Artículos de revista DIMI - MIIS Aldizkari artikuluak

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Open Access
Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
(Cambridge University Press, 2004) López García, José Luis; Temme, Nico M.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of functions that are special cases of the given polynomials. The method is based on expanding integrals in one or two points of the complex plane, these points being saddle points of the phase functions of the integrands.
Open Access
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
(EDP Sciences, 2006) Rapún Araiz, María Luisa; Sayas, Francisco Javier; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Gobierno de Navarra / Nafarroako Gobernua, 18/2005
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the bounded domain. For the boundary unknowns we take spaces of periodic splines. We show how to transmit information from the approximate boundary to the exact one in an efficient way and prove well-posedness of the Galerkin method. Error estimates are provided and experimentally corroborated at the end of the work.
Open Access
Hill problem analytical theory to the order four: application to the computation of frozen orbits around planetary satellites
(Hindawi Publishing Corporation, 2009) Lara, Martín; Palacián Subiela, Jesús Francisco; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.
Open Access
Formulas for the amplitude of the van der Pol limit cycle through the homotopy analysis method
(Hindawi / Wiley, 2009) López García, José Luis; Abbasbandy, S.; López Ruiz, R.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Gobierno de Navarra / Nafarroako Gobernua, Res. 07/05/2008
The limit cycle of the van der Pol oscillator, x¨+ε(x2−1)x˙+x=0, is studied in the plane (x,x˙) by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form of this limit cycle for the whole range of the parameter ε is obtained. These formulas generate the amplitude with an error less than 0.1%. To our knowledge, this is the first time where an analytical approximation of the amplitude of the van der Pol limit cycle, with validity from the weakly up to the strongly nonlinear regime, is given.
Open Access
IVAN: Intelligent van for the distribution of pharmaceutical drugs
(MDPI, 2012) Moreno, Asier; Angulo Martínez, Ignacio; Perallos Ruiz, Asier; Landaluce, Hugo; García Zuazola, Ignacio Julio; Azpilicueta Fernández de las Heras, Leyre; Astrain Escola, José Javier; Falcone Lanas, Francisco; Villadangos Alonso, Jesús; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza
This paper describes a telematic system based on an intelligent van which is capable of tracing pharmaceutical drugs over delivery routes from a warehouse to pharmacies, without altering carriers' daily conventional tasks. The intelligent van understands its environment, taking into account its location, the assets and the predefined delivery route; with the capability of reporting incidences to carriers in case of failure according to the established distribution plan. It is a non-intrusive solution which represents a successful experience of using smart environments and an optimized Radio Frequency Identification (RFID) embedded system in a viable way to resolve a real industrial need in the pharmaceutical industry. The combination of deterministic modeling of the indoor vehicle, the implementation of an ad-hoc radiating element and an agile software platform within an overall system architecture leads to a competitive, flexible and scalable solution.
Open Access
Generalization of Zernike polynomials for regular portions of circles and ellipses
(Optical Society of America, 2014) Navarro, Rafael; López García, José Luis; Díaz, José A.; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike basis for a variety of important optical apertures. On the contrary to ad hoc solutions, most of them based on the Gram-Schmidt orthonormalization method, here we apply the diffeomorphism (mapping that has a differentiable inverse mapping) that transforms the unit circle into an angular sector of an elliptical annulus. In this way, other apertures, such as ellipses, rings, angular sectors, etc. are also included as particular cases. This generalization, based on in-plane warping of the basis functions, provides a unique solution and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both, the general form and the explicit expressions for most common, elliptical and annular apertures are provided.
Open Access
Analysis of radio wave propagation for ISM 2.4 GHz wireless sensor networks in inhomogeneous vegetation environments
(MDPI, 2014) Azpilicueta Fernández de las Heras, Leyre; López Iturri, Peio; Aguirre Gallego, Erik; Mateo Zozaya, Ignacio; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniaritza Elektrikoa eta Elektronikoa; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
The use of wireless networks has experienced exponential growth due to the improvements in terms of battery life and low consumption of the devices. However, it is compulsory to conduct previous radio propagation analysis when deploying a wireless sensor network. These studies are necessary to perform an estimation of the range coverage, in order to optimize the distance between devices in an actual network deployment. In this work, the radio channel characterization for ISM 2.4 GHz Wireless Sensor Networks (WSNs) in an inhomogeneous vegetation environment has been analyzed. This analysis allows designing environment monitoring tools based on ZigBee and WiFi where WSN and smartphones cooperate, providing rich and customized monitoring information to users in a friendly manner. The impact of topology as well as morphology of the environment is assessed by means of an in-house developed 3D Ray Launching code, to emulate the realistic operation in the framework of the scenario. Experimental results gathered from a measurement campaign conducted by deploying a ZigBee Wireless Sensor Network, are analyzed and compared with simulations in this paper. The scenario where this network is intended to operate is a combination of buildings and diverse vegetation species. To gain insight in the effects of radio propagation, a simplified vegetation model has been developed, considering the material parameters and simplified geometry embedded in the simulation scenario. An initial location-based application has been implemented in a real scenario, to test the functionality within a context aware scenario. The use of deterministic tools can aid to know the impact of the topological influence in the deployment of the optimal Wireless Sensor Network in terms of capacity, coverage and energy consumption, making the use of these systems attractive for multiple applications in inhomogeneous vegetation environments.
Open Access
Radio characterization for ISM 2.4 GHz wireless sensor networks for judo monitoring applications
(MDPI, 2014) López Iturri, Peio; Aguirre Gallego, Erik; Azpilicueta Fernández de las Heras, Leyre; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniaritza Elektrikoa eta Elektronikoa; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In this work, the characterization of the radio channel for ISM 2.4GHz Wireless Sensor Networks (WSNs) for judo applications is presented. The environments where judo activity is held are usually complex indoor scenarios in terms of radiopropagation due to their morphology, the presence of humans and the electromagnetic interference generated by personal portable devices, wireless microphones and other wireless systems used by the media. For the assessment of the impact that the topology and the morphology of these environments have on electromagnetic propagation, an in-house developed 3D ray-launching software has been used in this study. Time domain results as well as estimations of received power level have been obtained for the complete volume of a training venue of a local judo club’s facilities with a contest area with the dimensions specified by the International Judo Federation (IJF) for international competitions. The obtained simulation results have been compared with measurements, which have been carried out deploying ZigBee-compliant XBee Pro modules at presented scenario, using approved Judogis (jacket, trousers and belt). The analysis is completed with the inclusion of an in-house human body computational model. Such analysis has allowed the design and development of an in house application devoted to monitor the practice of judo, in order to aid referee activities, training routines and to enhance spectator experience.
Open Access
Optimized strong stability preserving IMEX Runge-Kutta methods
(2014) Higueras Sanz, Inmaculada; Happenhofer, Natalie; Koch, Othmar; Kupka, Friedrich; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We construct and analyze robust strong stability preserving IMplicit-EXplicit Runge-Kutta (IMEX RK) methods for models of flow with diffusion as they appear in astrophysics and in many other fields where equations with similar structure arise. It turns out that besides the optimization of the region of absolute monotonicity, some other properties of the methods are crucial for the success of such simulations. In particular, the models in our focus dictate to also take into account the step size limits associated with dissipativity, positivity and the stiff parabolic terms which represent transport by diffusion, the uniform convergence with respect to different stiffness properties of those same terms, etc. Furthermore, in the literature, some other properties, like the inclusion of a part of the imaginary axis in the stability region, have been argued to be relevant. In this paper, we construct several new IMEX RK methods which differ from each other by taking various or even all of these constraints simultaneously into account. It is demonstrated for some simple examples as well as for the problem of double-diffusive convection, that the newly constructed schemes provide a significant computational advantage over other methods from the literature. Due to their accumulation of different stability properties, the optimized IMEX RK methods obtained in this paper are robust schemes that may also be useful for general models which involve the solution of advection-diffusion equations, or other transport equations with similar stability requirements.
Open Access
A fully discrete Calderón calculus for the two-dimensional elastic wave equation
(Elsevier, 2015) Domínguez Baguena, Víctor; Sánchez Vizuet, Tonatiuh; Sayas, Francisco Javier; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov–Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.
Open Access
New series expansions of the 3F2 function
(2015) López García, José Luis; Pagola Martínez, Pedro Jesús; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. Some of these expansions involve the polynomial 3F2(a1,−n, a3; b1, b2; z) evaluated at certain points z. Other expansions involve the Gauss hypergeometric function 2F1. The domain of convergence is sometimes a disk, other times a half-plane, other times the region |z|2 < 4|1 − z|. The accuracy of the approximation given by these expansions is illustrated with numerical experiments.
Open Access
Holographic acoustic elements for manipulation of levitated objects
(Nature Publishing Group, 2015) Marzo Pérez, Asier; Seah, Sue Ann; Drinkwater, Bruce W.; Sahoo, Deepak Ranjan; Long, Benjamin; Subramanian, Sriram; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Sound can levitate objects of different sizes and materials through air, water and tissue. This allows us to manipulate cells, liquids, compounds or living things without touching or contaminating them. However, acoustic levitation has required the targets to be enclosed with acoustic elements or had limited manoeuvrability. Here we optimize the phases used to drive an ultrasonic phased array and show that acoustic levitation can be employed to translate, rotate and manipulate particles using even a single-sided emitter. Furthermore, we introduce the holographic acoustic elements framework that permits the rapid generation of traps and provides a bridge between optical and acoustical trapping. Acoustic structures shaped as tweezers, twisters or bottles emerge as the optimum mechanisms for tractor beams or containerless transportation. Single-beam levitation could manipulate particles inside our body for applications in targeted drug delivery or acoustically controlled micro-machines that do not interfere with magnetic resonance imaging.
Open Access
Characterization of wireless channel impact on wireless sensor network performance in public transportation buses
(IEEE, 2015) Azpilicueta Fernández de las Heras, Leyre; López Iturri, Peio; Aguirre Gallego, Erik; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Zubiri Segura, Cristóbal; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza
Wireless communications systems are growing rapidly during the last two decades and they are gaining a significant role for multiple communication tasks within public transportation buses. In this work, the impact of topology and morphology of different types of urban buses is analyzed with the aid of an in-house developed 3D Ray Launching code and compared with on-board measurements of a deployed Wireless Sensor Network. The presence of human beings has been taken into account, showing a significant influence in the signal attenuation in the case of considering persons. In addition, the statistical analysis of simulation results considering both large and small-scale fading has been performed, providing good agreement with statistics for typical indoor environments. In addition, a Wireless Sensor Network has been programmed and deployed within the buses in order to analyze topological impact with overall system performance, with the aim of minimizing the energy consumption as well as non-desired interference levels. The use of deterministic techniques destined to consider the inherent complexity of the buses can aid in wireless system planning in order to minimize power consumption and increase overall system capacity.
Open Access
Analysis of wireless sensor network topology and estimation of optimal network deployment by deterministic radio channel characterization
(MDPI, 2015) Aguirre Gallego, Erik; López Iturri, Peio; Azpilicueta Fernández de las Heras, Leyre; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza
One of the main challenges in the implementation and design of context-aware scenarios is the adequate deployment strategy for Wireless Sensor Networks (WSNs), mainly due to the strong dependence of the radiofrequency physical layer with the surrounding media, which can lead to non-optimal network designs. In this work, radioplanning analysis for WSN deployment is proposed by employing a deterministic 3D ray launching technique in order to provide insight into complex wireless channel behavior in context-aware indoor scenarios. The proposed radioplanning procedure is validated with a testbed implemented with a Mobile Ad Hoc Network WSN following a chain configuration, enabling the analysis and assessment of a rich variety of parameters, such as received signal level, signal quality and estimation of power consumption. The adoption of deterministic radio channel techniques allows the design and further deployment of WSNs in heterogeneous wireless scenarios with optimized behavior in terms of coverage, capacity, quality of service and energy consumption.
Open Access
Improved accuracy for time-splitting methods for the numerical solution of parabolic equations
(Elsevier, 2015) Arrarás Ventura, Andrés; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In this work, we study time-splitting strategies for the numerical approximation of evolutionary reaction–diffusion problems. In particular, we formulate a family of domain decomposition splitting methods that overcomes some typical limitations of classical alternating direction implicit (ADI) schemes. The splitting error associated with such methods is observed to be O(t2) in the time step. In order to decrease the size of this splitting error to O(t3), we add a correction term to the right-hand side of the original formulation. This procedure is based on the improved initialization technique proposed by Douglas and Kim in the framework of ADI methods. The resulting non-iterative schemes reduce the global system to a collection of uncoupled subdomain problems that can be solved in parallel. Computational results comparing the newly derived algorithms with the Crank–Nicolson scheme and certain ADI methods are presented.
Open Access
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
(Rocky Mountain Mathematics Consortium, 2015) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) parameter . We consider here the second and third cases studied by Olver: differential equations with a turning point (second case) or a singular point (third case). It is well-known that his method gives the Poincar´e-type asymptotic expansion of two independent solutions of the equation in inverse powers of . In this paper we add initial conditions to the differential equation and consider the corresponding initial value problem. By using the Green function of an auxiliary problem, we transform the initial value problem into a Volterra integral equation of the second kind. Then, using a fixed point theorem, we construct a sequence of functions that converges to the unique solution of the problem. This sequence has also the property of being an asymptotic expansion for large (not of Poincar´e-type) of the solution of the problem. Moreover, we show
Open Access
Asymptotic behaviour of the Urbanik semigroup
(Elsevier, 2015) Berg, Christian; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c is indeterminate as Stieltjes moment sequence if and only if c > 2. When c is a natural number ec is a Meijer-G function. From the results about ec we obtain the asymptotic behaviour at 1 of the convolution roots of the Gumbel distribution.
Open Access
Convergent and asymptotic expansions of the Pearcey integral
(Elsevier, 2015) López García, José Luis; Pagola Martínez, Pedro Jesús; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techniques applied to the integral definition of P(x; y). In this paper we consider a different method: the iterative technique used for differential equations in [Lopez, 2012]. Using this technique in a differential equation satisfied by P(x; y) we obtain a new convergent expansion analytically simple that is valid for any complex x and y and has an asymptotic property when |x|→ ∞ uniformly for y in bounded sets. The accuracy of the approximation is illustrated with some numerical experiments and compared with other expansions given in the literature.
Open Access
Zernike-like systems in polygons and polygonal facets
(Optical Society of America, 2015) Ferreira González, Chelo; López García, José Luis; Navarro, Rafael; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit disk. In [Diaz et all, 2014] we introduced a new Zernike basis for elliptic and annular optical apertures based on an appropriate diffeomorphism between the unit disk and the ellipse and the annulus. Here, we present a generalization of this Zernike basis for a variety of important optical apertures, paying special attention to polygons and the polygonal facets present in segmented mirror telescopes. On the contrary to ad hoc solutions, most of them based on the Gram-Smith orthonormalization method, here we consider a piece-wise diffeomorphism that transforms the unit disk into the polygon under consideration. We use this mapping to define a Zernike-like orthonormal system over the polygon. We also consider ensembles of polygonal facets that are essential in the design of segmented mirror telescopes. This generalization, based on in-plane warping of the basis functions, provides a unique solution, and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both, the general form and the explicit expressions for a typical example of telescope optical aperture are provided.
Open Access
Orthogonal basis for the optical transfer function
(Optical Society of America, 2016) Ferreira González, Chelo; López García, José Luis; Navarro, Rafael; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0 OTF perfect. To this end, we apply a powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems. Here we depart from Legendre polynomials for the particular case of rotationally symmetric OTF and from spherical harmonics for the general case. Numerical experiments with different examples show that the number of terms necessary to obtain an accurate linear expansion of the OTF mainly depends on the image quality. In the rotationally symmetric case we obtained a reasonable accuracy with approximately 10 basis functions, but in general, for cases of poor image quality, the number of basis functions may increase and hence affect the efficiency of the method. Other potential applications, such as new image quality metrics are also discussed.