Invariant manifolds of the Bonhoeffer-van der Pol oscillator

The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale horseshoes) and the chaos observed in the bifurcation diagram is described. It is observed that in the non-chaotic zones of the bifurcation diagram, there may or may not be Smale horseshoes, but there are no homoclinic tangencies.Comment: 14 pages, 15 figure

A probabilistic model for crystal growth applied to protein deposition at the microscale

A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the model great flexibility. The accuracy of the simulation is tested against a real protein (SbpA) crystallization experiment showing high agreement between the proposed model and the actual images of the nucleation process. Finally, it is also discussed how the regularity of the interface (i.e. the curve that separates the crystal from the substrate) affects to the evolution of the simulation.Comment: 13 pages, 12 figure

A simple formula to find the closest consistent matrix to a reciprocal matrix

Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. (C) 2014 Elsevier Inc. All rights reserved.This work has been performed with the support of the project IDAWAS, DPI2009-11591 of the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain), with the supplementary support of ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana, and the support given to the first author by the Spanish project MTM2010-18539. The use of English in this paper was revised by John Rawlins; and the revision was funded by the Universitat Politecnica de Valencia, Spain.Benítez López, J.; Izquierdo Sebastián, J.; Pérez García, R.; Ramos Martínez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling. 38(15-16):3968-3974. https://doi.org/10.1016/j.apm.2014.01.007S396839743815-1

The ALHAMBRA photometric system

This paper presents the characterization of the optical range of the ALHAMBRA photometric system, a 20 contiguous, equal-width, medium-band CCD system with wavelength coverage from 3500A to 9700A. The photometric description of the system is done by presenting the full response curve as a product of the filters, CCD and atmospheric transmission curves, and using some first and second order moments of this response function. We also introduce the set of standard stars that defines the system, formed by 31 classic spectrophotometric standard stars which have been used in the calibration of other known photometric systems, and 288 stars, flux calibrated homogeneously, from the Next Generation Spectral Library (NGSL). Based on the NGSL, we determine the transformation equations between Sloan Digital Sky Survey (SDSS) ugriz photometry and the ALHAMBRA photometric system, in order to establish some relations between both systems. Finally we develop and discuss a strategy to calculate the photometric zero points of the different pointings in the ALHAMBRA project.Comment: Astronomical Journal on the 14th of January 201

nlstac: Non-Gradient Separable Nonlinear Least Squares Fitting

A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be fitted. One notable feature of this method is the absence of initialization which is typically necessary for nonlinear fitting gradient-based algorithms. Instead, just some bounds for the nonlinear parameters are required. Even though convergence for this method is guaranteed for exponential decay using the max-norm, the algorithm exhibits remarkable robustness, and its use has been extended to a wide range of functions using the Euclidean norm. Furthermore, this data-fitting package can also serve as a valuable resource for providing accurate initial parameters to other algorithms that rely on them

LensPerfect: Gravitational Lens Massmap Reconstructions Yielding Exact Reproduction of All Multiple Images

We present a new approach to gravitational lens massmap reconstruction. Our massmap solutions perfectly reproduce the positions, fluxes, and shears of all multiple images. And each massmap accurately recovers the underlying mass distribution to a resolution limited by the number of multiple images detected. We demonstrate our technique given a mock galaxy cluster similar to Abell 1689 which gravitationally lenses 19 mock background galaxies to produce 93 multiple images. We also explore cases in which far fewer multiple images are observed, such as four multiple images of a single galaxy. Massmap solutions are never unique, and our method makes it possible to explore an extremely flexible range of physical (and unphysical) solutions, all of which perfectly reproduce the data given. Each reconfiguration of the source galaxies produces a new massmap solution. An optimization routine is provided to find those source positions (and redshifts, within uncertainties) which produce the "most physical" massmap solution, according to a new figure of merit developed here. Our method imposes no assumptions about the slope of the radial profile nor mass following light. But unlike "non-parametric" grid-based methods, the number of free parameters we solve for is only as many as the number of observable constraints (or slightly greater if fluxes are constrained). For each set of source positions and redshifts, massmap solutions are obtained "instantly" via direct matrix inversion by smoothly interpolating the deflection field using a recently developed mathematical technique. Our LensPerfect software is straightforward and easy to use and is made publicly available via our website.Comment: 17 pages, 18 figures, accepted by ApJ. Software and full-color version of paper available at http://www.its.caltech.edu/~coe/LensPerfect

The ALHAMBRA Project: A large area multi medium-band optical and NIR photometric survey

(ABRIDGED) We describe the first results of the ALHAMBRA survey which provides cosmic tomography of the evolution of the contents of the Universe over most of Cosmic history. Our approach employs 20 contiguous, equal-width, medium-band filters covering from 3500 to 9700 A, plus the JHKs bands, to observe an area of 4 sqdeg on the sky. The optical photometric system has been designed to maximize the number of objects with accurate classification by SED and redshift, and to be sensitive to relatively faint emission lines. The observations are being carried out with the Calar Alto 3.5m telescope using the cameras LAICA and O-2000. The first data confirm that we are reaching the expected magnitude limits of AB<~25 mag in the optical filters from the blue to 8300 A, and from AB=24.7 to 23.4 for the redder ones. The limit in the NIR is (Vega) K_s~20, H~21, J~22. We expect to obtain accurate redshift values, Delta z/(1+z) <~ 0.03 for about 5x10^5 galaxies with I<~25 (60% complete), and z_med=0.74. This accuracy, together with the homogeneity of the selection function, will allow for the study of the redshift evolution of the large scale structure, the galaxy population and its evolution with redshift, the identification of clusters of galaxies, and many other studies, without the need for any further follow-up. It will also provide targets for detailed studies with 10m-class telescopes. Given its area, spectral coverage and its depth, apart from those main goals, the ALHAMBRA-Survey will also produce valuable data for galactic studies.Comment: Accepted to the Astronomical Journal. 43 pages, 18 figures. The images have been reduced in resolution to adapt to standard file sizes. Readers can find the full-resolution version of the paper at the ALHAMBRA web site (http://www.iaa.es/alhambra) under the "Publications" lin

Exact solution of the two-dimensional Dirac oscillator

In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.Comment: revtex, 6pp. IVIC-CFLE 93/0

New non-unitary representations in a Dirac hydrogen atom

New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require integer or half integer labels. The set of operators defined are used to span the complete space of bound state eigenstates of the problem thus solving it in an essentially algebraic way