Towards a covariant canonical formulation for closed topological defects without boundaries

On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We discuss the future extensions of the present results.Comment: LaTeX, 12 pages, submitted to Phys. Lett. B. (2002

Visibility Contractors: Application to Mobile Robot Localization

Visibility is studied and used in several fields: computer graphics, telecommunication, robotics... For instance, in Computer-aided design (CAD) synthesis images are created by simulating light propagation in a scene. Visibility notions are then necessary to compute the visible objects from a point of view, and the shadow of those objects. In mobile robotics the visibility is used for path planning (visibility graph) and localization problems. This presentation is about visibility information for mobile robot localization. The objective is twofold. First a visibility notion based on segment intersections is presented. By considering a set-membership approach it is possible to develop contractors associated to this visibility relation. Then two applications of those visibility contractors to mobile robot localization are presented. The first one corresponds to the pose tracking of a team of robots. The idea is to use a Boolean information (the visibility between two robots: two robots are visible or not) in order to avoid the drifting of those robots (in order to maintain the precision of their position estimations). The second application corresponds to the processing of an original constraint for a set-membership global localization algorithm. This global localization algorithm is based on a CSP approach (Constraint Satisfaction Problem). Adding a visibility constraint to this CSP improves the accuracy of the algorithm

Interpreting the photometry and spectroscopy of directly imaged planets: a new atmospheric model applied to beta Pictoris b and SPHERE observations

We aim to interpret future photometric and spectral measurements from these instruments, in terms of physical parameters of the planets, with an atmospheric model using a minimal number of assumptions and parameters. We developed Exoplanet Radiative-convective Equilibrium Model (Exo-REM) to analyze the photometric and spectro- scopic data of directly imaged planets. The input parameters are a planet's surface gravity (g), effective temperature (Teff ), and elemental composition. The model predicts the equilibrium temperature profile and mixing ratio profiles of the most important gases. Opacity sources include the H2-He collision-induced absorption and molecular lines from eight compounds (including CH4 updated with the Exomol line list). Absorption by iron and silicate cloud particles is added above the expected condensation levels with a fixed scale height and a given optical depth at some reference wavelength. Scattering was not included at this stage. We applied Exo-REM to photometric and spectral observations of the planet beta Pictoris b obtained in a series of near-IR filters. We derived Teff = 1550 +- 150 K, log(g) = 3.5 +- 1, and radius R = 1.76 +- 0.24 RJup (2-{\sigma} error bars from photometric measurements). These values are comparable to those found in the literature, although with more conservative error bars, consistent with the model accuracy. We were able to reproduce, within error bars, the J- and H-band spectra of beta Pictoris b. We finally investigated the precision to which the above parameterComment: 15 pages, 14 figures, accepted by A&

Interval Analysis for Kidnapping Problem using Range Sensors

This paper presents a new method to deal with thekidnapping problem of mobile robots. By using a range sensor and a discrete map of the indoor environment, the robot has to determine its pose (position and orientation). The idea is to obtain the smallest set of feasible poses compatible with the mesurements and the map. This method is a set membership approach based on interval analysis and constraint propagation, which allows to get results in a guaranteed way

Rigidity transitions and constraint counting in amorphous networks: beyond the mean-field approach

Subj-class: Disordered Systems and Neural NetworksComment: 12 pages, revtex, 3 figure

Model-based approach for fault diagnosis using set-membership formulation

This paper describes a robust model-based fault diagnosis approach that enables to enhance the sensitivity analysis of the residuals. A residual is a fault indicator generated from an analytical redundancy relation which is derived from the structural and causal properties of the signed bond graph model. The proposed approach is implemented in two stages. The first stage consists in computing the residuals using available input and measurements while the second level leads to moving horizon residuals enclosures according to an interval consistency technique. These enclosures are determined by solving a constraint satisfaction problem which requires to know the derivatives of measured outputs as well as their boundaries. A numerical differentiator is then proposed to estimate these derivatives while providing their intervals. Finally, an inclusion test is performed in order to detect a fault upon occurrence. The proposed approach is well suited to deal with different kinds of faults and its performances are demonstrated through experimental data of an omni-directional robot

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article physics/0410123. It includes new figures, equations and logical conten

The Lie-Poisson structure of the reduced n-body problem

The classical n-body problem in d-dimensional space is invariant under the Galilean symmetry group. We reduce by this symmetry group using the method of polynomial invariants. As a result we obtain a reduced system with a Lie-Poisson structure which is isomorphic to sp(2n-2), independently of d. The reduction preserves the natural form of the Hamiltonian as a sum of kinetic energy that depends on velocities only and a potential that depends on positions only. Hence we proceed to construct a Poisson integrator for the reduced n-body problem using a splitting method.Comment: 26 pages, 2 figure