Méthode de génération de colonnes pour les problèmes de conception de réseaux avec coûts d’ajout de capacité

Les problèmes de conception de réseaux ont reçu un intérêt particulier et ont été largement étudiés de par leurs nombreuses applications dans différents domaines, tels que les transports et les télécommunications. Nous nous intéressons dans ce mémoire au problème de conception de réseaux avec coûts d’ajout de capacité. Il s’agit d’installer un ensemble d’équipements sur un réseau en vue de satisfaire la demande, tout en respectant les contraintes de capacité, chaque arc pouvant admettre plusieurs équipements. L’objectif est de minimiser les coûts variables de transport des produits et les coûts fixes d’installation ou d’augmentation de capacité des équipements. La méthode que nous envisageons pour résoudre ce problème est basée sur les techniques utilisées en programmation linéaire en nombres entiers, notamment celles de génération de colonnes et de coupes. Ces méthodes sont introduites dans un algorithme général de branch-and-bound basé sur la relaxation linéaire. Nous avons testé notre méthode sur quatre groupes d’instances de tailles différentes, et nous l’avons comparée à CPLEX, qui constitue un des meilleurs solveurs permettant de résoudre des problèmes d’optimisation, ainsi qu’à une méthode existante dans la littérature combinant des méthodes exactes et heuristiques. Notre méthode a été plus performante que ces deux méthodes, notamment pour les instances de très grandes tailles.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

MAGNETOHYDRODYNAMIC SIMULATIONS OF RECONNECTION AND PARTICLE ACCELERATION: THREE-DIMENSIONAL EFFECTS

Magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first-order Fermi process. In this work we study the properties of particle acceleration inserted in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in magnetohydrodynamic (MHD) domains of reconnection without including kinetic effects, such as pressure anisotropy, the Hall term, or anomalous effects, increases exponentially. Also, the acceleration of the perpendicular component is always possible in such models. We find that within contracting magnetic islands or current sheets the particles accelerate predominantly through the first-order Fermi process, as previously described, while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients. Considering two-dimensional MHD models without a guide field, we find that the parallel acceleration stops at some level. This saturation effect is, however, removed in the presence of an out-of-plane guide field or in three-dimensional models. Therefore, we stress the importance of the guide field and fully three-dimensional studies for a complete understanding of the process of particle acceleration in astrophysical reconnection environments.

Hydrodynamical simulations of Galactic fountains - I. Evolution of single fountains

The ejection of the gas out of the disc in late-type galaxies is related to star formation and is due mainly to Type II supernovae. In this paper, we studied in detail the development of the Galactic fountains in order to understand their dynamical evolution and their influence on the redistribution of the freshly delivered metals over the disc. To this aim, we performed a number of 3D hydrodynamical radiative cooling simulations of the gas in the Milky Way where the whole Galaxy structure, the Galactic differential rotation and the supernova explosions generated by a single OB association are considered. A typical fountain powered by 100 Type II supernovae may eject material up to similar to 2 kpc which than collapses back mostly in the form of dense, cold clouds and filaments. The majority of the gas lifted up by the fountains falls back on the disc remaining within a radial distance Delta R = 0.5 kpc from the place where the fountain originated. This localized circulation of disc gas does not influence the radial chemical gradients on large scale, as required by the chemical models of the Milky Way which reproduce the metallicity distribution without invoking large fluxes of metals. Simulations of multiple fountains fuelled by Type II supernovae of different OB associations will be presented in a companion paper.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

Hydrodynamical simulations of Galactic fountains - II. Evolution of multiple fountains

The ejection of gas out of the disc in late-type galaxies is related to star formation and is mainly due to the explosion of Type II supernovae (SN II). In a previous paper, we considered the evolution of a single Galactic fountain, that is, a fountain powered by a single SN cluster. Using three-dimensional hydrodynamical simulations, we studied in detail the fountain flow and its dependence with several factors, such as the Galactic rotation, the distance to the Galactic centre and the presence of a hot gaseous halo. As a natural followup, this paper investigates the dynamical evolution of multiple generations of fountains generated by similar to 100 OB associations. We have considered the observed size-frequency distribution of young stellar clusters within the Galaxy in order to appropriately fuel the multiple fountains in our simulations. Most of the results of the previous paper have been confirmed, like for example the formation of intermediate velocity clouds above the disc by the multiple fountains. Also, this work confirms the localized nature of the fountain flows: the freshly ejected metals tend to fall back close to the same Galactocentric region where they are delivered. Therefore, the fountains do not change significantly the radial profile of the disc chemical abundance. The multiple fountain simulations also allowed us to consistently calculate the feedback of the star formation on the halo gas. We found that the hot gas gains about 10 per cent of all the SN II energy produced in the disc. Thus, the SN feedback more than compensate for the halo radiative losses and allow for a quasi steady-state disc-halo circulation to exist. Finally, we have also considered the possibility of mass infall from the intergalactic medium and its interaction with the clouds that are formed by the fountains. Though our simulations are not suitable to reproduce the slow rotational pattern that is typically observed in the haloes around the disc galaxies, they indicate that the presence of an external gas infall may help to slow down the rotation of the gas in the clouds and thus the amount of angular momentum that they transfer to the coronal gas, as previously suggested in the literature.

Cross-entropy optimizer: a new tool to study precession in astrophysical jets

Evidence of jet precession in many galactic and extragalactic sources has been reported in the literature. Much of this evidence is based on studies of the kinematics of the jet knots, which depends on the correct identification of the components to determine their respective proper motions and position angles on the plane of the sky. Identification problems related to fitting procedures, as well as observations poorly sampled in time, may influence the follow-up of the components in time, which consequently might contribute to a misinterpretation of the data. In order to deal with these limitations, we introduce a very powerful statistical tool to analyse jet precession: the cross-entropy method for continuous multi-extremal optimization. Only based on the raw data of the jet components (right ascension and declination offsets from the core), the cross-entropy method searches for the precession model parameters that better represent the data. In this work we present a large number of tests to validate this technique, using synthetic precessing jets built from a given set of precession parameters. With the aim of recovering these parameters, we applied the cross-entropy method to our precession model, varying exhaustively the quantities associated with the method. Our results have shown that even in the most challenging tests, the cross-entropy method was able to find the correct parameters within a 1 per cent level. Even for a non-precessing jet, our optimization method could point out successfully the lack of precession.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS: THE MAGNETIC FIELD GEOMETRY AND THE INFLUENCE OF THE WIND ON GIANT PLANET MIGRATION

By means of numerical simulations, we investigate magnetized stellar winds of pre-main-sequence stars. In particular, we analyze under which circumstances these stars will present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind. We show that the plasma-beta parameter (the ratio of thermal to magnetic energy densities) is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta(0) << 1. Using our self-consistent three-dimensional magnetohydrodynamics model, we estimate for these stellar winds the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter. In contrast to the findings of Lovelace et al., who estimated such timescales using the Weber and Davis model, our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on hot-Jupiters migration. Further simulations are necessary to investigate this result under more intense surface magnetic field strengths (similar to 2-3 kG) and higher coronal base densities, as well as in a tilted stellar magnetosphere.

MODELING VERY LONG BASELINE INTERFEROMETRIC IMAGES WITH THE CROSS-ENTROPY GLOBAL OPTIMIZATION TECHNIQUE

We present a new technique for obtaining model fittings to very long baseline interferometric images of astrophysical jets. The method minimizes a performance function proportional to the sum of the squared difference between the model and observed images. The model image is constructed by summing N(s) elliptical Gaussian sources characterized by six parameters: two-dimensional peak position, peak intensity, eccentricity, amplitude, and orientation angle of the major axis. We present results for the fitting of two main benchmark jets: the first constructed from three individual Gaussian sources, the second formed by five Gaussian sources. Both jets were analyzed by our cross-entropy technique in finite and infinite signal-to-noise regimes, the background noise chosen to mimic that found in interferometric radio maps. Those images were constructed to simulate most of the conditions encountered in interferometric images of active galactic nuclei. We show that the cross-entropy technique is capable of recovering the parameters of the sources with a similar accuracy to that obtained from the very traditional Astronomical Image Processing System Package task IMFIT when the image is relatively simple (e. g., few components). For more complex interferometric maps, our method displays superior performance in recovering the parameters of the jet components. Our methodology is also able to show quantitatively the number of individual components present in an image. An additional application of the cross-entropy technique to a real image of a BL Lac object is shown and discussed. Our results indicate that our cross-entropy model-fitting technique must be used in situations involving the analysis of complex emission regions having more than three sources, even though it is substantially slower than current model-fitting tasks (at least 10,000 times slower for a single processor, depending on the number of sources to be optimized). As in the case of any model fitting performed in the image plane, caution is required in analyzing images constructed from a poorly sampled (u, v) plane.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

SPH simulations of clumps formation by dissipative collisions of molecular clouds - II. Magnetic case

We performed computer simulations of interstellar cloud-cloud collisions using the three-dimensional smoothed particle magnetohydrodynamics method. In order to study the role of the magnetic field on the process of collision-triggered fragmentation, we focused our attention on head-on supersonic collisions between two identical spherical molecular-clouds. Two extreme configurations of the magnetic field were adopted: parallel and perpendicular to the initial clouds motion. The initial magnetic field strength was approximately 12.0 muG. In the parallel case, much more of the collision debris were retained in the shocking region than in the non-magnetic case where gas escaped freely throughout the symmetry plane. Differently from the non-magnetic case, eddy-like vortices were formed. The regions of highest vorticity and the the regions of highest density are offset. We found clumps formation only in the parallel case, however, they were larger, hotter and less dense than in the analogous non-magnetic case. In the perpendicular case, the compressed field works as a magnetic wall, preventing a stronger compression of the colliding clouds. This last effect inhibits direct contact of the two clouds. In both cases, we found that the field lines show a chaotic aspect in large scales. Also, the field magnitude is considerably amplified in the shock layer. However, the field distribution is almost coherent in the higher density regions.

SPH simulations of clumps formation by dissipative collision of molecular clouds - I. Non magnetic case

Computer experiments of interstellar cloud collisions were performed with a new smoothed-particle-hydrodynamics (SPH) code. The SPH quantities were calculated by using spatially adaptive smoothing lengths and the SPH fluid equations of motion were solved by means of a hierarchical multiple time-scale leapfrog. Such a combination of methods allows the code to deal with a large range of hydrodynamic quantities. A careful treatment of gas cooling by H, H(2), CO and H II, as well as a heating mechanism by cosmic rays and by H(2) production on grains surface, were also included in the code. The gas model reproduces approximately the typical environment of dark molecular clouds. The experiments were performed by impinging two dynamically identical spherical clouds onto each other with a relative velocity of 10 km s(-1) but with a different impact parameter for each case. Each object has an initial density profile obeying an r(-1)-law with a cutoff radius of 10 pc and with an initial temperature of 20 K. As a main result, cloud-cloud collision triggers fragmentation but in expense of a large amount of energy dissipated, which occurred in the head-on case only. Off-center collision did not allow remnants to fragment along the considered time (similar to 6 Myr). However, it dissipated a considerable amount of orbital energy. Structures as small as 0.1 pc, with densities of similar to 10(4) cm(-3), were observed in the more energetic collision.

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).