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Peer Reviewed
See detailDiscrete Harmonic Oscillator: A Short Compendium of Formulas
Antippa, Adel F.; Dubois, Daniel ULg

in Dubois, Daniel (Ed.) COMPUTING ANTICIPATORY SYSTEMS (2010)

Since 2002, we have, in seven papers, studied the problem of the discrete harmonic oscillator, analytically, numerically, and graphically, and made progress on a number of fronts. We identified the ... [more ▼]

Since 2002, we have, in seven papers, studied the problem of the discrete harmonic oscillator, analytically, numerically, and graphically, and made progress on a number of fronts. We identified the natural frequency of oscillation of the dual incursive oscillators, studied the system bifurcation generated by incursive discretization, and the frequency dependent correlation between the resulting incursive oscillators. We also studied the synchronization of the discretizing time interval with the frequency of oscillation. From this analysis there emerged a nonlinear (or more precisely bilinear) formalism that is perfectly stable at all time scales, and fully conserves the total energy of the system. The formalism is applicable to the discrete harmonic oscillator specifically, and to discrete Hamiltonian systems in general. In retrospect the important themes and crucial steps can more easily be identified, and this is the purpose of this short note. In it we give, in a unified notation, a short compendium of the key formulas. This summary can serve as a guide for navigating through the seven papers, as well as a practical concise manual for using the formalism. [less ▲]

Detailed reference viewed: 35 (1 ULg)
Peer Reviewed
See detailDiscrete Harmonic Oscillator: Evolution of Notation and Cumulative Erratum
Antippa, Adel F.; Dubois, Daniel ULg

in Dubois, Daniel (Ed.) COMPUTING ANTICIPATORY SYSTEMS (2010)

As the project on the discrete harmonic oscillator advanced, the notation evolved in parallel with our understanding of the problem, and it became progressively clear that a change of notation concerning ... [more ▼]

As the project on the discrete harmonic oscillator advanced, the notation evolved in parallel with our understanding of the problem, and it became progressively clear that a change of notation concerning the natural angular frequency of oscillation of the system, and related parameters, was required in order to conform to the spirit of the physics being developed. Specifically the notation needed to reflect the fact that the discrete harmonic oscillator is the more general entity, with the continuous harmonic oscillator being a special (and to some extent unrealistic) limiting case corresponding to dt-->0, where dt is the discretizing time interval. Furthermore, as the discrete nature of time (and eventually space), incursion (anticipation), system bifurcation, hyperincursion, frequency dependent correlation, and synchronization, where progressively integrated into the fabric of the discretizing algorithm, a new discrete, perfectly stable and energy conserving, formalism emerged, and with it evolved, in parallel, the expression for the total energy. In this short note we will focus on the evolution, throughout the project, of the notation for frequency, and the expression for the discrete total energy. We also provide a cumulative erratum for the seven papers in the project so far, as well as a table summarizing the evolution of the notation for the angular frequency and related parameters. [less ▲]

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See detailDiscrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems
Wallek, Thomas; Pfleger, Martin; Pfennig, Andreas ULg

in Industrial & Engineering Chemistry Research (2016), 55(8), 2483-2492

Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamic models that can describe fluid-phase behavior. While previous papers have focused on reviewing its ... [more ▼]

Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamic models that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background and application to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models for strongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approach is based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete local compositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of its partition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement to systems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis for introducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibrium distribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to those derived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that this applicability of discrete modeling to systems of finite size suggests new possibilities for model development. [less ▲]

Detailed reference viewed: 9 (4 ULg)
Peer Reviewed
See detailDiscrete Modeling: The Concept of Shannon Entropy used for Thermodynamic Model Development
Wallek, Thomas; Pfleger, Martin; Pfennig, Andreas ULg

Conference (2016, August)

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See detailDiscrete Modeling: Thermidynamics Based on Shannon Entropy and Discrete States of Molecules
Pfleger, Martin; Wallek, Thomas; Pfennig, Andreas ULg

in Industrial and Engineering Chemistry (2015), 54

Thermodynamic modeling using the concept of Shannon entropy is a promising approach, especially in the field of describing fluid-phase behavior. This paper introduces the method of discrete modeling ... [more ▼]

Thermodynamic modeling using the concept of Shannon entropy is a promising approach, especially in the field of describing fluid-phase behavior. This paper introduces the method of discrete modeling, using the ideal-gas model as an illustrative example, and derives a general equation of state. Discrete modeling is based on discrete states of individual molecules. It utilizes the special characteristics of Shannon entropy to model the statistical behavior of systems by applying the maximum entropy principle to its constituents in a straightforward manner. The presented method and the general form of the equation of state thus obtained allow the derivation of equations of states for real fluids. As a novelty, it also allows for the description of the microscopic distribution of the mechanical states of individual molecules. Considering the kinetic states of the particles this includes the Maxwell−Boltzmann distribution, the caloric equation of state, and the heat capacity of the ideal gas. [less ▲]

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See detailDiscrete Modelling - a Statistical Approach to account for Detailed States of Individual Molecules
Wallek, T; Pfleger, M; König, L M et al

Conference (2013)

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See detailDiscrete optimization
Louveaux, Quentin ULg

Poster (2005, September)

Have you ever wondered what is the shortest route to join the office? What is the best way to plan a trip through several cities? You have maybe already played with magical squares? Then you have met one ... [more ▼]

Have you ever wondered what is the shortest route to join the office? What is the best way to plan a trip through several cities? You have maybe already played with magical squares? Then you have met one of the nu- merous instances of discrete optimization. Discrete optimization is a field of mathematics which deals with any problem where parts of the solutions cannot be divided or fractional. And as one may guess, this is the case in many real-life problems. This poster is divided in three main topics. The first part focuses on formulating those problems. We will start from one of the industrial appli- cations and show how we can model it as a mathematical problem. In the second part we sketch the main tools and algorithms used to tackle those problems. In particular we point out the fact that requiring integrality leads to extremely hard problems to solve. We show that despite this fact, we are able to solve problems of substantial size. However there remain some problems that are hard to solve using the state-of-the-art techniques. In the third part we indicate what are the chal- lenges of the field. In particular we will give an overview of the research car- ried out in the universities supported by the Marie-Curie network ADONET. [less ▲]

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Peer Reviewed
See detailA discrete population of squamocolumnar junction cells implicated in the pathogenesis of cervical cancer.
Herfs, Michael ULg; Yamamoto, Yusuke; Laury, Anna et al

in Proceedings of the National Academy of Sciences of the United States of America (2012), 109(26), 10516-21

Infection by carcinogenic human papillomaviruses (HPV) results in precancers [cervical intraepithelial neoplasia (CIN)] and cancers near the ectoendocervical squamocolumnar (SC) junction of the cervix ... [more ▼]

Infection by carcinogenic human papillomaviruses (HPV) results in precancers [cervical intraepithelial neoplasia (CIN)] and cancers near the ectoendocervical squamocolumnar (SC) junction of the cervix. However, the specific cells targeted by HPV have not been identified and the cellular origin of cervical cancer remains elusive. In this study, we uncovered a discrete population of SC junctional cells with unique morphology and gene-expression profile. We also demonstrated that the selected junctional biomarkers were expressed by a high percentage of high-grade CIN and cervical cancers associated with carcinogenic HPVs but rarely in ectocervical/transformation zone CINs or those associated with noncarcinogenic HPVs. That the original SC junction immunophenotype was not regenerated at new SC junctions following excision, not induced by expression of viral oncoproteins in foreskin keratinocytes, and not seen in HPV-related precursors of the vagina, vulva, and penis further support the notion that junctional cells are the source of cervical cancer. Taken together, our findings suggest that carcinogenic HPV-related CINs and cervical cancers are linked to a small, discrete cell population that localizes to the SC junction of the cervix, expresses a unique gene expression signature, and is not regenerated after excision. The findings in this study uncover a potential target for cervical cancer prevention, provide insight into the risk assessment of cervical lesions, and establish a model for elucidating the pathway to cervical cancer following carcinogenic HPV infection. [less ▲]

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Peer Reviewed
See detailA Discrete Sequence Associated with Mixed Finite Elements and its Gauge Condition for Vector Potentials
Dular, Patrick ULg; Nicolet, André; Genon, André et al

in IEEE Transactions on Magnetics (1995), 31(3), 1356-1359

A sequence of finite element spaces built on tetrahedra, hexahedra and prisms, is presented, and a gauge condition for vector potentials is shown to be well defined in these spaces. Results are presented ... [more ▼]

A sequence of finite element spaces built on tetrahedra, hexahedra and prisms, is presented, and a gauge condition for vector potentials is shown to be well defined in these spaces. Results are presented for a modified vector potential formulation for 3D eddy current problems. [less ▲]

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See detailDiscrete symmetries in the three-Higgs-doublet model
Ivanov, Igor ULg; Vdovin, Evgeny

in Physical Review. D : Particles and Fields (2012), 86(9), 0950305

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a ... [more ▼]

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model by making use of Burnside’s theorem and other results from pure finite group theory which are rarely exploited in physics. Our method and results can also be used beyond high-energy physics, for example, in the study of possible symmetries in three-band superconductors. [less ▲]

Detailed reference viewed: 17 (3 ULg)
See detailDiscrete Valued Optimal Design Problems
Fleury, Claude ULg

in Bendsoe, Martin P.; Mota Soares, Carlos A. (Eds.) Topology design of structures: Proceedings of the NATO Advanced Workshop, Sesimbra, Portugal, June 20-26, 1992 (1992)

Detailed reference viewed: 8 (0 ULg)
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See detailDiscrete Vortex Simulations of the torsional flutter oscillations of a 4:1 rectangular cylinder
Andrianne, Thomas ULg; Dimitriadis, Grigorios ULg

in Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (2012, April 24)

This work presents aeroelastic simulations of a 2D bluff-body around its pitching degree of freedom. The numerical tool consists in an aerodynamic solver based on the Discrete Vortex Method (DVM), coupled ... [more ▼]

This work presents aeroelastic simulations of a 2D bluff-body around its pitching degree of freedom. The numerical tool consists in an aerodynamic solver based on the Discrete Vortex Method (DVM), coupled with a linear structural model. The shape of the bluff-body is a sharp edged rectangular cylinder with a side ratio equal to 4. The numerical results are compared to the experimental measurements recently obtained by the authors.8 The validation is carried out in three steps: first the frequency content of the flow-field in the wake of the static body is investigated. Then the simulated unsteady flow-field around the imposed pitching motion of the body is compared to experimental flow visualizations. This comparison is performed using Proper Orthogonal Decomposition (POD). Finally, the simulation of the global aeroelastic behaviour, based on the coupling of the DVM code to the structural model of the pitching degree of freedom is carried out and the results are compared to measured aeroelastic responses.. Very good agreements are found between numerical and experimental results, demonstrating the capabilities of the numerical tool to simulate complex unsteady aerodynamics around an oscillating bluff-body. [less ▲]

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

in Proceedings of the 17th MTNS Symposium, Kyoto 2006 (2006, August)

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with ... [more ▼]

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous synchronization results that have focused on convergence in the Euclidean space (R^n)^N. We address the question from a control perspective, but make several connections with existing models, including the Hopfield network, the Vicsek model and the (continuous-time) Kuramoto model. We propose two different distributed algorithms. The first one achieves convergence to equilibria in shape space that are the local extrema of a potential U_L built on the graph Laplacian associated to a fixed, undirected interconnection topology; it can be implemented with sensor-based interaction only, since each agent just relies on the relative position of its neighbors. The second one achieves synchronization under varying and/or directed communication topology using local estimates of a consensus variable that are communicated between interacting agents. Both algorithms are based on the notion of centroid and can be interpreted as descent algorithms. The proposed approach can be extended to other embedded compact manifolds. [less ▲]

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

Conference (2006, March)

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See detailThe Discretionary Use of Strasbourg Jurisprudence by the International Criminal Court
Deprez, Christophe ULg

Conference (2014, June 13)

Although the case law of the European Court of Human Rights ("ECtHR") has had and still shows critical influence on the development of the practice of the International Criminal Court ("ICC"), it remains ... [more ▼]

Although the case law of the European Court of Human Rights ("ECtHR") has had and still shows critical influence on the development of the practice of the International Criminal Court ("ICC"), it remains unclear what the authority of such external jurisprudence is vis-à-vis the international criminal judge. While it is virtually undisputed that human rights law, in general terms, is applicable to proceedings before the ICC, many scholars tend to adopt a much nuanced approach to the authority of human rights case law in particular. This paper aims to shed further light on the issue by addressing the question whether ICC judges have used Strasbourg jurisprudence in a consistent manner, in particular as regards the authority which they decided to vest the latter with. It demonstrates that ICC Chambers have relied on European human rights practice, alternatively, as a mere source of inspiration, as binding interpretation, as a corpus having ambivalent authority, or as a source whose legal value it simply left unspecified. This leads us to conclude that, on the whole, the ICC has been mostly inconsistent regarding the value of ECtHR case law in the context of international criminal proceedings. Such inconsistency, we argue, amounts to a discretionary use of Strasbourg jurisprudence that further reinforces the Court's paradoxical position as the ultimate authority for defining the boundaries of its own human rights constraint. [less ▲]

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Peer Reviewed
See detailDiscretization of Sources of Integral Operators
Tarhasaari, T.; Kettunen, L.; Geuzaine, Christophe ULg

in IEEE Transactions on Magnetics (2000), 36(4), 659--662

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Peer Reviewed
See detailDiscretization of Sources of Integral Operators
Tarhasaari, T.; Kettunen, L.; Geuzaine, Christophe ULg

in Proceedings of the 12th COMPUMAG Conference on the Computation of Electromagnetic Fields (1999)

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Peer Reviewed
See detailDiscretization of the divergence formulation of the bed slope term in the shallow-water equations and consequences in terms of energy balance
Bruwier, Martin ULg; Archambeau, Pierre ULg; Erpicum, Sébastien ULg et al

in Applied Mathematical Modelling (2016)

In this research, the influence on energy balance of the discretization scheme of the divergence formulation of the bed slope term in the shallow-water equations is analysed theoretically (for a single ... [more ▼]

In this research, the influence on energy balance of the discretization scheme of the divergence formulation of the bed slope term in the shallow-water equations is analysed theoretically (for a single topographic step) and based on two numerical tests. Different values of the main parameter controlling the discretization scheme of the divergence formulation are analysed to identify the formulation which minimizes the energy variation resulting from the discretization. For a wide range of ambient Froude numbers and relative step heights, the theoretical value of the control parameter minimizing the energy variation falls within a very narrow range, which can reasonably be approximated by a single “optimal” value. This is a result of high practical relevance for the design of accurate numerical schemes, as confirmed by the results of the numerical tests. [less ▲]

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See detailDiscretization Schemes for Hybrid Methods
Geuzaine, Christophe ULg; Tarhasaari, T.; Kettunen, L. et al

in IEEE Transactions on Magnetics (2001), 37(5), 3112--3115

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See detailDiscrets et méconnus...les reptiles
Graitson, Eric ULg

Book published by Service public de Wallonie (2011)

"En Wallonie, sept espèces de reptiles composent le « petit peuple des broussailles ». Discrets et silencieux, ils passent bien souvent inaperçus. Ils sont pourtant bien là sous une pierre, tapis dans la ... [more ▼]

"En Wallonie, sept espèces de reptiles composent le « petit peuple des broussailles ». Discrets et silencieux, ils passent bien souvent inaperçus. Ils sont pourtant bien là sous une pierre, tapis dans la végétation dense, à l’intérieur des fissures d’un muret ou sous un tas de compost, cherchant la température idéale a leur survie ou simplement un abri pour fuir leurs prédateurs." Après une présentation des différentes espèces de reptiles indigènes présentes en Wallonie, le livre aborde les causes de régression de ces animaux et les mesures de protection applicables par le monde agricole. Plusieurs exemples d'aménagements réalisés en faveur des reptiles en milieu agricole sont présentés à la fin de l'ouvrage. [less ▲]

Detailed reference viewed: 90 (8 ULg)