founded in the materials behavior depending on the mathematical model used.
- PublicationEl concepto de métrica fuzzy a través del filtrado de imágenes digitales(Universitat Politècnica de València, 2013-06-02) Camarena, Joan-Gerard; Gregori, Valentín; Morillas Gómez, Samuel; Sapena, Almanzor; Departamento de Matemática Aplicada; Instituto Universitario de Matemática Pura y Aplicada; Escuela Técnica Superior de Ingeniería Informática; Ministerio de Ciencia e Innovación; Ministerio de Economía y Competitividad[EN] Fuzzy logic has been recently successfully used in several Engineering applications. In particular, fuzzy metrics have been applied to color image filtering improving, in many cases, classical filters results. In this work we study the notion of fuzzy metric and present a simulation model which allows postgraduate students to understand this notion and study the fuzzy metrics properties through color image filtering.
- PublicationDemostració pràctica de la validesa dels models matemàtics en elements finits. Aplicació al model de Cross(Universitat Politècnica de València, 2013-06-02) Ferrándiz, Santiago; Arrieta, Marina; López, Juan; Navarro García, Roberto; Departamento de Máquinas y Motores Térmicos; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial; Instituto Universitario de Investigación CMT - Clean Mobility & Thermofluids[EN] The mathematical model's validity used in computer programs are based on a specific formula implemented leading commercial software. Since these programs use their own databases of materials sometimes the question arises of what the miscalculation in what we are committing or sometimes what can happen when incorporating external data materials tested in other laboratories. In the present work, developed the practice's materials engineering used in the formulation of the model to calculate cross what the viscosity behavior in some recycled materials that are not included in the databases of package's calculations and also allows us to calculate deviations with respect to the real transformation of specimens tested.
- PublicationEncriptación óptica empleando llaves Weierstrass-Mandelbrot(Universitat Politècnica de València, 2013-06-02) Giménez, Fernando; Monsoriu, Juan A.; Barrera, John Fredy; Furlan, Walter D.; Tebaldi, Myrian; Bolognini, Néstor; Torroba, Roberto; Ministerio de Ciencia e Innovación; Universitat Politècnica de València[EN] This paper presents the generation of encryption keys using the local oscillating properties of the partial sums of Weierstrass-Mandelbrot fractal function. In this way, the security key can be replicated if the parameters used to obtain it are known. Therefore, these parameters can be sent instead of sending the key. This procedure reduces the amount of information to be sent and prevents possible interception of the key. Moreover, the key can not be affected by data loss or pollution. The effectiveness of the Weierstrass-Mandelbrot keys were demonstrated by computer simulation in a 4f optical encryption system and the double random phase encoding technique. These keys allow us to encrypt and to retrieve the information, which is the evidence of their effectiveness for data security. Furthermore, it is shown that if the encrypted data is obtained under an attack, it is not possible to access the information without the security key.
- PublicationEstudio de la eliminación de arritmias cardíacas mediante el uso de la modelización matemática(Universitat Politècnica de València, 2013-06-02) González-Suárez, Ana; Trujillo, Macarena; Berjano Zanón, Enrique; Departamento de Ingeniería Electrónica; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial; Biosignals & Minimally Invasive Technologies-BioMIT; Ministerio de Ciencia e Innovación; Universitat Politècnica de València; Generalitat Valenciana[EN] Mathematical modeling is a fast and low cost tool used as a first approach to solve certain problems in real contexts. In this paper we present an example of how a real clinical problem, in the context of cardiac surgery, can be simulated and responded to through mathematical models. Specifically, the resolution of these models, which are based on a coupled electric-thermal problem, allows us to assess in detail the temperature distribution and the geometry of the thermal lesion created in the ventricular wall after radiofrequency ablation in order to eliminate cardiac arrhythmias.
- PublicationIntegración de investigación y docencia de posgrado a través del diseño eficiente de estructuras(Universitat Politècnica de València, 2013-06-02) Torres-Machí, Cristina; Yepes, Víctor; Alcalá, Julián; Pellicer Armiñana, Eugenio; Departamento de Ingeniería de la Construcción y de Proyectos de Ingeniería Civil; Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos; Grupo de Gestión del Proceso Proyecto-Construcción; Ministerio de Ciencia e Innovación[EN] This paper describes, with a case study, the teaching methodology in which a research perspective is introduced in a master program. Throughout the semester, students are asked to apply and analyze the results obtained with the implementation of different heuristic algorithms for the optimal design of a concrete structure. As a final report, students should implement a heuristic algorithm different to those implemented in class for the optimal design of the concrete structure. The results obtained should be presented in the format of a scientific paper. The case study presented in this paper consists on the optimization of the mix design of simply supported beams made of high-performance concrete (HPC). The optimization algorithm implemented is an hybrid strategy based on a variable neighborhood search and threshold acceptance algorithm. This paper begins by defining the optimization problem. It will then go on to present the results of applying the optimization algorithm. Finally, a parametric study is undertaken, analyzing beams with lengths varying from 10 to 20 m. The application of this teaching methodology has supposed an aditional challenge to postgraduate students, as they not only have to adquire the technical competences of the subject but they also have to apply them in a practical example and publish the results in the format of a scientific journal.
- PublicationMathematical modelling applied to LiDAR data(Universitat Politècnica de València, 2013-06-02) Estornell, Javier; Martí-Gavilá, Jesus M.; Sebastiá, M. Teresa; González, Juan Andres[EN] The aim of this article is to explain the application of several mathematic calculations to LiDAR (Light Detection And Ranging) data to estimate vegetation parameters and modelling the relief of a forest area in the town of Chiva (Valencia). To represent the surface that describes the topography of the area, firstly, morphological filters were applied iteratively to select LiDAR ground points. From these data, the Triangulated Irregular Network (TIN) structure was applied to model the relief of the area. From LiDAR data the canopy height model (CHM) was also calculated. This model allowed obtaining bare soil, shrub and tree vegetation mapping in the study area. In addition, biomass was estimated from measurements taken in the field in 39 circular plots of radius 0.5 m and the 95th percentile of the LiDAR height datanincluded in each plot. The results indicated a high relationship between the two variables (measurednbiomass and 95th percentile) with a coeficient of determination (R2) of 0:73. These results reveal the importance of using mathematical modelling to obtain information of the vegetation and land relief from LiDAR data.
- PublicationModeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues(Universitat Politècnica de València, 2013-06-02) Sánchez-Morcillo, Víctor; Jiménez, Noé; González, Nuria; Dos Santos, Serge; Bouakaz, Ayache; Chaline, Jennifer; Ministerio de Ciencia e Innovación[EN] The dynamics of continuous systems that exhibit circular or spherical symmetry like drops, bubbles or some macromolecules, under the influence of some external excitation, develop surface patters that are hard to predict in most practical situations. In the particular case of acoustically driven microbubbles (ultrasound contrast agent), the study of the behavior of the bubble shell requires complex modeling even for describe the most simple oscillation patterns. Furthermore, due to the smallness of the spatio-temporal scale of the problem, an experimental approach requires expensive hardware setup. Despite the complexity of the particular physical problem, the basic dynamical features of some continuous physical systems can be captured by simple models of coupled oscillators. In this work we consider an analogy between a shelled-gas bubble cavitating under the action of an acoustic field and a discrete mechanical system. Thus, we present a theoretical and experimental study of the spatial instabilities of a circular ring of coupled pendulums parametrically driven by a vertical harmonic force. The system is capable of wave propagation and exhibit nonlinearities and dispersion, so manifest rich dynamics: normal oscillation modes (breathing, dipole, quadrupole...) and localized patterns of different types (breathers and kinks) witch are predicted by finite-differences numerical solutions and observed experimentally. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.
- PublicationModelos compartimentales para el cálculo de dosis interna(Universitat Politècnica de València, 2013-06-02) Carlos Alberola, Sofía; Gallardo Bermell, Sergio; Martorell Alsina, Sebastián Salvador; Departamento de Ingeniería Química y Nuclear; Escuela Técnica Superior de Ingeniería Industrial; Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental; Grupo de Medioambiente y Seguridad Industrial. MEDASEGI[EN] Dosimetría de la Radiación is a subject to be coursed in the Master de Seguridad Industrial y Medioambiente. One of the main objectives of this subject is to provide the appropriate tools to the students for the estimation of external and internal dose. The course is organized with many practical sessions, in which the students use calculation tools to estimate the dose produced by diferent exposure pathways. One of the problems proposed is to determine the dose received in the thyroid by the inhalation of a certain amount of Iodine-131. In this case, the International Commission on Radiological Protection, has published two guides to estimate the transfer of radionuclides inside the human respiratory tract and the thyroid. Both estimations are obtained using biokinetic models, in which each organ is considered as a compartment and a mass balance is performed for each compartment. So the dose in a certain organ can be estimated by solving a system of differential equations with constants coefficients, what can be done using MatLab.
- PublicationPoincaré: el método, lo inconsciente y el caso Dreyfus(Universitat Politècnica de València, 2013-06-02) Escudero, Miquel[EN] The last man who had an universal knowledge of mathematics and its applications died just a hundred years ago. He always said that mathematics should be encouraged for themselves, and its first aim was to enjoy them in the same way that painting and music allow us to. He did never pretend to be only a specialist, his way of working was to choose the ‘interesting’ facts. On the other hand, maybe we could find serendipity. It is worthwhile to know how to implement the unconscious machine, the unconscious ego beside the conscious ego. In the famous a aire Dreyfus, Poincare was asked for advise and he wrote a dossier about the graphological system that had been erroneously used.
- PublicationSimulación numérica de una cerámica piezoeléctrica(Universitat Politècnica de València, 2013-06-02) González-Salido, Nuria; Ferri, Marcelino; Jiménez, Noé; Camarena, Francisco; Picó, Rubén; Redondo Pastor, Francisco Javier; Roig Sala, Bernardino; Departamento de Física Aplicada; Departamento de Matemática Aplicada; Escuela Politécnica Superior de Gandia; Instituto de Investigación para la Gestión Integrada de Zonas Costeras; Universitat Politècnica de València[EN] In this paper, a mathematical model describing the dynamic behavior of a commercial piezoelectric ceramic, vibrating in thickness, is presented. This model solves, by finite differences, the piezoelectric equations which relate he mechanical and electrical phenomena produced in this kind of material. The behavior in time domain of some physical variables, as the electric field and particle velocity, is simulated too. In addition, we have implemented a GUI in Matlab that allows simple and affordable simulations for all users. The implemented interface provides two kind of study: Broadband and single frequency excitation. The output parameters, obtained after time domain simulation, are piezoelectric constants of the ceramic and the electric response in frequency domain, i.e. admittance and impedance curves. The results allow predicting vibration modes, electrical response and understanding the effect of piezoelectricity on the mechanical response.