Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

The role of computational logic as a hinge paradigm among deduction, problem solving, programming, and parallelism

This paper presents some brief considerations on the role of Computational Logic in the construction of Artificial Intelligence systems and in programming in general. It does not address how the many problems in AI can be solved but, rather more modestly, tries to point out some advantages of Computational Logic as a tool for the AI scientist in his quest. It addresses the interaction between declarative and procedural views of programs (deduction and action), the impact of the intrinsic limitations of logic, the relationship with other apparently competing computational paradigms, and finally discusses implementation-related issues, such as the efficiency of current implementations and their capability for efficiently exploiting existing and future sequential and parallel hardware. The purpose of the discussion is in no way to present Computational Logic as the unique overall vehicle for the development of intelligent systems (in the firm belief that such a panacea is yet to be found) but rather to stress its strengths in providing reasonable solutions to several aspects of the task.

The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

Decelerator elements for ramp transfer points in fruit packing lines

Two different decelerator elements used to reduce impacts on fruits on ramp transfer points in fruit packing lines were designed and tested. The performance of these elements, a powered decelerator and a multiple curtain, was compared to commercial decelerators (blankets). A ramp of length 60 cm was placed at an angle of 30º in an experimental fruit packing line between a roller transporter and a conveyor. The decelerators were placed on top of the ramp. Different tests were carried out to study the performance of the decelerators using instrumented spheres (IS 100) of various sizes. Results showed that decelerators can reduce the impact intensity down to safe thresholds. The powered decelerator was the most effective because it reduced the speed of fruits and did not cause retention of the fruit, when correctly regulated.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Passing or stopping by: meeting points on the fly

In traditional nomadic societies, social life was created around mobile points rekindled in different places each time. After the settled urbanization period, where social life centred on fixed attractions, we are opening a new era, where thanks to technology, we are able to create meeting points on the fly. Contemporary public space for passer-by users will be again based on traces instead of lines, reflecting current reality far more accurately.

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compresor Rotor

Recently, a theoretical criterion to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. This theoretical criterion was used for determining the locus of the stability line over the rotor map and for predicting the post-stall evolution of the constant-speed line of a rotor. The main objective of this paper is to improve the predictions of such a model. To do that, the paper proposes a different characterization of the characteristic azimuthal length and a calculation of the ratio of specific heats based on a polytropic exponent. Thanks to these new values, the model predicts two bifurcation points in the behaviour of the flow: the inception point of the instability and the surge point. Experimental data from a pure axial compressor are used to validate the model showing that the prediction of the flow coefficient at the surge point has an error inferior to 5%. For the rotor studied, the paper provides a quantitative and qualitative description of the inception of the instability and of the mechanism involved in the instable region of the compressor map. The paper also discusses the role of rotor efficiency in the position of the bifurcations and gives a sensitivity analysis of its position. Finally, it presents a discussion about how the model can explain the different behaviours exhibited by the same rotor when the flow coefficient is reduced

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Sharp imaging of Multiple object pointS: how and why

Is it possible to sharply image M object points with N surfaces when N menor que M? Under what conditions? Why is it interesting for optimization? What is the role of the SMS method?

Concept of operations for ATM by managing uncertainty through multiple metering points

This paper presents an operational concept for Air Traffic Management, and in particular arrival management, in which aircraft are permitted to operate in a manner consistent with current optimal aircraft operating techniques. The proposed concept allows aircraft to descend in the fuel efficient path managed mode and with arrival time not actively controlled. It will be demonstrated how the associated uncertainty in the time dimension of the trajectory can be managed through the application of multiple metering points strategically chosen along the trajectory. The proposed concept does not make assumptions on aircraft equipage (e.g. time of arrival control), but aims at handling mixed-equipage scenarios that most likely will remain far into the next decade and arguably beyond.

Estudio teórico-experimental para la mejora de la resistencia estructural de autocares basado en el diseño de uniones y asientos

La presente tesis analiza la mejora de la resistencia estructural ante vuelco de autocares enfocando dos vías de actuación: análisis y propuestas de requisitos reglamentarios a nivel europeo y la generación de herramientas que ayuden al diseño y a la verificación de estos requisitos. Los requisitos reglamentarios de resistencia estructural a vuelco contemplan la superestructura de los vehículos pero no para los asientos y sistemas de retención. La influencia de los pasajeros retenidos es superior a la incluida en reglamentación (Reg. 66.01) debiendo considerarse unida al vehículo un porcentaje de la masa de los pasajeros del 91% para cinturón de tres puntos y del 52% para cinturón subabdominal frente al 50% reglamentario para todos los casos. Se ha determinado la cinemática y dinámica del vuelco normativo en sus diferentes fases, formulando las energías en las fases iniciales (hasta el impacto contra el suelo) y determinando la fase final de deformación a través del análisis secuencial de ensayos de módulos reales. Se han determinado los esfuerzos para los asientos que se dividen en dos fases diferenciadas temporalmente: una primera debida a la deformación estructural y una segunda debida al esfuerzo del pasajero retenido que se produce en sentido opuesto (con una deceleración del pasajero en torno a 3.3 g). Se ha caracterizado a través de ensayos cuasi.estáticos el comportamiento de perfiles a flexión y de las uniones estructurales de las principales zonas del vehículo (piso, ventana y techo) verificándose la validez del comportamiento plástico teórico Kecman.García para perfiles de hasta 4 mm de espesor y caracterizando la resistencia y rigidez en la zona elástica de las uniones en función del tipo de refuerzo, materiales y perfiles (análisis de más de 180 probetas). Se ha definido un método de ensayo cuasi.estático para asientos ante esfuerzos de vuelco, ensayándose 19 butacas y determinándose que son resistentes (salvo las uniones a vehículo con pinzas), que son capaces de absorber hasta más de un 17% de la energía absorbida, aunque algunos necesitan optimización para llegar a contribuir en el mecanismo de deformación estructural. Se han generado modelos simplificados para introducir en los modelos barra.rótula plástica: un modelo combinado unión+rótula plástica (que incluye la zona de rigidez determinada en función del tipo de unión) para la superestructura y un modelo simplificado de muelles no.lineales para los asientos. Igualmente se ha generado la metodología de diseño a través de ensayos virtuales con modelos de detalle de elementos finitos tanto de las uniones como de los asientos. Se ha propuesto una metodología de diseño basada en obtener el “mecanismo óptimo de deformación estructural” (elevando la zona de deformación lateral a nivel de ventana y en pilar o en costilla en techo). Para ello se abren dos vías: diseño de la superestructura (selección de perfiles y generación de uniones resistentes) o combinación con asientos (que en lugar de solo resistir las cargas pueden llegar a modificar el mecanismo de deformación). Se ha propuesto una metodología de verificación alternativa al vuelco de vehículo completo que contempla el cálculo cuasi.estático con modelos simplificados barra.rótula plástica más el ensayo de una sección representativa con asientos y utillajes antropomórficos retenidos que permite validar el diseño de las uniones, determinar el porcentaje de energía que debe absorberse por deformación estructural (factor C) y verificar el propio asiento como sistema de retención. ABSTRACT This research analyzes the improvement of the structural strength of buses and coaches under rollover from two perspectives: regulatory requirements at European level and generation of tools that will help to the design and to the verification of requirements. European Regulations about rollover structural strength includes requirements for the superstructure of the vehicles but not about seats, anchorages and restraint systems. The influence of the retained passengers is higher than the one included currently in the Regulations (Reg. 66.01), being needed to consider a 91% of the passenger mass as rigidly joint to the vehicle (for 3 points’ belt, a 52% for 2 points’ belt) instead of the 50% included in the Regulation. Kinematic and dynamic of the normative rollover has been determined from testing of different sections, formulating the energies of the first phases (up to the first impact with the ground) and determining the last deformation phase through sequential analysis of movements and deformations. The efforts due to rollover over the seats have been established, being divided in two different temporal phases: a first one due to the structural deformation of the vehicle and a second one due to the effort of the restrained passenger being this second one in opposite sense (with a passenger deceleration around 3.3 g). From quasi.static testing, the behavior of the structural tubes under flexural loads, including the principal joints in the vehicle (floor, window and roof), the validity of the theoretical plastic behavior according Kecman.García theories have been verified up to 4 mm of thickness. Strength of the joints as well as the stiffness of the elastic zone has been determined in function of main parameters: type of reinforcement, materials and section of the tubes (more than 180 test specimens). It has been defined a quasi.static testing methodology to characterize the seats and restrain system behavior under rollover, testing 19 double seats and concluding that they are resistant (excepting clamping joints), that they can absorb more than a 17 of the absorbed energy, and that some of them need optimization to contribute in the structural deformation mechanism. It has been generated simplified MEF models, to analyze in a beam.plastic hinge model: a combined model joint+plastic hinge (including the stiffness depending on the type of joint) for the superstructure and a simplified model with non.lineal springs to represent the seats. It has been detailed methodologies for detailed design of joints and seats from virtual testing (MEF models). A design methodology based in the “optimized structural deformation mechanism” (increasing the height of deformation of the lateral up to window level) is proposed. Two possibilities are analyzed: design of the superstructure based on the selection of profiles and design of strength joints (were seats only resist the efforts and contribute in the energy absorption) or combination structure.seats, were seats contributes in the deformation mechanism. An alternative methodology to the rollover of a vehicle that includes the quasi.static calculation with simplified models “beam.joint+plastic hinge” plus the testing of a representative section of the vehicle including seats and anthropomorphic ballast restrained by the safety belts is presented. The test of the section allows validate the design of the joints, determine the percentage of energy to be absorbed by structural deformation (factor C) and verify the seat as a retention system.

Hysteresis in transverse galloping: the role of the inflection points

Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which are described by using the quasi-steady hypothesis. The hysteresis of transverse galloping is also analyzed. Approximate solutions of the model are obtained by assuming that the aerodynamic and damping forces are much smaller than the inertial and stiffness ones. The analysis of the approximate solution, which is obtained by means of the method of Krylov–Bogoliubov, reveals the existing link between the hysteresis phenomenon and the number of inflection points at the aerodynamic force coefficient curve, Cy(α)Cy(α); CyCy and αα being, respectively, the force coefficient normal to the incident flow and the angle of attack. The influence of the position of these inflection points on the range of flow velocities in which hysteresis takes place is also analyzed.

Multiple feature points representation in target localization of wireless visual sensor networks

This paper discusses the target localization problem in wireless visual sensor networks. Additive noises and measurement errors will affect the accuracy of target localization when the visual nodes are equipped with low-resolution cameras. In the goal of improving the accuracy of target localization without prior knowledge of the target, each node extracts multiple feature points from images to represent the target at the sensor node level. A statistical method is presented to match the most correlated feature point pair for merging the position information of different sensor nodes at the base station. Besides, in the case that more than one target exists in the field of interest, a scheme for locating multiple targets is provided. Simulation results show that, our proposed method has desirable performance in improving the accuracy of locating single target or multiple targets. Results also show that the proposed method has a better trade-off between camera node usage and localization accuracy.