Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Influence of Current Pulse Shape on Directly Modulated Systems Performance in Metro Area Optical Networks

Due to the fact that a metro network market is very cost sensitive, direct modulated schemes appear attractive. In this paper a CWDM (Coarse Wavelength Division Multiplexing) system is studied in detail by means of an Optical Communication System Design Software; a detailed study of the modulated current shape (exponential, sine and gaussian) for 2.5 Gb/s CWDM Metropolitan Area Networks is performed to evaluate its tolerance to linear impairments such as signal-to-noise-ratio degradation and dispersion. Point-to-point links are investigated and optimum design parameters are obtained. Through extensive sets of simulation results, it is shown that some of these shape pulses are more tolerant to dispersion when compared with conventional gaussian shape pulses. In order to achieve a low Bit Error Rate (BER), different types of optical transmitters are considered including strongly adiabatic and transient chirp dominated Directly Modulated Lasers (DMLs). We have used fibers with different dispersion characteristics, showing that the system performance depends, strongly, on the chosen DML?fiber couple.

Level Set Segmentation with Shape and Appearance Models Using Affine Moment Descriptors

We propose a level set based variational approach that incorporates shape priors into edge-based and region-based models. The evolution of the active contour depends on local and global information. It has been implemented using an efficient narrow band technique. For each boundary pixel we calculate its dynamic according to its gray level, the neighborhood and geometric properties established by training shapes. We also propose a criterion for shape aligning based on affine transformation using an image normalization procedure. Finally, we illustrate the benefits of the our approach on the liver segmentation from CT images.

A static heap analysis for shape and connectivity: Unified memory analysis: The base framework

Modeling the evolution of the state of program memory during program execution is critical to many parallehzation techniques. Current memory analysis techniques either provide very accurate information but run prohibitively slowly or produce very conservative results. An approach based on abstract interpretation is presented for analyzing programs at compile time, which can accurately determine many important program properties such as aliasing, logical data structures and shape. These properties are known to be critical for transforming a single threaded program into a versión that can be run on múltiple execution units in parallel. The analysis is shown to be of polynomial complexity in the size of the memory heap. Experimental results for benchmarks in the Jolden suite are given. These results show that in practice the analysis method is efflcient and is capable of accurately determining shape information in programs that créate and manipúlate complex data structures.

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Use of calculus of variations to determine the shape of hovering rotors of minimum power and its application to micro air vehicles

In this paper, calculus of variations and combined blade element and momentum theory (BEMT) are used to demonstrate that, in hover, when neither root nor tip losses are considered; the rotor, which minimizes the total power (MPR), generates an induced velocity that varies linearly along the blade span. The angle of attack of every blade element is constant and equal to its optimum value. The traditional ideal twist (ITR) and optimum (OR) rotors are revisited in the context of this variational framework. Two more optimum rotors are obtained considering root and tip losses, the ORL, and the MPRL. A comparison between these five rotors is presented and discussed. The MPR and MPRL present a remarkable saving of power for low values of both thrust coefficient and maximum aerodynamic efficiency. The result obtained can be exploited to improve the aerodynamic behaviour of rotary wing micro air vehicles (MAV). A comparison with experimental results obtained from the literature is presented.

Automatic segmentation of abdominal aortic aneurysm from medical images based on active shape models and texture models

A semi-automatic segmentation algorithm for abdominal aortic aneurysms (AAA), and based on Active Shape Models (ASM) and texture models, is presented in this work. The texture information is provided by a set of four 3D magnetic resonance (MR) images, composed of axial slices of the abdomen, where lumen, wall and intraluminal thrombus (ILT) are visible. Due to the reduced number of images in the MRI training set, an ASM and a custom texture model based on border intensity statistics are constructed. For the same reason the shape is characterized from 35-computed tomography angiography (CTA) images set so the shape variations are better represented. For the evaluation, leave-one-out experiments have been held over the four MRI set.

Aerodynamic Optimization of the Nose Shape of a High-speed Train

La influencia de la aerodinámica en el diseño de los trenes de alta velocidad, unida a la necesidad de resolver nuevos problemas surgidos con el aumento de la velocidad de circulación y la reducción de peso del vehículo, hace evidente el interés de plantear un estudio de optimización que aborde tales puntos. En este contexto, se presenta en esta tesis la optimización aerodinámica del testero de un tren de alta velocidad, llevada a cabo mediante el uso de métodos de optimización avanzados. Entre estos métodos, se ha elegido aquí a los algoritmos genéticos y al método adjunto como las herramientas para llevar a cabo dicha optimización. La base conceptual, las características y la implementación de los mismos se detalla a lo largo de la tesis, permitiendo entender los motivos de su elección, y las consecuencias, en términos de ventajas y desventajas que cada uno de ellos implican. El uso de los algorimos genéticos implica a su vez la necesidad de una parametrización geométrica de los candidatos a óptimo y la generación de un modelo aproximado que complementa al método de optimización. Estos puntos se describen de modo particular en el primer bloque de la tesis, enfocada a la metodología seguida en este estudio. El segundo bloque se centra en la aplicación de los métodos a fin de optimizar el comportamiento aerodinámico del tren en distintos escenarios. Estos escenarios engloban los casos más comunes y también algunos de los más exigentes a los que hace frente un tren de alta velocidad: circulación en campo abierto con viento frontal o viento lateral, y entrada en túnel. Considerando el caso de viento frontal en campo abierto, los dos métodos han sido aplicados, permitiendo una comparación de las diferentes metodologías, así como el coste computacional asociado a cada uno, y la minimización de la resistencia aerodinámica conseguida en esa optimización. La posibilidad de evitar parametrizar la geometría y, por tanto, reducir el coste computacional del proceso de optimización es la característica más significativa de los métodos adjuntos, mientras que en el caso de los algoritmos genéticos se destaca la simplicidad y capacidad de encontrar un óptimo global en un espacio de diseño multi-modal o de resolver problemas multi-objetivo. El caso de viento lateral en campo abierto considera nuevamente los dos métoxi dos de optimización anteriores. La parametrización se ha simplificado en este estudio, lo que notablemente reduce el coste numérico de todo el estudio de optimización, a la vez que aún recoge las características geométricas más relevantes en un tren de alta velocidad. Este análisis ha permitido identificar y cuantificar la influencia de cada uno de los parámetros geométricos incluídos en la parametrización, y se ha observado que el diseño de la arista superior a barlovento es fundamental, siendo su influencia mayor que la longitud del testero o que la sección frontal del mismo. Finalmente, se ha considerado un escenario más a fin de validar estos métodos y su capacidad de encontrar un óptimo global. La entrada de un tren de alta velocidad en un túnel es uno de los casos más exigentes para un tren por el pico de sobrepresión generado, el cual afecta a la confortabilidad del pasajero, así como a la estabilidad del vehículo y al entorno próximo a la salida del túnel. Además de este problema, otro objetivo a minimizar es la resistencia aerodinámica, notablemente superior al caso de campo abierto. Este problema se resuelve usando algoritmos genéticos. Dicho método permite obtener un frente de Pareto donde se incluyen el conjunto de óptimos que minimizan ambos objetivos. ABSTRACT Aerodynamic design of trains influences several aspects of high-speed trains performance in a very significant level. In this situation, considering also that new aerodynamic problems have arisen due to the increase of the cruise speed and lightness of the vehicle, it is evident the necessity of proposing an optimization study concerning the train aerodynamics. Thus, the aerodynamic optimization of the nose shape of a high-speed train is presented in this thesis. This optimization is based on advanced optimization methods. Among these methods, genetic algorithms and the adjoint method have been selected. A theoretical description of their bases, the characteristics and the implementation of each method is detailed in this thesis. This introduction permits understanding the causes of their selection, and the advantages and drawbacks of their application. The genetic algorithms requirethe geometrical parameterization of any optimal candidate and the generation of a metamodel or surrogate model that complete the optimization process. These points are addressed with a special attention in the first block of the thesis, focused on the methodology considered in this study. The second block is referred to the use of these methods with the purpose of optimizing the aerodynamic performance of a high-speed train in several scenarios. These scenarios englobe the most representative operating conditions of high-speed trains, and also some of the most exigent train aerodynamic problems: front wind and cross-wind situations in open air, and the entrance of a high-speed train in a tunnel. The genetic algorithms and the adjoint method have been applied in the minimization of the aerodynamic drag on the train with front wind in open air. The comparison of these methods allows to evaluate the methdology and computational cost of each one, as well as the resulting minimization of the aerodynamic drag. Simplicity and robustness, the straightforward realization of a multi-objective optimization, and the capability of searching a global optimum are the main attributes of genetic algorithm. However, the requirement of geometrically parameterize any optimal candidate is a significant drawback that is avoided with the use of the adjoint method. This independence of the number of design variables leads to a relevant reduction of the pre-processing and computational cost. Considering the cross-wind stability, both methods are used again for the minimization of the side force. In this case, a simplification of the geometric parameterization of the train nose is adopted, what dramatically reduces the computational cost of the optimization process. Nevertheless, some of the most important geometrical characteristics are still described with this simplified parameterization. This analysis identifies and quantifies the influence of each design variable on the side force on the train. It is observed that the A-pillar roundness is the most demanding design parameter, with a more important effect than the nose length or the train cross-section area. Finally, a third scenario is considered for the validation of these methods in the aerodynamic optimization of a high-speed train. The entrance of a train in a tunnel is one of the most exigent train aerodynamic problems. The aerodynamic consequences of high-speed trains running in a tunnel are basically resumed in two correlated phenomena, the generation of pressure waves and an increase in aerodynamic drag. This multi-objective optimization problem is solved with genetic algorithms. The result is a Pareto front where a set of optimal solutions that minimize both objectives.

SMS freeforms for illumination

SMS 3D (simultaneous multiple surfaces in their three-dimensional version) is a well-known design method comprising two freeform surfaces that allow the perfect coupling of two wavefronts with another two. The design algorithm provides a collection of line pairs on both surfaces (called SMS spines), whose three-dimensional shape seems arbitrary at first sight. This paper shows that the shapes of the spines are partially governed by applying the étendue conservation theorem to the biparametric bundle of rays linking the paired spines, which is one lesser known étendue invariants found by Poincaré. The resulting formulae for the spines in three-dimensional space happen to coincide with the conventional étendue formulas of two-dimensional geometry, like for instance, the Hottel formula.

The influence of the section shape of box-girder decks on the steady aerodynamic yawing moment of double cantilever bridges under construction

The yawing moment acting on the box-girder deck of reinforced concrete bridges constructed using the balanced cantilever method during the erection stage has been experimentally analyzed by testing different types of bridge cross-sections. Experimental results show that the yawing moment coefficient decreases as the bridge decks become streamlined, and that the yawing moment coefficient reaches a maximum when the bridge deck length is nearly twice the deck width.

Pulse-Shape Analysis of PDM-QPSK Modulation Formats for 100 and 200 Gb/s DWDM transmissions

Advanced optical modulation format polarization-division multiplexed quadrature phase shift keying (PDM-QPSK) has become a key ingredient in the design of 100 and 200-Gb/s dense wavelength-division multiplexed (DWDM) networks. The performance of this format varies according to the shape of the pulses employed by the optical carrier: non-return to zero (NRZ), return to zero (RZ) or carrier-suppressed return to zero (CSRZ). In this paper we analyze the tolerance of PDM-QPSK to linear and nonlinear optical impairments: amplified spontaneous emission (ASE) noise, crosstalk, distortion by optical filtering, chromatic dispersion (CD), polarization mode dispersion (PMD) and fiber Kerr nonlinearities. RZ formats with a low duty cycle value reduce pulse-to-pulse interaction obtaining a higher tolerance to CD, PMD and intrachannel nonlinearities.