Nonlinear self-collimated sound beams in sonic crystals

We report the propagation of high-intensity sound beams in a sonic crystal, under self-collimation or reduced-divergence conditions. The medium is a fluid with elastic quadratic nonlinearity, where the dominating nonlinear effect is harmonic generation. The conditions for the efficient generation of narrow, non-diverging beam of second harmonic are discussed. Numerical simulations are in agreement with the analytical predictions made, based on the linear dispersion characteristics in modulated media and the nonlinear interaction in a quadratic medium under phase matching conditions.Comment: Sent to PR

Introducción de las técnicas de modelización para el estudio de la física y de las matemáticas en los primeros cursos de las carreras técnicas

In this article we present a program of interdisciplinary practices for a first engineering course. We followed this program during the course 1996-1997, and we give several examples of the kind of exercises that we used. We also present some remarks and conclusions that we have achieved in our experience. Our purpose is to introduce a teaching strategy for Mathematics and Physics at the University level

Ecoesferas: una propuesta de modelización en el ámbito de la escuela de Caminos

[EN] This article is the result of the work developed by students in the subject “Introducción a las Técnicas de Modelización Matemática" at School of Civil Engineering in Valencia. The topic was proposed by one of the students and its development has been done in the classroom throughout working sessions, seminar and discussion sessions. All of the students have participated in the development of the model on biological self-portable systems that have its origin in the space exploration. The mathematical tools used are the differential equations systems and numerical methods. The resolution shows that there is an stable solution for the system modeled.[ES] Este artículo es el resultado del trabajo final de curso desarrollado por los alumnos de la asignatura Introducción a las Técnicas de Modelización Matemática impartida en la escuela de Caminos. El tema fue propuesto por uno de los estudiantes y el desarrollo del mismo se ha realizado en el aula a través de sesiones tipo seminario de trabajo con discusión y participación de todos los estudiantes y desarrollo del esquema completo de modelización. en él se describen los sistemas autosuficientes que tienen su origen en la investigación espacial, se encuentran las ecuaciones diferenciales que modelan el sistema y se resuelven, comprobando que existe una solución estable autosuficiente.Anton, Á.; De Julián, G.; Delicado, A.; Sánchez, P.; Valero, D.; García Raffi, LM.; Sánchez Pérez, EA. (2013). Ecoesferas: una propuesta de modelización en el ámbito de la escuela de Caminos. Modelling in Science Education and Learning. 6(2):21-31. doi:10.4995/msel.2013.1852SWORD21316

Nonlinear propagation and control of acoustic waves in phononic superlattices

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.Work supported by Spanish Ministry of Economy and Innovation and European Union FEDER through projects FIS2011-29731-C02-02 and MTM2012-36740-C02-02. AM and LMGR acknowledge Generalitat Valenciana under grants Santiago Grisolia program (grant 2012/029) and BEST2015/279 respectively. RP and VJSM acknowledge the Spanish Ministry of Economy and Innovation under grants CAS14/00232 and PRX14/00705 respectively.Jimenez, N.; Mehrem, A.; Picó Vila, R.; García-Raffi, LM.; Sánchez Morcillo, VJ. (2016). Nonlinear propagation and control of acoustic waves in phononic superlattices. Comptes Rendus Physique. 17(5):543-554. https://doi.org/10.1016/j.crhy.2016.02.004S54355417

Análisis de los modelos matemáticos producidos durante la resolución de problemas de Fermi

En este trabajo presentamos un estudio en el que analizamos las producciones escritas de estudiantes de 16 años con diferentes niveles de experiencia en modelización al resolver Problemas de Estimación de Grandes Cantidades (PEGC). Estos problemas son un tipo concreto de los Problemas de Fermi y permiten introducir los procesos de modelización en las aulas de Educación Secundaria. Nuestro análisis se soporta en la caracterización de los modelos matemáticos que producen los alumnos, basada en la definición de modelo matemático propuesta por Lesh y Harel. Los resultados muestran que, a través del análisis de las resoluciones de PEGC, se pueden distinguir aspectos diferenciadores entre los modelos producidos por alumnos sin experiencia modelizadora de aquellos producidos por alumnos con experiencia previa, especialmente en los conceptos y lenguajes utilizados para dar forma a los modelos matemáticos construidosIn this paper, we present an analysis of written productions of 16 year-old students while solving Estimation Problems involving Big Numbers (EPiBN). This kind of problems is a particular type of Fermi problems and allows us to introduce modelling processes in Secondary school classrooms. Our analysis supports on the characterization of mathematical models developed by students based on the model definition of Lesh and Harel. The results show that, through the analysis of EPiBN resolutions, differentiating aspects can be distinguished between the models produced by students without modelling experience of those produced by students with prior experience, especially in the concepts and language used to shape the built mathematical model

Ecoesferas: una propuesta de modelización en el ámbito de la escuela de Caminos

This article is the result of the work developed by students in the subject “Introducción a las Técnicas de Modelización Matemática" at School of Civil Engineering in Valencia. The topic was proposed by one of the students and its development has been done in the classroom throughout working sessions, seminar and discussion sessions. All of the students have participated in the development of the model on biological self-portable systems that have its origin in the space exploration. The mathematical tools used are the differential equations systems and numerical methods. The resolution shows that there is an stable solution for the system modeled