Fernando Giménez

Fractal photon sieve.

A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.

A quantitative analysis of coupled oscillations using mobile accelerometer sensors

In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses. (Some figures may appear in colour only in the online journal)

Lacunar fractal photon sieves

We present a new family of diffractive lenses whose structure is based on the combination of two concepts: photon sieve and fractal zone plates with variable lacunarity. The focusing properties of different members of this family are examined. It is shown that the sieves provide a smoothing effect on the higher order foci of a conventional lacunar fractal zone plate. However, the characteristic self-similar axial response of the fractal zone plates is always preserved.

Multifractal zone plates

We present multifractal zone plates (MFZPs) as what is to our knowledge a new family of diffractive lenses whose structure is based on the combination of fractal zone plates (FZPs) of different orders. The typical result is a composite of two FZPs with the central one having a first-order focal length f surrounded by outer zones with a third-order focal length f. The focusing properties of different members of this family are examined and compared with conventional composite Fresnel zone plates. It is shown that MFZPs improve the axial resolution and also give better performance under polychromatic illumination.

Bifractal focusing and imaging properties of Thue-Morse Zone Plates.

We present a new family of Zone Plates (ZPs) designed using the Thue-Morse sequence. The focusing and imaging properties of these aperiodic diffractive lenses coined Thue-Morse Zone Plates (TMZPs) are examined. It is demonstrated that TMZPs produce a pair of self-similar and equally intense foci along the optical axis. As a consequence of this property, under broadband illumination, a TMZP produces two foci with an extended depth of focus and a strong reduction of the chromatic aberration compared with conventional periodic ZPs. This distinctive optical characteristic is experimentally confirmed.

Cantor Dust Zone Plates

In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.

Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureKH≥4λ and antiholomorphic Ricci curvatureρA≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=CPn−1(λ) andM=CPn(λ). Moreover, we give some results on the volume of of tubes aboutP inM.

Analysis of the efficiency of golf tourism via the Internet. Application to the Mediterranean countries

This article aims to establish a methodology for comparing golf-tourism efficiency of a set of 14 Mediterranean countries easily using three Data Envelopment Analysis (DEA) models. We have compared three DEA models. The first model resorts only to physical variables, while the latter two also consider cybermetric variables. Approximately one-third of the 14 analysed Mediterranean countries are rated efficient by any of our models (Bosnia-Herzegovina, France, Slovenia, and Spain), while 9 countries appear inefficient in all three models. Our results show that resorting to the model exclusively based on cybermetric variables ranks the non-efficient countries exactly the same way as the model based on physical variables. We have also found an interesting result that gives us a guide for developing golf tourism at the country level.This article aims to establish a methodology for comparing golf-tourism efficiency of a set of 14 Mediterranean countries easily using three Data Envelopment Analysis (DEA) models. We have compared three DEA models. The first model resorts only to physical variables, while the latter two also consider cybermetric variables. Approximately one-third of the 14 analysed Mediterranean countries are rated efficient by any of our models (Bosnia-Herzegovina, France, Slovenia, and Spain), while 9 countries appear inefficient in all three models. Our results show that resorting to the model exclusively based on cybermetric variables ranks the non-efficient countries exactly the same way as the model based on physical variables. We have also found an interesting result that gives us a guide for developing golf tourism at the country level.

Immersions of compact riemannian manifolds into a ball of a complex space form

There are some classical theorems on non-immersibility of compact riemannian manifolds with sectional curvature bounded from above given by Tompkins, O’Neill, Chern, Kuiper and Moore (see [3], pages 221-226). More recently, attention has been paid to the case of immersions into a geodesic ball of a simply connected space form, and some conditions of non-immersibility in such a ball have been proved. In particular, estimates for the mean curvature of a complete immersion into a geodesic ball have been obtained by Jorge and Xavier [11] and a corresponding rigidity theorem for compact hypersurfaces has been proved by Markvorsen [14]. In this paper we give the Kahler analogs of the theorems of Jorge and Xavier (only for the compact case) and Markvorsen, and get some other new results for the Kahler case that have no Riemannian analog. In order to state our results we shall introduce some notation and terminology. Given a real number λ, let us consider the functions

A generalized finite difference method using Coatmèlec lattices

Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmelec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.