Geometric quantities associated to differential operators

in Communications in Algebra (2000), 28(2), 699-718

Denote by F_lambda the space of fields of tensor densities of weight -lambda over a manifold M. The space D^p_{lambda,mu} of differential operators of order at most p that map F_lambda onto F_mu are ... [more ▼]

Denote by F_lambda the space of fields of tensor densities of weight -lambda over a manifold M. The space D^p_{lambda,mu} of differential operators of order at most p that map F_lambda onto F_mu are modules over the Lie algebra of vector fields Vect(M). We compute all the Vect(M)-invariant mappings from D^p_{lambda,mu} onto F_nu. [less ▲]

Geometrical considerations for evaluation of reserve design.

in Web Ecology (2001), (2), 65-70

Geometrical Effects on the Dynamical Behavior of MEMS structures

(2010, May 16)

The influence of geometrical dimensions on the dynamical behavior of polysilicon MEMS structures configurations is studied and presented in this paper. Electrostatically actuated MEMS components as ... [more ▼]

The influence of geometrical dimensions on the dynamical behavior of polysilicon MEMS structures configurations is studied and presented in this paper. Electrostatically actuated MEMS components as microbridges and microcantilevers are used to investigate the coupled electro-mechanic effect, frequency responses and the dynamic bending stress. The electrostatic principle is common in sensing and acting devices and there are many MEMS structures subjected to electrostatic forces. [less ▲]

Geometrical Validity of Curvilinear Finite Elements

in William Roshan, Quadros (Ed.) Proceedings of the 20th International Meshing Roundtable (2011, October 25)

Geometrically non linear analysis of steel Storage racks submitted to earthquake loading

in International Journal of Structural Stability & Dynamics (2011), 11(5), 949-967

Steel storage racks are light and flexible structures. When submitted to earthquake loading, they can exhibit very large transverse displacements and are thus prone to significant consequences of second ... [more ▼]

Steel storage racks are light and flexible structures. When submitted to earthquake loading, they can exhibit very large transverse displacements and are thus prone to significant consequences of second-order geometrical effects. In the context of the drafting of European recommendations for the design of steel pallet racks for their seismic resistance, this paper presents a parameter study comparing the various methods commonly used in practice for analyzing the seismic structural behavior of racks (i.e. "modal response spectrum analysis" and "lateral force method analysis") as well as the different ways to account for geometrically nonlinear effects in these conventional methods of analysis in the case of structures designed for low ductility. [less ▲]

La géométrie de la spatiocarte : corrections et validations, Spatiocartographie

in Société géographique de Liège (2000), (38(1)), 25-43

Géométrie des matrices positives semi-définies de rang fixé : un peu de théorie et beaucoup d’applications

in Proceedings of Sixième Conférence Internationale Francophone d'Automatique (CIFA 2010) (2010, June)

Cet article est une introduction au calcul et `a l’optimisation sur les matrices sym´etriques positives semid ´efinies de rang (faible) fix´e. L’approche propos´ee est bas´ee sur deux g´eom´etries ... [more ▼]

Cet article est une introduction au calcul et `a l’optimisation sur les matrices sym´etriques positives semid ´efinies de rang (faible) fix´e. L’approche propos´ee est bas´ee sur deux g´eom´etries riemanniennes quotient, qui permettent de calculer efficacement tout en pr´eservant le rang et le caract` ere positif des matrices consid´er´ees. Le champ d’applications est vaste, et l’article survole quelques d´eveloppements r´ecents qui illustrent l’int´erˆet de l’approche consid´er´ee dans les probl`emes de tr`es grande taille rencontr´es en contrˆole, statistiques, et apprentissage. [less ▲]

Geometry and Symmetries in Coordination Control

Doctoral thesis (2009)

The present dissertation studies specific issues related to the coordination of a set of “agents” evolving on a nonlinear manifold, more particularly a homogeneous manifold or a Lie group. The viewpoint is ... [more ▼]

The present dissertation studies specific issues related to the coordination of a set of “agents” evolving on a nonlinear manifold, more particularly a homogeneous manifold or a Lie group. The viewpoint is somewhere between control algorithm design and system analysis, as algorithms are derived from simple principles — often retrieving existing models — to highlight specific behaviors. With a fair amount of approximation, the objective of the dissertation can be summarized by the following question: Given a swarm of identical agents evolving on a nonlinear, nonconvex configuration space with high symmetry, how can you define specific collective behavior, and how can you design individual agent control laws to get a collective behavior, without introducing hierarchy nor external reference points that would break the symmetry of the configuration space? Maintaining the basic symmetries of the coordination problem lies at the heart of the contributions. The main focus is on the global geometric invariance of the configuration space. This contrasts with most existing work on coordination, where either the agents evolve on vector spaces — which, to some extent, can cover local behavior on manifolds — or coordination is coupled to external reference tracking such that the reference can serve as a beacon around which the geometry is distorted towards vector space-like properties. A second, more standard symmetry is to treat all agents identically. Another basic ingredient of the coordination problem that has important implications in this dissertation is the reduced agent interconnectivity: each agent only gets information from a limited set of other agents, which can be varying. In order to focus on issues related to geometry / symmetry and reduced interconnectivity, individual agent dynamics are drastically simplified to simple integrators. This is justified at a “planning” level. Making the step towards realistic dynamics is illustrated for the specific case of rigid body attitude synchronization. The main contributions of this dissertation are I. an extensive study of synchronization on the circle, (a) highlighting difficulties encountered for coordination and (b) proposing simple strategies to overcome these difficulties; II. (a) a geometric definition and related control law for “consensus” configurations on compact homogeneous manifolds, of which synchronization — all agents at the same point — is a special case, and (b) control laws to (almost) globally reach synchronization and “balancing”, its opposite, under general interconnectivity conditions; III. several propositions for rigid body attitude synchronization under mechanical dynamics; IV. a geometric framework for “coordinated motion” on Lie groups, (a) giving a geometric definition of coordinated motion and investigating its implications, and (b) providing systematic methods to design control laws for coordinated motion. Examples treated for illustration of the theoretical concepts are the circle S^1 (sometimes the sphere S^n ), the rotation group SO(n), the rigid-body motion groups SE(2) and SE(3) and the Grassmann manifolds Grass(p,n). The developments in this dissertation remain at a rather theoretical level; potential applications are briefly discussed. [less ▲]

Geometry of the mass-outflows around broad absorption line QSOs and formation of the complex Ly-alpha + N V line profile

in Astronomy and Astrophysics (1987), 177

The possibility that the observed broad absorption line (BAL) profiles are formed in spherically symmetric atmospheres is investigated, and it is found that BAL and non-BAL QSOs form two distinct classes ... [more ▼]

The possibility that the observed broad absorption line (BAL) profiles are formed in spherically symmetric atmospheres is investigated, and it is found that BAL and non-BAL QSOs form two distinct classes of quasars. It is shown that the small residual intensity and large equivalent width noted for some absorption troughs may be reproduced by the resonance scattering of line photons across spherically symmetric BAL regions. N V emission strength is found to be higher in the spectrum of BAL QSOs than in that of non-BAL QSOs. Good agreement between theory and the observed attenuation of the Ly-alpha emission line, the observed enhancement of the N V emission strength, and the possible presence of a shoulderlike feature in the red wing of the N V emission profile is obtained. [less ▲]

Géomorphologie du milieu littoral et aménagement

in Fierro, Giuliano (Ed.) MED PICTURE : Mediterranean Project for the Improvement of Cooperation in Training between Universities, Regions and Enterprises (2002)