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See detailRelativité générale
De Rop, Yves ULg

Learning material (2014)

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See detailLes pavages réguliers du plan
De Rop, Yves ULg

Learning material (2012)

La classification des pavages réguliers du plan, connue depuis Fedorov (1891), permet d'illustrer d'importantes structures algébriques (notions de groupe discret, groupe quotient, produit semi-direct ... [more ▼]

La classification des pavages réguliers du plan, connue depuis Fedorov (1891), permet d'illustrer d'importantes structures algébriques (notions de groupe discret, groupe quotient, produit semi-direct, groupe symorphique). Elle constitue aussi une introduction à la cristallographie. Nous établissons cette classification en sollicitant au maximum l'intuition du lecteur. Une brève annexe justifie les développements mathématiques essentiels. Public visé : étudiants en fin de cycle secondaire, intéressés par les arts et les mathématiques. [less ▲]

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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 detailQu'est-ce que la relativité générale?
De Rop, Yves ULg

Article for general public (2009)

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See detailRelativité générale II
De Rop, Yves ULg

Learning material (2008)

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See detailLes ondes gravitationnelles
De Rop, Yves ULg

in Revue des Questions Scientifiques (2007), 178(1), 113-138

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See detailQSO 2237+0305 VR light curves from Gravitational Lenses International Time Project optical monitoring
Alcalde, D.; Mediavilla, E.; Moreau, O. et al

in Astrophysical Journal (2002), 572(2, Part 1), 729-734

We present VR observations of QSO 2237+ 0305 conducted by the Gravitational Lensing International Time Project collaboration from 1999 October 1 to 2000 February 3. The observations were made with the 2 ... [more ▼]

We present VR observations of QSO 2237+ 0305 conducted by the Gravitational Lensing International Time Project collaboration from 1999 October 1 to 2000 February 3. The observations were made with the 2.56 m Nordic Optical Telescope at Roque de los Muchachos Observatory, La Palma ( Spain). The pointspread function ( PSF) fitting method and an adapted version of the ISIS subtraction method have been used to derive the VR light curves of the four components ( A D) of the quasar. The mean errors range in the intervals 0.01-0.04 mag ( PSF fitting) and 0.01-0.02 mag ( ISIS subtraction), with the faintest component ( D) having the largest uncertainties. We address the relatively good agreement between the A and D light curves derived using different filters, photometric techniques, and telescopes. The new VR light curves of component A extend the time coverage of a high-magnification microlensing peak, which was discovered by the OGLE team. [less ▲]

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See detailLa précession du plan d'oscillation du pendule de Foucault : une approche géométrique intuitive
De Rop, Yves ULg; Moreau, Olivier

in Revue des Questions Scientifiques (2002), 173(3), 261-276

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See detailQuelques réflexions de nature didactique concernant l'introduction de la courbure en relativité générale
De Rop, Yves ULg

in Revue des Questions Scientifiques (2001), 172(4), 335-346

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See detailAlbert Einstein et la physique théorique
De Rop, Yves ULg

Article for general public (1997)

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See detailÀ propos de la loi fondamentale de la dynamique
De Rop, Yves ULg

Article for general public (1994)

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See detailIsaac Newton
De Rop, Yves ULg

Article for general public (1994)

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See detailMixmaster universe in fourth-order gravity theories
Cotsakis, S.; Demaret, Jacques; De Rop, Yves ULg et al

in Physical Review. D : Particles and Fields (1993), 48

We analyze the behavior of the Bianchi type-IX cosmological model in the full fourth-order theory of gravity in four space-time dimensions on approach to the singularity both analytically and numerically ... [more ▼]

We analyze the behavior of the Bianchi type-IX cosmological model in the full fourth-order theory of gravity in four space-time dimensions on approach to the singularity both analytically and numerically. By directly analyzing the full fourth-order field equations we prove explicitly that the Belinski-Khalatnikov-Lifshitz (BKL) analytic solution (and the accompanying bounce law) is also a solution to the more general case that we consider. But it appears to be nongeneric, because a perturbation analysis shows that power-law Kasner asymptotes are unstable on approach to the singularity. On the other hand, we find that the model possesses a stable isotropic monotonic power-law asymptotic solution and accordingly we show that there is a general solution which is nonchaotic near the space-time singularity. Numerical experiments confirm the existence of such a behavior. The inclusion of matter fields does not alter the evolution in the neighborhood of the singularity. The role of space-time dimensionality on the chaotic evolution of the mixmaster universe in these theories is also spelled out. In particular, we show that it is impossible to build a mixmaster universe in space-time dimensions higher than four in the full fourth-order gravity theory based on the BKL approximation scheme. [less ▲]

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See detailThe fractal nature of the power spectrum as an indicator of chaos in the Bianchi-IX cosmological model
Demaret, Jacques; De Rop, Yves ULg

in Physics Letters B (1993), 299(3-4), 223-228

Using two different methods, we compute the fractal dimension of the power spectrum associated with numerical solutions of the spatially homogeneous Bianchi IX cosmological model in Misner-Chitre ... [more ▼]

Using two different methods, we compute the fractal dimension of the power spectrum associated with numerical solutions of the spatially homogeneous Bianchi IX cosmological model in Misner-Chitre coordinates. According to Perdang's criterion, the noninteger character of this dimension is reflection of chaos and can be used to measure it, in the same spirit as the Lyapunov exponent of the Kolmogorov entropy. The results obtained indicate the chaotic nature of the behaviour of the Bianchi IX model near the cosmological singularity. [less ▲]

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See detailAutour du pendule de Foucault
Barsics, Joseph; De Rop, Yves ULg; Lausberg, André ULg et al

in Liege: Societe Astronomique de Liege (SAL), |c1993 (1993)

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See detailQualitative analysis of ten-dimensional lovelock cosmological models
Demaret, Jacques; De Rop, Yves ULg; Tombal, P. et al

in General Relativity & Gravitation (1992), 24

The Einstein-like field equations obtained from the variation of a Lagrangian containing linear, quadratic (Gauss-Bonnet) and quartic terms for a ten-dimensional cosmological model cannot be solved ... [more ▼]

The Einstein-like field equations obtained from the variation of a Lagrangian containing linear, quadratic (Gauss-Bonnet) and quartic terms for a ten-dimensional cosmological model cannot be solved analytically. However, we can reduce them to a system of dynamical equations for the “Hubble parameters”. The study of the mathematical properties of the fixed points of this system gives a qualitative picture of the behaviour of a class of possible solutions. The inclusion of a quartic term generates an extremely rich structure for the corresponding dynamical system. Some solutions are shown to exhibit the interesting property of dimensional reduction, which has been proposed as a possible explanation of the three-dimensional character of our universe. [less ▲]

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See detailGalilée et la naissance de la science moderne
De Rop, Yves ULg

Article for general public (1992)

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See detailQualitative approach of the general vacuum Bianchi VI and VII cosmological models near the singularity
De Rop, Yves ULg

in General Relativity & Gravitation (1989), 21

We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that ... [more ▼]

We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that the Kasnerian metric is a general solution for these models in the neighborhood of the initial singularity. Then, using a method developed by Jantzen, we reduce the field equations to a nonautonomous system of order two. A numerical integration leads to the explicit four-parameter asymptotic form of a general solution, which is indeed Kasnerian in the canonical invariant basis. [less ▲]

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See detailAre Kaluza-Klein models of the universe chaotic?
Demaret, Jacques; De Rop, Yves ULg; Henneaux, Marc

in International Journal of Theoretical Physics (1989), 28

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions ≥ 11, the ... [more ▼]

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions ≥ 11, the generalized Kasner solution, with monotonic power-law behavior of the spatial distances, becomes a general solution of the Einstein vacuum field equations and that, moreover, the chaotic oscillatory behavior disappears. On the other hand, the chaotic oscillatory behavior, absent in diagonal spatially homogeneous cosmological models in space-time dimensions between 5 and 10, can be reestablished when off-diagonal terms are included. [less ▲]

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See detailUsing EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies.
De Rop, Yves ULg; Demaret, Jacques

in General Relativity & Gravitation (1988), 20

The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models ... [more ▼]

The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models, making use of the time-dependent automorphisms of the Lie algebra, it is possible to obtain a compact form of Einstein's field equations for general models of this type. The explicit expression of the equations, obtained with the help of EXCALC2, is given here for two nondiagonal five-dimensional spatially homogeneous models, namely G[SUB]1[/SUB] and G[SUB]8[/SUB]. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G[SUB]1[/SUB], while model G[SUB]8[/SUB] exhibits a monotonous kasnerian mode of approach to the initial singularity. [less ▲]

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