Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Disseny, modelat i fabricació d'una antena "trap" per aplicacions WLAN

En aquest treball s’ha dissenyat i fabricat una antena monopol en estructura planar capaç de treballar correctament a les freqüències WLAN de 2,45-2,5 GHz (802.11b/g) i 4,9-5,875 GHz (802.11a/h/j). Per arribar a aquest objectiu primer s’ha presentat el model de línia de transmissió acabada en circuit obert per simular el comportament d’una antena. S’han comparat i verificat els resultats amb el model d’antena de fil. Seguidament, s’ha estudiat el comportament que introdueix el fet de carregar l’antena amb un ressonador LC. Finalment, s’ha passat del model d’antena de fil a una estructura planar. Aquesta geometria ha permès la realització del trap LC de forma distribuïda a través d’un ressonador CLL. El principi de disseny de l’antena està basat en la introducció d’aquest ressonador CLL amb freqüència de ressonància situada entre les dos bandes de treball i que junt amb l’ajust dels diversos paràmetres que defineixen l’antena han permès obtenir més 1 GHz d’ample de banda a la freqüència de 5 GHz.

Control of optical fields and single photon emitters by advanced nanoantenna structures

The control of optical fields on the nanometre scale is becoming an increasingly important tool in many fields, ranging from channelling light delivery in photovoltaics and light emitting diodes to increasing the sensitivity of chemical sensors to single molecule levels. The ability to design and manipulate light fields with specific frequency and space characteristics is explored in this project. We present an alternative realisation of Extraordinary Optical Transmission (EOT) that requires only a single aperture and a coupled waveguide. We show how this waveguide-resonant EOT improves the transmissivity of single apertures. An important technique in imaging is Near-Field Scanning Optical Microscopy (NSOM); we show how waveguide-resonant EOT and the novel probe design assist in improving the efficiency of NSOM probes by two orders of magnitude, and allow the imaging of single molecules with an optical resolution of as good as 50 nm. We show how optical antennas are fabricated into the apex of sharp tips and can be used in a near-field configuration.

Caracterización de materiales en banda W

Para medir los coeficientes de transmisión y reflexión, S21 y S11, de diferentes materiales o muestras planas, se usa un sistema de toma de medidas en espacio libre operando banda W (75 – 110 GHz). Usando estos parámetros, S21 y S11, podemos calcular la permitividad dieléctrica relativa compleja (Er ) y la permeabilidad magnética relativa compleja (μr) mediante un proceso llamado NRW (Nicolson-Ross-Weir). El sistema para medir consiste en dos antenas de bocina, una transmisora y otra receptora, dos espejos con los que obtenemos una onda plana para medir las propiedades del material y un ordenador o dispositivo que calcula los resultados. Este dispositivo requiere de calibración para la obtención de resultados óptimos. Dicho sistema se puede simular de manera ideal con un software llamado ADS (Assistance Design System) para el estudio y comparación de grosores, permitividades dieléctricas relativas y permeabilidades magnéticas relativas de los materiales en función de la frecuencia.

Robust decoupled visual servoing based on structured light

This paper focuses on the problem of realizing a plane-to-plane virtual link between a camera attached to the end-effector of a robot and a planar object. In order to do the system independent to the object surface appearance, a structured light emitter is linked to the camera so that 4 laser pointers are projected onto the object. In a previous paper we showed that such a system has good performance and nice characteristics like partial decoupling near the desired state and robustness against misalignment of the emitter and the camera (J. Pages et al., 2004). However, no analytical results concerning the global asymptotic stability of the system were obtained due to the high complexity of the visual features utilized. In this work we present a better set of visual features which improves the properties of the features in (J. Pages et al., 2004) and for which it is possible to prove the global asymptotic stability

Plane-to-plane positioning from image-based visual servoing and structured light

In this paper we face the problem of positioning a camera attached to the end-effector of a robotic manipulator so that it gets parallel to a planar object. Such problem has been treated for a long time in visual servoing. Our approach is based on linking to the camera several laser pointers so that its configuration is aimed to produce a suitable set of visual features. The aim of using structured light is not only for easing the image processing and to allow low-textured objects to be treated, but also for producing a control scheme with nice properties like decoupling, stability, well conditioning and good camera trajectory

SLAM using an Imaging Sonar for Partially Structured Underwater Environments

In this paper we describe a system for underwater navigation with AUVs in partially structured environments, such as dams, ports or marine platforms. An imaging sonar is used to obtain information about the location of planar structures present in such environments. This information is incorporated into a feature-based SLAM algorithm in a two step process: (I) the full 360deg sonar scan is undistorted (to compensate for vehicle motion), thresholded and segmented to determine which measurements correspond to planar environment features and which should be ignored; and (2) SLAM proceeds once the data association is obtained: both the vehicle motion and the measurements whose correct association has been previously determined are incorporated in the SLAM algorithm. This two step delayed SLAM process allows to robustly determine the feature and vehicle locations in the presence of large amounts of spurious or unrelated measurements that might correspond to boats, rocks, etc. Preliminary experiments show the viability of the proposed approach

Underwater SLAM in a marina environment

This paper describes a navigation system for autonomous underwater vehicles (AUVs) in partially structured environments, such as dams, harbors, marinas or marine platforms. A mechanical scanning imaging sonar is used to obtain information about the location of planar structures present in such environments. A modified version of the Hough transform has been developed to extract line features, together with their uncertainty, from the continuous sonar dataflow. The information obtained is incorporated into a feature-based SLAM algorithm running an Extended Kalman Filter (EKF). Simultaneously, the AUV's position estimate is provided to the feature extraction algorithm to correct the distortions that the vehicle motion produces in the acoustic images. Experiments carried out in a marina located in the Costa Brava (Spain) with the Ictineu AUV show the viability of the proposed approach

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

Restricted Hartree-Fock 6-31G calculations of electrical and mechanical anharmonicity contributions to the longitudinal vibrational second hyperpolarizability have been carried out for eight homologous series of conjugated oligomers - polyacetylene, polyyne, polydiacetylene, polybutatriene, polycumulene, polysilane, polymethineimine, and polypyrrole. To draw conclusions about the limiting infinite polymer behavior, chains containing up to 12 heavy atoms along the conjugated backbone were considered. In general, the vibrational hyperpolarizabilities are substantial in comparison with their static electronic counterparts for the dc-Kerr and degenerate four-wave mixing processes (as well as for static fields) but not for electric field-induced second harmonic generation or third harmonic generation. Anharmonicity terms due to nuclear relaxation are important for the dc-Kerr effect (and for the static hyperpolarizability) in the σ-conjugated polymer, polysilane, as well as the nonplanar π systems polymethineimine and polypyrrole. Restricting polypyrrole to be planar, as it is in the crystal phase, causes these anharmonic terms to become negligible. When the same restriction is applied to polymethineimine the effect is reduced but remains quantitatively significant due to the first-order contribution. We conclude that anharmonicity associated with nuclear relaxation can be ignored, for semiquantitative purposes, in planar π-conjugated polymers. The role of zero-point vibrational averaging remains to be evaluated

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Identification of geometrically consistent interest points for 3D scene reconstruction

We propose an algorithm that extracts image features that are consistent with the 3D structure of the scene. The features can be robustly tracked over multiple views and serve as vertices of planar patches that suitably represent scene surfaces, while reducing the redundancy in the description of 3D shapes. In other words, the extracted features will off er good tracking properties while providing the basis for 3D reconstruction with minimum model complexity

Low-loss rib waveguides containing Si nanocrystals embedded in SiO2

We report on the study and modeling of the structural and optical properties of rib-loaded waveguides working in the 600-900-nm spectral range. A Si nanocrystal (Si-nc) rich SiO2 layer with nominal Si excess ranging from 10% to 20% was produced by quadrupole ion implantation of Si into thermal SiO2 formed on a silicon substrate. Si-ncs were precipitated by annealing at 1100°C, forming a 0.4-um-thick core layer in the waveguide. The Si content, the Si-nc density and size, the Si-nc emission, and the active layer effective refractive index were determined by dedicated experiments using x-ray photoelectron spectroscopy, Raman spectroscopy, energy-filtered transmission electron microscopy, photoluminescence and m-lines spectroscopy. Rib-loaded waveguides were fabricated by photolithographic and reactive ion etching processes, with patterned rib widths ranging from 1¿to¿8¿¿m. Light propagation in the waveguide was observed and losses of 11dB/cm at 633 and 780 nm were measured, modeled and interpreted.

Fine speckle contrast in InGaAs/InP systems: Influence of layer thickness, missmatch, and growing temperature

This work is focused on the study of the fine speckle contrast present in planar view observations of matched and mismatched InGaAs layers grown by molecular beam epitaxy on InP substrates. Our results provide experimental evidence of the evolution of this fine structure with the mismatch, layer thickness, and growth temperature. The correlation of the influence of all these parameters on the appearance of the contrast modulation points to the development of the fine structure during the growth. Moreover, as growth proceeds, this structure shows a dynamic behavior which depends on the intrinsic layer substrate stress.