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See detailGeometric Study of Mixed-integer Sets from Two Rows of Two Adjacent Simplex Bases
Louveaux, Quentin ULg

Conference (2009, August)

We generalize the study of sets arising from two rows of a simplex tableau by considering bounds on the nonbasic variables. We show that new classes of facets arise that cannot be obtained from triangles ... [more ▼]

We generalize the study of sets arising from two rows of a simplex tableau by considering bounds on the nonbasic variables. We show that new classes of facets arise that cannot be obtained from triangles and quadrilaterals. Specifically, when exactly one upper bound on a non-basic variable is introduced, inequalities that can be derived from pentagons involving up to six variables also appear. [less ▲]

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See detailA Geometrical Acoustics Approach Linking Surface Scattering and Reverberation in Room Acoustics
Embrechts, Jean-Jacques ULg

in Acta Acustica United with Acustica (2014), 100(5), 864-879

A general model of the influence of surface scattering on the reverberation time would have several applications in room acoustics. Such a model is not yet available, and it is the purpose of this paper ... [more ▼]

A general model of the influence of surface scattering on the reverberation time would have several applications in room acoustics. Such a model is not yet available, and it is the purpose of this paper to investigate a geometrical acoustics approach. Starting from the radiative transfer equation, an exponential solution is first developed for the reverberation energy decay in rooms with diffusely reflecting boundaries. Differences with the diffuse sound field (Sabine) theory are highlighted, leading to a modified formula for the reverberation time which is shown to be more in accordance with ray tracing simulations. A general model is then proposed for rooms in which specular and diffuse reflections coexist. This general model is applied in rooms where the specular contribution can be assumed to be quasi-isotropic and uniform. Under this assumption, the reverberation decay is represented by the sum of two exponential functions, depending on the scattering coefficients. However, it is shown that the influence of surfaces’ scattering on reverberation is rather limited in this case. On the contrary, rooms with a pair of parallel surfaces are prone to create significant anisotropy in the cloud of image sources. An analytical formulation is proposed in this case for the specular and diffuse contributions, provided that some assumptions are again made on the specularly reflected sound field. The final expression is not really intuitive concerning the relation between scattering coefficients and reverberation, but it contains all the variables influencing this relation. This allows fast evaluations of the effect of surface scattering in particular situations. Finally, the application of this model to room acoustics computer simulations is illustrated by an example. [less ▲]

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See detailGeometrical approach to the proton spin decomposition
Lorce, Cédric ULg

in Physical Review. D, Particles, Fields, Gravitation, and Cosmology (2013), D87

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition ... [more ▼]

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of this approach follows from a mechanism similar to the one used in the famous Stueckelberg trick. Stressing the fact that the Lorentz symmetry does not force the gauge potential to transform as a Lorentz four-vector, we show that the Chen et al. approach is Lorentz covariant provided that one uses the suitable Lorentz transformation law. We also make an attempt to summarize the present situation concerning the proton spin decomposition. We argue that the ongoing debates concern essentially the physical interpretation and are because of the plurality of the adopted pictures. We discuss these different pictures and propose a pragmatic point of view. [less ▲]

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See detailGeometrical considerations for evaluation of reserve design.
Bogaert, Jan ULg; Salvador-Van Eysenrode, D; Van Hecke, P et al

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

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See detailGeometrical CP violation in the N-Higgs-doublet model
Ivanov, Igor ULg; Lavoura, Luis

in European Physical Journal C -- Particles & Fields (2013), 73

Geometrical CP violation is a particular type of spontaneous CP violation in which the vacuum expectation values have phases which are calculable, i.e. stable against the variation of the free parameters ... [more ▼]

Geometrical CP violation is a particular type of spontaneous CP violation in which the vacuum expectation values have phases which are calculable, i.e. stable against the variation of the free parameters of the scalar potential. Although originally suggested within a specific version of the three-Higgs-doublet model, it is a generic phenomenon. We investigate its viability and characteristic features in models with several Higgs doublets. Our work contains both general results and illustrative examples. [less ▲]

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See detailGeometrical Effects on the Dynamical Behavior of MEMS structures
Pustan, Marius ULg; Golinval, Jean-Claude ULg; Rochus, Véronique ULg

(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 ▲]

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See detailGeometrical guidance and trapping transition of human sperm cells
Guidobaldi, Alejandro; Jeyaram, Yogesh; Berdakin, Ivan et al

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2014), 89

The guidance of human sperm cells under con finement in quasi 2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations ... [more ▼]

The guidance of human sperm cells under con finement in quasi 2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations are performed with diluted sperm populations, for which eff ects of geometrical guidance and concentration are studied in detail. In particular, a trapping transition at convex angular wall features is identi ed and analyzed. We also show that highly efficient microratchets can be fabricated by using curved asymmetric obstacles to take advantage of the spermatozoa specifi c swimming strategy. [less ▲]

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See detailGeometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, J.-F.; Geuzaine, Christophe ULg

in Journal of Computational Physics (2013), 233

In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid ... [more ▼]

In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the distortion of curvilinear elements. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using B ́ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

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See detailGeometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, Jean-François; Geuzaine, Christophe ULg

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

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See detailGeometrical validity of high-order pyramidal finite elements
Johnen, Amaury ULg; Geuzaine, Christophe ULg

Conference (2014, July 24)

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See detailGeometrical Validity of High-Order Triangular Finite Elements
Johnen, Amaury ULg; Remacle, Jean-François; Geuzaine, Christophe ULg

in Engineering with Computers (2012)

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is ... [more ▼]

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an e cient way to measure the quality the triangles. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using B ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

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See detailGeometrically exact beam finite element formulated on the special Euclidean group SE(3)
Sonneville, Valentin ULg; Cardona, Alberto; Bruls, Olivier ULg

in Computer Methods in Applied Mechanics & Engineering (2014), 268

This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this ... [more ▼]

This paper describes a dynamic formulation of a straight beam finite element in the setting of the special Euclidean group SE(3). First, the static and dynamic equilibrium equations are derived in this framework from variational principles. Then, a non-linear interpolation formula using the exponential map is introduced. It is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables. Next, the discretized internal and inertia forces are developed. The semi-discrete equations of motion take the form of a second-order ordinary differential equation on a Lie group, which is solved using a Lie group time integration scheme. It is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed Lie group framework leads to a compact and easy-to-implement formulation. Some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. For instance, the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element. The proposed formulation is successfully tested in several numerical static and dynamic examples. [less ▲]

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See detailGeometrically non linear analysis of steel Storage racks submitted to earthquake loading
Degée, Hervé ULg; Rossi, Barbara ULg; Jehin, Denis

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 ▲]

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See detailGeometrically non linear dynamic behavior of steel storage racks subjected to earthquake loading
Degée, Hervé ULg; Dufoing, C.; Jehin, D.

in Proceedings of the ESMC 2009 Conference (2009)

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See detailLa géométrie de la spatiocarte : corrections et validations, Spatiocartographie
Cornélis, Bernard; Billen, Roland ULg

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

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See detailLa géométrie de Lobachevski
De Rop, Yves ULg; Sprimont, Pierre-Guillaume

E-print/Working paper (2011)

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See detailGéométrie des matrices positives semi-définies de rang fixé : un peu de théorie et beaucoup d’applications
Sepulchre, Rodolphe ULg; Absil, Pierre-Antoine; Bonnabel, Silvère

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 ▲]

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See detailGéométrie et géométrie analytique
Belligoi, Thomas

Learning material (2011)

L’étudiant préparant l’examen d’admission trouvera dans ces notes des notions qu’il est important de maîtriser pour aborder l’examen de géométrie et géométrie analytique et, plus largement, le cours de ... [more ▼]

L’étudiant préparant l’examen d’admission trouvera dans ces notes des notions qu’il est important de maîtriser pour aborder l’examen de géométrie et géométrie analytique et, plus largement, le cours de géométrie de premier bachelier. [less ▲]

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See detailGeometry and Symmetries in Coordination Control
Sarlette, Alain ULg

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 ▲]

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See detailGeometry module for next-generation computational electromagnetics software
Geuzaine, Christophe ULg

in Proceedings of the 4th Advanced Computational Electromagnetics workshop (2009, January 13)

Detailed reference viewed: 5 (0 ULg)