Carolina Pascual Villalobos

Carolina Pascual Villalobos
University of Alicante | UA

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43
Publications
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Publications

Publications (43)
Article
Full-text available
Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parame...
Article
Full-text available
Closed-form exact solutions for the periodic motion of the one-dimensional, undamped, quintic oscillator are derived from the first integral of the nonlinear differential equation which governs the behaviour of this oscillator. Two parameters characterize this oscillator: one is the coefficient of the linear term and the other is the coefficient of...
Article
Full-text available
Approximate solutions for small and large amplitude oscillations of conservative systems with odd nonlinearity are obtained using a "cubication" method. In this procedure, the Chebyshev polynomial expansion is used to replace the nonlinear function by a third-order polynomial equation. The original second-order differential equation, which governs...
Article
Full-text available
The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, unforced cubic–quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobi elliptic funct...
Conference Paper
The adaptation to the European Space of Higher Education has meant a deep change in University education in many aspects, such as the degree organization, subject contents and teaching methodologies. The aim of this work is to show the coordination work on the Bachelor's Degree in Sound and Image in Telecommunications and the Master's Degree in Tel...
Article
A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of no...
Article
The exact solution of the anti-symmetric quadratic truly nonlinear oscillator is derived from the first integral of the nonlinear differential equation which governs the behavior of this oscillator. This exact solution is expressed as a piecewise function including Jacobi elliptic cosine functions. The Fourier series expansion of the exact solution...
Article
En el presente proyecto hemos desarrollado un sistema de evaluación integral para las asignaturas de Física y Óptica del Grado en Ingeniería en Sonido e Imagen de la Universidad de Alicante. Nuestro sistema de evaluación contempla tres etapas fundamentales: una evaluación inicial para detectar las ideas previas del alumnado favoreciendo su otivació...
Article
A modified He’s homotopy perturbation method is used to calculate the periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). The He’s homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introduci...
Article
Full-text available
The analytical approximate technique developed by Wu et al. for conservative oscillators with odd nonlinearity is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining Newton's method with the method of harmonic balance, analytical approximations to the oscillation period and...
Article
In this paper He’s homotopy perturbation method has been adapted to calculate higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term is an anti-symmetric and quadratic term. We find that He’s homotopy perturbation method works very well for the whole range of initial amplitudes, an...
Article
Full-text available
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modifie...
Article
The harmonic balance method is used to construct approximate frequency–amplitude relations and periodic solutions to the relativistic oscillator. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To s...
Article
Full-text available
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second...
Article
Approximate analytical solutions for the oscillation of conservative nonlinear systems with odd nonlinearities are presented. The approximation is based on combining linearization of the governing equation with the analysis of the asymptotic behaviour of the exact period for small amplitudes. The approximate period for the nonlinear differential eq...
Article
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency–amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential...
Article
A modified He’s homotopy perturbation method (HHPM) is used to calculate the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x1/3. The He’s homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing...
Article
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the behaviour of a relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. The approximate formulas obtained show excellent agreement with the exact solutions, and...
Article
He's homotopy perturbation method is used to solve the nonlinear differential equation that governs the oscillations of a relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Unlike the usual non-relativistic harmonic oscillator, the velocity of the relativis...
Article
Full-text available
Comunicación presentada en las V Jornadas de Investigación en Docencia Universitaria, Universidad de Alicante, 4-5 junio 2007 En esta investigación se pretende analizar el impacto de las nuevas tecnologías (web, Powerpoint, formularios, e-mail, simuladores, etc.) en el proceso de enseñanza-aprendizaje en diferentes áreas de conocimiento de la Unive...
Article
Full-text available
This paper deals with the nonlinear oscillation of a simple pendulum and presents not only the exact formula for the period but also the exact expression of the angular displacement as a function of the time, the amplitude of oscillations and the angular frequency for small oscillations. This angular displacement is written in terms of the Jacobi e...
Article
Full-text available
Este artigo aborda a oscilação não-linear de um pêndulo simples e apresenta não apenas a fórmula exata do período mas também a dependencia temporal do deslocamento angular para amplitudes das oscilações e a freqüência angular para pequenas oscilações. O deslocamento angular é escrito em termos da função elíptica de Jacobi sn(u;m) usando as seguinte...
Article
Different electromagnetic theories have been applied in order to understand the interaction of the electromagnetic radiation with diffraction gratings. Kogelnik's Coupled Wave Theory, for instance, has been applied with success to describe the diffraction properties of sinusoidal volume gratings. Nonetheless the predictions of Kogelnik's theory dev...
Article
In this work we make a comparative study between different theories to predict the efficiencies of the different orders that propagate inside a volume phase grating. For the case of a pure sinusoidal grating, transmission and reflection, the theories of Rigorous Coupled Wave Theory (RCW), Coupled Wave Theory (CW) and Kogelnik's Theory are compared....
Article
Full-text available
In this work we have reviewed the contribution of POLINSAR to the detection of buried objects (e.g. mines). The starting point, derived from an analysis performed by the polarization subspace method (PSM), is the fact that the scatter- ing mechanisms which maximize the interferometric coherence correspond to circular polarizations (or nearly circul...
Article
The coupled wave theory of Kogelnik has given a well-established basis for the comprehension of how light propagates inside a volume hologram. This theory gives a good approximation for the diffraction efficiency of both volume phase holograms and volume absorption holograms. Mixed holograms (phase and absorption) have also been dealt with from the...
Article
Full-text available
RESUMEN En este trabajo se ha analizado la asignatura de electrónica analógica, asignatura troncal de Ingeniería Técnica de Telecomunicación, especialidad en Sonido e Imagen. El resultado final de este trabajo de investigación docente ha derivado en la elaboración de una guía docente adaptada al nuevo sistema de créditos ECTS, donde el proceso educ...
Article
Este trabajo ha sido financiado por el Ministerio de Educación y Ciencia a través de los proyectos FIS2005-05881-C01-01 y FIS2005-05881-C01-02.

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