Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

Using GPU to exploit parallelism on cryptography

In this article we explore the NVIDIA graphical processing units (GPU) computational power in cryptography using CUDA (Compute Unified Device Architecture) technology. CUDA makes the general purpose computing easy using the parallel processing presents in GPUs. To do this, the NVIDIA GPUs architectures and CUDA are presented, besides cryptography concepts. Furthermore, we do the comparison between the versions executed in CPU with the parallel version of the cryptography algorithms Advanced Encryption Standard (AES) and Message-digest Algorithm 5 (MD5) wrote in CUDA. © 2011 AISTI.

Nebular gas drag and planetary accretion with eccentric high-mass planets

Aims.We investigate the dynamics of pebbles immersed in a gas disk interacting with a planet on an eccentric orbit. The model has a prescribed gap in the disk around the location of the planetary orbit, as is expected for a giant planet with a mass in the range of 0.1-1 Jupiter masses. The pebbles with sizes in the range of 1 cm to 3 m are placed in a ring outside of the giant planet orbit at distances between 10 and 30 planetary Hill radii. The process of the accumulation of pebbles closer to the gap edge, its possible implication for the planetary accretion, and the importance of the mass and the eccentricity of the planet in this process are the motivations behind the present contribution. Methods. We used the Bulirsch-Stoer numerical algorithm, which is computationally consistent for close approaches, to integrate the Newtonian equations of the planar (2D), elliptical restricted three-body problem. The angular velocity of the gas disk was determined by the appropriate balance between the gravity, centrifugal, and pressure forces, such that it is sub-Keplerian in regions with a negative radial pressure gradient and super-Keplerian where the radial pressure gradient is positive. Results. The results show that there are no trappings in the 1:1 resonance around the L 4 and L5 Lagrangian points for very low planetary eccentricities (e2 < 0.07). The trappings in exterior resonances, in the majority of cases, are because the angular velocity of the disk is super-Keplerian in the gap disk outside of the planetary orbit and because the inward drift is stopped. Furthermore, the semi-major axis location of such trappings depends on the gas pressure profile of the gap (depth) and is a = 1.2 for a planet of 1 MJ. A planet on an eccentric orbit interacts with the pebble layer formed by these resonances. Collisions occur and become important for planetary eccentricity near the present value of Jupiter (e 2 = 0.05). The maximum rate of the collisions onto a planet of 0.1 MJ occurs when the pebble size is 37.5 cm ≤ s < 75 cm; for a planet with the mass of Jupiter, it is15 cm ≤ s < 30 cm. The accretion stops when the pebble size is less than 2 cm and the gas drag dominates the motion. © 2013 ESO.

ISW effect through dark energy quintessence and ΛCDM models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Predição de sítios de ligação para a cisplatina e transplatina baseada em ligações de hidrogênio

Pós-graduação em Biofísica Molecular - IBILCE

Bounds for the zeros of symmetric kravchuk polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of nonlinear stiffness on the dynamics of a slender elastic beam under torsional oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

The SUGAR Toolbox

The SUGAR Toolbox contains scripts coded in MATLAB for calculating various thermodynamic, kinetic, and geologic properties of substances occurring in the marine environment, particularly gas hydrate and seep systems. Brief descriptions of the toolbox scripts and some notes on the underlying basic theory as well as tables of additional property values can be found in the accompanying documentation.

Higher-order regularization and morphological techniques for image segmentation

La segmentación de imágenes es un campo importante de la visión computacional y una de las áreas de investigación más activas, con aplicaciones en comprensión de imágenes, detección de objetos, reconocimiento facial, vigilancia de vídeo o procesamiento de imagen médica. La segmentación de imágenes es un problema difícil en general, pero especialmente en entornos científicos y biomédicos, donde las técnicas de adquisición imagen proporcionan imágenes ruidosas. Además, en muchos de estos casos se necesita una precisión casi perfecta. En esta tesis, revisamos y comparamos primero algunas de las técnicas ampliamente usadas para la segmentación de imágenes médicas. Estas técnicas usan clasificadores a nivel de pixel e introducen regularización sobre pares de píxeles que es normalmente insuficiente. Estudiamos las dificultades que presentan para capturar la información de alto nivel sobre los objetos a segmentar. Esta deficiencia da lugar a detecciones erróneas, bordes irregulares, configuraciones con topología errónea y formas inválidas. Para solucionar estos problemas, proponemos un nuevo método de regularización de alto nivel que aprende información topológica y de forma a partir de los datos de entrenamiento de una forma no paramétrica usando potenciales de orden superior. Los potenciales de orden superior se están popularizando en visión por computador, pero la representación exacta de un potencial de orden superior definido sobre muchas variables es computacionalmente inviable. Usamos una representación compacta de los potenciales basada en un conjunto finito de patrones aprendidos de los datos de entrenamiento que, a su vez, depende de las observaciones. Gracias a esta representación, los potenciales de orden superior pueden ser convertidos a potenciales de orden 2 con algunas variables auxiliares añadidas. Experimentos con imágenes reales y sintéticas confirman que nuestro modelo soluciona los errores de aproximaciones más débiles. Incluso con una regularización de alto nivel, una precisión exacta es inalcanzable, y se requeire de edición manual de los resultados de la segmentación automática. La edición manual es tediosa y pesada, y cualquier herramienta de ayuda es muy apreciada. Estas herramientas necesitan ser precisas, pero también lo suficientemente rápidas para ser usadas de forma interactiva. Los contornos activos son una buena solución: son buenos para detecciones precisas de fronteras y, en lugar de buscar una solución global, proporcionan un ajuste fino a resultados que ya existían previamente. Sin embargo, requieren una representación implícita que les permita trabajar con cambios topológicos del contorno, y esto da lugar a ecuaciones en derivadas parciales (EDP) que son costosas de resolver computacionalmente y pueden presentar problemas de estabilidad numérica. Presentamos una aproximación morfológica a la evolución de contornos basada en un nuevo operador morfológico de curvatura que es válido para superficies de cualquier dimensión. Aproximamos la solución numérica de la EDP de la evolución de contorno mediante la aplicación sucesiva de un conjunto de operadores morfológicos aplicados sobre una función de conjuntos de nivel. Estos operadores son muy rápidos, no sufren de problemas de estabilidad numérica y no degradan la función de los conjuntos de nivel, de modo que no hay necesidad de reinicializarlo. Además, su implementación es mucho más sencilla que la de las EDP, ya que no requieren usar sofisticados algoritmos numéricos. Desde un punto de vista teórico, profundizamos en las conexiones entre operadores morfológicos y diferenciales, e introducimos nuevos resultados en este área. Validamos nuestra aproximación proporcionando una implementación morfológica de los contornos geodésicos activos, los contornos activos sin bordes, y los turbopíxeles. En los experimentos realizados, las implementaciones morfológicas convergen a soluciones equivalentes a aquéllas logradas mediante soluciones numéricas tradicionales, pero con ganancias significativas en simplicidad, velocidad y estabilidad. ABSTRACT Image segmentation is an important field in computer vision and one of its most active research areas, with applications in image understanding, object detection, face recognition, video surveillance or medical image processing. Image segmentation is a challenging problem in general, but especially in the biological and medical image fields, where the imaging techniques usually produce cluttered and noisy images and near-perfect accuracy is required in many cases. In this thesis we first review and compare some standard techniques widely used for medical image segmentation. These techniques use pixel-wise classifiers and introduce weak pairwise regularization which is insufficient in many cases. We study their difficulties to capture high-level structural information about the objects to segment. This deficiency leads to many erroneous detections, ragged boundaries, incorrect topological configurations and wrong shapes. To deal with these problems, we propose a new regularization method that learns shape and topological information from training data in a nonparametric way using high-order potentials. High-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher order potential defined over many variables is computationally infeasible. We use a compact representation of the potentials based on a finite set of patterns learned fromtraining data that, in turn, depends on the observations. Thanks to this representation, high-order potentials can be converted into pairwise potentials with some added auxiliary variables and minimized with tree-reweighted message passing (TRW) and belief propagation (BP) techniques. Both synthetic and real experiments confirm that our model fixes the errors of weaker approaches. Even with high-level regularization, perfect accuracy is still unattainable, and human editing of the segmentation results is necessary. The manual edition is tedious and cumbersome, and tools that assist the user are greatly appreciated. These tools need to be precise, but also fast enough to be used in real-time. Active contours are a good solution: they are good for precise boundary detection and, instead of finding a global solution, they provide a fine tuning to previously existing results. However, they require an implicit representation to deal with topological changes of the contour, and this leads to PDEs that are computationally costly to solve and may present numerical stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the contour evolution PDE by the successive application of a set of morphological operators defined on a binary level-set. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier than their PDE counterpart, since they do not require the use of sophisticated numerical algorithms. From a theoretical point of view, we delve into the connections between differential andmorphological operators, and introduce novel results in this area. We validate the approach providing amorphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.

Collision avoidance maneuver optimization

The paper presents a high accuracy fully analytical formulation to compute the miss distance and collision probability of two approaching objects following an impulsive collision avoidance maneuver. The formulation hinges on a linear relation between the applied impulse and the objects relative motion in the b-plane, which allows to formulate the maneuver optimization problem as an eigenvalue problem. The optimization criterion consists of minimizing the maneuver cost in terms of delta-V magnitude in order to either maximize collision miss distance or to minimize Gaussian collision probability. The algorithm, whose accuracy is verified in representative mission scenarios, can be employed for collision avoidance maneuver planning with reduced computational cost when compared to fully numerical algorithms.