Propuesta de modelización: Reflexión de ondas por una superficie rugosa

[EN] Within the framework of the new curriculum, where active learning is the student, we propose a practice of modelling in science education to work with basics of mathematics and physics. The practice involves the modelling of wave reflection by rough surfaces. In a first stage, the reflection is analysed by a completely flat surface using geometric and physical concepts. The wave reflected from the surface is calculated from the waves emitted by a virtual source placed at the position symmetrical to the source position with respect to the mirror surface. To calculate the reflected wave, probability concepts are introduced. The wave reflection by a rough surface is obtained from the waves emitted by different sources for virtually every point of reflection. Courses in architecture and basic engineering, or even a master of acoustics are exceptional framework for the implementation of this practice.[ES] Dentro del marco de los nuevos planes de estudio, donde el activo del aprendizaje es el alumno, se propone una práctica de modelización para trabajar conceptos básicos de matemáticas y física en los primeros cursos Universitarios. La práctica consiste en la modelización de la reflexión de ondas por superficies rugosas. En un primer estadio de la práctica se analiza la reflexión por una superficie totalmente plana usando conceptos geométricos y físicos. La onda reflejada por la superficie plana se calcula a partir de las ondas emitidas por una fuente virtual colocada en la posición totalmente simétrica a la posición de la fuente respecto a la superficie especular. Para el cálculo de la onda reflejada se introducen conceptos de probabilidad. La reflexión de la onda por una superficie rugosa se obtiene a partir de las ondas emitidas por diferentes fuentes virtuales para cada punto de reflexión. Cursos de arquitectura y de ingeniería básica, o incluso algún máster de acústica, son marcos excepcionales para la aplicación de esta práctica.Garcia-Raffi, L.; Romero-García, V. (2011). Propuesta de modelización: Reflexión de ondas por una superficie rugosa. Modelling in Science Education and Learning. 4:195-205. doi:10.4995/msel.2011.3072SWORD1952054Sánchez-Pérez, E.A., Garcia-Raffi, L. M., Sánchez-Pérez, J. V. Introducción a las Técnicas de Modelización para la ense-anza de la Física y las Matemáticas en los primeros cursos de Ingeniería. Ense-anza de las Ciencias 17(1) (1999), pp. 119-129.E. Osborn, and Garrett J. Stuck, A guide to MatlabQc : for beginners and experienced users. Cambridge University Press. Cambridge (2001)

Obtenció dels modes de resonancia a una geometria complexa: proposta didàctica de modelització amb elements finits

[EN] Finite Elements Method is a well established mathematical technique for solving Partial Derivative Differential Equations. In this article we present an example of application of Finite Elements Method: the harmonic resonance modes of a guitar obtained from the resolution of the eigenvalues equation via the Finite Elements Method. Graphical output and direct comparison with experiments facilitates the understanding of the method and an extra motivation, establishing a link between Mathematics and the resolution of real engineering problems than is specially necessary in the teaching of Mathematics in the engineering schools.[CA] Els elements finits actualment constitueixen una eina fonamental per a resolució d’equacions diferencials en contextos reals. En aquest article presentem un bon exemple per al mètode: l’obtenció dels modes de ressonància sobre la tapa harmònica d’una guitarra, a partir de la resolució d’una equació d’autovalors amb el mètode dels elements finits. Per la facilitat de interpretació i contrastació experimental dels resultats obtinguts, pot oferir a mès una gratificació i motivació addicional, molt necessària en tot procès d’aprenentatge.Fuster-Garcia, E.; Garcia Raffi, L.; Romero-Garcia, V. (2009). Obtenció dels modes de resonancia a una geometria complexa: proposta didàctica de modelització amb elements finits. Modelling in Science Education and Learning. 2:57-65. doi:10.4995/msel.2009.3123SWORD57652Zienkiewicz, Olgierd Cecil. The fi element method. Oxford: Butterworth-Heinemann, 2000, 5th ed

Modelling of continuous elastic systems by using the Finite Element Method

Propagation of mechanical waves in unidimensional systems is a fundamental part of physics, necessary for learning subjects such as acoustics and vibrations. The vibration of transverse waves in strings is the easiest case of elastic system. Usually, this is the first continuous elastic system in which students apply fundamental mathematical concepts as vibration mode, equation of motion and boundary condition. In this work the use of simulation methods is proposed to reinforce the understanding of vibratory and acoustic simple phenomena. This will be applied to the case of a string, a beam and a membrane of  finite length with different physical characteristics and boundary conditions

Modelling of continuous elastic systems byusing the Finite Element Method

[EN] Propagation of mechanical waves in unidimensional systems is a fundamental part of physics, necessaryfor learning subjects such as acoustics and vibrations. The vibration of transverse waves in strings isthe easiest case of elastic system. Usually, this is the rst continuous elastic system in which studentsapply fundamental mathematical concepts as vibration mode, equation of motion and boundary condition.In this work the use of simulation methods is proposed to reinforce the understanding of vibratory andacoustic simple phenomena. This will be applied to the case of a string, a beam and a membrane of nitelength with di erent physical characteristics and boundary condition[ES] La propagación de ondas mecánicas en sistemas unidimensionales es una parte fundamental de la física, necesaria para el aprendizaje de asignaturas como acústica y vibraciones. La vibración de ondas transversales en cuerdas es el caso más sencillo de sistema elástico. Habitualmente, este es el primer sistema elástico continuo en el cual los alumnos aplican conceptos matemáticos fundamentales como modo de vibración, ecuación de movimiento y condición de contorno. En este trabajo se propone el uso de los métodos de simulación para reforzar la comprensión de fenómenos simples en acústica y vibraciones. Lo aplicaremos a los casos de cuerda vibrante, barras y membranas de longitud finita con diferentes características físicas y condiciones de contornoHerrero-Durá, I.; Picó, R.; Sánchez-Morcillo, V.; Garcia-Raffi, L. (2017). Modelización de sistemas elásticos continuos mediante el Método de Elementos Finitos. Modelling in Science Education and Learning. 10(2):193-202. doi:10.4995/msel.2017.7659SWORD193202102Giere, R. N. (1988). Explaining Science. doi:10.7208/chicago/9780226292038.001.0001Gilbert, S. W. (1991). Model building and a definition of science. Journal of Research in Science Teaching, 28(1), 73-79. doi:10.1002/tea.3660280107Tomasi, J. (1988). Models and modeling in theoretical chemistry. Journal of Molecular Structure: THEOCHEM, 179(1), 273-292. doi:10.1016/0166-1280(88)80128-3Gobert, J. D., & Buckley, B. C. (2000). Introduction to model-based teaching and learning in science education. International Journal of Science Education, 22(9), 891-894. doi:10.1080/095006900416839Gilbert, J. K. (2004). Models and Modelling: Routes to More Authentic Science Education. International Journal of Science and Mathematics Education, 2(2), 115-130. doi:10.1007/s10763-004-3186-4Kinzl, M., Schwiedrzik, J., Zysset, P. K., & Pahr, D. H. (2013). An experimentally validated finite element method for augmented vertebral bodies. Clinical Biomechanics, 28(1), 15-22. doi:10.1016/j.clinbiomech.2012.09.008Kabir, K. M. M., Matthews, G. I., Sabri, Y. M., Russo, S. P., Ippolito, S. J., & Bhargava, S. K. (2016). Development and experimental verification of a finite element method for accurate analysis of a surface acoustic wave device. Smart Materials and Structures, 25(3), 035040. doi:10.1088/0964-1726/25/3/035040Yu, C.-C., Chu, J. P., Jia, H., Shen, Y.-L., Gao, Y., Liaw, P. K., & Yokoyama, Y. (2017). Influence of thin-film metallic glass coating on fatigue behavior of bulk metallic glass: Experiments and finite element modeling. Materials Science and Engineering: A, 692, 146-155. doi:10.1016/j.msea.2017.03.071Oladejo K.A., Abu R. and Adewale M.D. (2012). Effective Modeling and Simulation of Engineering Problems with COMSOL Multiphysics. International Journal of Science and Technology 2(10), 742-748.Kinsler L.E., Frey A.R., Coppens A.B. and Sanders J.V. (2000). Fundamentals of Acoustics (4th ed.). United States of America: John Wiley & Sons, Inc

Experimental evidence for 56Ni-core breaking from the low-spin structure of the N=Z nucleus 58Cu

Low-spin states in the odd-odd N=Z nucleus 58Cu were investigated with the 58Ni(p,n gamma)58Cu fusion evaporation reaction at the FN-tandem accelerator in Cologne. Seventeen low spin states below 3.6 MeV and 17 new transitions were observed. Ten multipole mixing ratios and 17 gamma-branching ratios were determined for the first time. New detailed spectroscopic information on the 2+,2 state, the Isobaric Analogue State (IAS) of the 2+,1,T=1 state of 58Ni, makes 58Cu the heaviest odd-odd N=Z nucleus with known B(E2;2+,T=1 --> 0+,T=1) value. The 4^+ state at 2.751 MeV, observed here for the first time, is identified as the IAS of the 4+,1,T=1 state in 58Ni. The new data are compared to full pf-shell model calculations with the novel GXPF1 residual interaction and to calculations within a pf5/2 configurational space with a residual surface delta interaction. The role of the 56Ni core excitations for the low-spin structure in 58Cu is discussed.Comment: 15 pages, 7 figures, submitted to Phys. Rev.

The Dual space of an asymmetric normed linear space

Given an asymmetric normed linear space (X, q), we construct and study its dual space (X*, q*). In particular, we show that (x*, q*) is a biBanach semilinear space and prove that (X, q) can be identified as a subspace of its bidual by an isometric isomorphism.We also introduce and characterize the so-called weak* topology which is generated in a natural way by the relation between (X, q) and its dual, and an extension of the celebrated Alaoglu's theorem is obtained.Some parts of our theory are presented in the more general setting of the space LC(X, Y) of all linear continuous mappings from the asymmetric normed linear space X to the asymmetric normed linear space Y. In particular, we show that LC(X, Y) can be endowed with the structure of an asymmetric normed semilinear space and prove that it is a biBanach space if Y is so.Mathematics Subject Classification (2000): 46B10, 54E50, 54E15, 54H99.Key words: Asymmetric normed linear space; semilinear space; continuous linear map­ping; dual space; bidual space; biBanach space; quasi-metric; weak* topology; compact­ness.Quaestiones Mathematicae 26(2003), 83-96

Neural Network for Estimating Energy Expenditure in Paraplegics from Heart Rate

The aim of the present study is to obtain models for estimating energy expenditure based on the heart rates of people with spinal cord injury without requiring individual calibration. A cohort of 20 persons with spinal cord injury performed a routine of 10 activities while their breath-by-breath oxygen consumption and heart rates were monitored. The minute-by-minute oxygen consumption collected from minute 4 to minute 7 was used as the dependent variable. A total of 7 features extracted from the heart rate signals were used as independent variables. 2 mathematical models were used to estimate the oxygen consumption using the heart rate: a multiple linear model and artificial neural networks. We determined that the artificial neural network model provided a better estimation (r = 0.88, MSE = 4.4 ml.kg(-1).min(-1)) than the multiple linear model (r = 0.78; MSE = 7.63 ml.kg(-1).min(-1)). The goodness of fit with the artificial neural network was similar to previous reported linear models involving individual calibration. In conclusion, we have validated the use of the heart rate to estimate oxygen consumption in paraplegic persons without individual calibration and, under this constraint, we have shown that the artificial neural network is the mathematical tool that provides the better estimation.L. M. Garcia-Raffi and E. A. Sanchez-Perez gratefully acknowledge the support of the Ministerio de Economia y Competitividad under project #MTM2012-36740-c02-02. X. Garcia-Masso is a Vali + D researcher in training with support from the Generalitat Valenciana.Garcia Masso, X.; Serra Añó, P.; García-Raffi, LM.; Sánchez Pérez, EA.; Giner-Pascual, M.; González, L. (2014). Neural Network for Estimating Energy Expenditure in Paraplegics from Heart Rate. International Journal of Sports Medicine. 35(12):1037-1043. doi:10.1055/s-0034-1368722S10371043351