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Peer Reviewed
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)

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See detailGeometry of the mass-outflows around broad absorption line QSOs and formation of the complex Ly-alpha + N V line profile
Surdej, Jean ULg; Hutsemekers, Damien ULg

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 ▲]

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See detailThe geometry of the quadruply imaged quasar PG 1115+080: implications for H_0_.
Courbin, F.; Magain, Pierre ULg; Keeton, C. R. et al

in Astronomy and Astrophysics (1997), 324

Time delay measurements have recently been reported for the lensed quasar PG 1115+080. These measurements can be used to derive H_0_, but only if we can constrain the lensing potential. We have applied a ... [more ▼]

Time delay measurements have recently been reported for the lensed quasar PG 1115+080. These measurements can be used to derive H_0_, but only if we can constrain the lensing potential. We have applied a recently developed deconvolution technique to analyze sub-arcsecond I band images of PG 1115+080, obtained at the Nordic Optical Telescope (NOT) and the Canada France Hawaii Telescope (CFHT). The high performance of the deconvolution code allows us to derive precise positions and magnitudes for the four lensed images of the quasar, as well as for the lensing galaxy. The new measurement of the galaxy position improves its precision by a factor of 3 and thus strengthens the constraints on the lensing potential. With the new data, a range of models incorporating some of the plausible systematic uncertainties yields H_0_=53^+10^_-7_km/s/Mpc. [less ▲]

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See detailGéomorphologie du milieu littoral et aménagement
Ozer, André ULg; Ozer, Pierre ULg

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

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See detailGeomorphology of streams and rivers
Bravard, J. P.; Petit, François ULg

in Encyclopedia of Inland Waters (2009)

Detailed reference viewed: 62 (18 ULg)
Peer Reviewed
See detailGeophysical characterisation of a former waste disposal site in the context of landfill mining
Dumont, Gaël ULg; Robert, Tanguy ULg; Pilawski, Tamara et al

in EarthDoc - Near Surface Geoscience 2013 – 19th European Meeting of Environmental and Engineering Geophysics (2013, September 11)

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See detailGeophysical identification, characterization, and monitoring of preferential groundwater flow paths in fractured media
Robert, Tanguy ULg

Doctoral thesis (2012)

This thesis investigates fractured zones leading to preferential groundwater flow paths. In this context, we used the electrical resistivity tomography (ERT) and the self-potential (SP) methods to ... [more ▼]

This thesis investigates fractured zones leading to preferential groundwater flow paths. In this context, we used the electrical resistivity tomography (ERT) and the self-potential (SP) methods to identify, characterize, monitor, and finally model preferential flow in hydraulically-active fractured zones at a scale representative of real world applications. From an experimental point of view, we first identified the magnitude of self-potential signature, a -15 mV anomaly that could be associated with preferential groundwater flow in a shallow quartzite aquitard whereas the streaming potential theory was originally developed for porous media. This signature was confirmed experimentally in limestone aquifers at greater depths. The joint use of surface ERT and SP allowed the identification of water-bearing fractured areas which were electrically more conductive, presenting contrasts from 1 to 10 and which were hydraulically-active presenting negative SP anomalies ranging from -10 to -30 mV. We were also able to correlate hydraulic heads and SP gradients during a low and a high groundwater level period leading to interesting perspectives in understanding the dynamics of complex groundwater flow systems. Finally, a preferential flow and rapid transport path, over 10 m/h, was highlighted in a 20 m deep fractured and karstified limestone valley by monitoring a salt tracer test with only surface ERT. This methodology was being mostly used for relatively shallow and homogeneous aquifers up to now. Such information is crucial to set up new monitoring wells or to define the sampling rates of classic tracer test. From a methodological point of view, we quantitatively assessed the efficiency of blocky and minimum-gradient-support regularizations in electrical imaging to recover sharp interfaces on numerical benchmarks and with field data. The usefulness of resolution indicators such as the cumulative sensitivity matrix and the resolution matrix were also assessed in this context. We demonstrated that noise characterization is crucial in time-lapse inversion and may supplant the choice of the time-lapse inversion scheme, calling for a systematic analysis of reciprocal measurements (or a subset of them). We also showed that, when using data differences in an inversion scheme, the data error, as estimated by time-lapse reciprocal measurements, depends on the mean measured resistance. These error characterization studies should always be performed if one wants to avoid wrong interpretations about the hydrodynamics. We further showed that focused inversion techniques (blocky inversion, minimum-gradient-support) may offer great perspectives when recovering model changes in time-lapse inversion. Finally, ERT and SP were jointly used to conceptualize a physically-based and spatially distributed hydrogeological model, in particular to characterize the preferential flow paths. Predicted hydraulic heads and SP-derived hydraulic heads using the water table model showed a clear correlation, leading to perspectives in terms of hydrogeological model calibration. Further experiments are however needed to fully estimate the streaming potential apparent coupling coefficient, but the use of the full SP signals for hydrogeological model calibration is a clear perspective to this work. [less ▲]

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See detailGeophysical investigation and numerical modelling of unstable slopes: case-study of Kainama (Kyrgyzstan)
Danneels, Gaëlle ULg; Bourdeau, Céline ULg; Torgoev, I. et al

in Geophysical Journal International (2008), 175

The presence of massive Quaternary loess units at the eastern border of the Fergana Basin (Kyrgyzstan, Central Asia) makes this area particularly prone to the development of catastrophic loess earthflows ... [more ▼]

The presence of massive Quaternary loess units at the eastern border of the Fergana Basin (Kyrgyzstan, Central Asia) makes this area particularly prone to the development of catastrophic loess earthflows, causing damages and injuries almost every year. Efficient disaster management requires a good understanding of the main causes of these mass movements, that is, increased groundwater pressure and seismic shaking. This paper focuses on the Kainama earthflow, mainly composed of loess, which occurred in 2004 April. Its high velocity and the long run-out zone caused the destruction of 12 houses and the death of 33 people. In summer 2005, a field survey consisting of geophysical and seismological measurements was carried out along the adjacent slope. By combination and geostatistical analysis of these data, a reliable 3-D model of the geometry and properties of the subsurface layers, as shown in the first part of the paper, was created. The analysis of the seismological data allowed us to point out a correlation between the thickness of the loess cover and the measured resonance frequencies and associated amplification potential. The second part of this paper is focused on the study of the seismic response of the slope by numerical simulations, using a 2-D finite difference code named FLAC.Modelling of the seismic amplification potential along the slope confirmed the results obtained from the seismological survey—strong amplifications at the crest and bottom of the slope where there is a thick loess cover and almost no amplification in the middle part of the slope. Furthermore, dynamic slope stability analyses were conducted to assess the influence of local amplifications and increased groundwater pressures on the slope failure. The results of the dynamic modelling, although preliminary, show that a combination of seismic and hydrologic origin (pore pressure build-up during the seismic shaking) is the most probable scenario responsible for the 2004 failure. [less ▲]

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See detailGEOPHYSICAL INVESTIGATIONS OF SEISMICALLY INDUCED SURFACE EFFECTS: CASE STUDY OF A LANDSLIDE IN THE SUUSAMYR VALLEY, KYRGYZSTAN
Havenith, Hans-Balder ULg; Jongmans, D.; Abdrakhmatov, K. et al

in Surveys in Geophysics (2000), 21

In summer 1998, a geophysical survey including seismic profiles and electrical tomography has been carried out in the Suusamyr valley, Kyrgyzstan. The scope was to investigate surface effects induced by ... [more ▼]

In summer 1998, a geophysical survey including seismic profiles and electrical tomography has been carried out in the Suusamyr valley, Kyrgyzstan. The scope was to investigate surface effects induced by the Ms = 7.3 Suusamyr earthquake, the 19th of August, 1992. In this paper, special attention is paid to the case study of a debris slide triggered by the earthquake. Seismic data are analysed by P-wave refraction technique and by surface wave inversion. Electrical tomographic profiles are processed by 2D-inversion. Using geotechnical and geological information, P-velocity models and resistivity sections are interpreted in terms of geological materials, in order to build a geological 3D model. On the basis of the latter, we carried out static finite element computations as well as static and pseudo-static calculations with Janbu’s method. Newmark displacement was computed, considering or not the influence of the shallow soft deposits. The results are compared to the real displacement observed in the field and conclusions are drawn about the mechanism of the landslide. [less ▲]

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