Discrete embeddings for Lagrangian and Hamiltonian systems

The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with variational problems attached to a least action principle. Considering a partial differential equation (PDE) deriving from such a variational principle, a natural question is to know whether this structure at the continuous level is preserved at the discrete level when discretising the PDE. To address this question a concept of \textit{coherence} is introduced. Both the differential equation (the PDE translating the least action principle) and the variational structure can be embedded at the discrete level. This provides two discrete embeddings for the original problem. In case these procedures finally provide the same discrete problem we will say that the discretisation is \textit{coherent}. Our purpose is illustrated with the Poisson problem. Coherence for discrete embeddings of Lagrangian structures is studied for various classical discretisations (finite elements, finite differences and finite volumes). Hamiltonian structures are shown to provide coherence between a discrete Hamiltonian structure and the discretisation of the mixed formulation of the PDE, both for mixed finite elements and mimetic finite differences methods.Comment: Acta Mathematica Vietnamica, Springer Singapore, A Para{\^i}tr

Raviart-Thomas finite elements of Petrov-Galerkin type

The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of Petrov-Galerkin type for this problem to ensure a local computation of the gradient at the interfaces of the elements. The shape functions are the Raviart-Thomas finite elements. Our goal is to define test functions that are in duality with these shape functions: Precisely, the shape and test functions will be asked to satisfy a L2-orthogonality property. The general theory of Babu\v{s}ka brings necessary and sufficient stability conditions for a Petrov-Galerkin mixed problem to be convergent. We propose specific constraints for the dual test functions in order to ensure stability. With this choice, we prove that the mixed Petrov-Galerkin scheme is identical to the four point finite volumes scheme of Herbin, and to the mass lumping approach developed by Baranger, Maitre and Oudin. Finally, we construct a family of dual test functions that satisfy the stability conditions. Convergence is proven with the usual techniques of mixed finite elements

Defying marketing sovereignty: Voluntary simplicity at new consumption communities

Purpose of this paper: To broaden the scope of or knowledge of collective voluntarily simplified lifestyles in the UK, by exploring whether voluntary simplifiers achieve their goals by adopting a simpler life. Design/methodology/approach: Radical forms of voluntary simplifier groups were explored through participant-observation research. The methodology can be broadly classified as critical ethnography, and a multi-locale approach has been used in designing the field. Findings: Although for some of these consumers voluntary simplicity seems to have reinstated the enjoyment of life, certain goals remain unfulfilled and other unexpected issues arise, such as the challenges of mobility in the attainment of environmental goals. Research limitations/implications (if applicable): This is an ongoing research, however many opportunities for further research have arisen from this study. Quantitative research could be undertaken on the values and attitudes buttressing voluntary simplicity specifically in the UK. The extent to which such communities influence mainstream consumers could be studied both quantitatively and qualitatively. Mainstream consumers’ attitudes to the practices of such communities could prove useful for uncovering real consumer needs. Practical implications: Despite these communities position in the extreme end of the voluntary simplicity spectrum, their role in shaping the practices and attitudes of other consumers is clear. What is original/value of paper: This paper provides new consumer insights that can re-shape policy-making and marketing practice aimed at achieving a sustainable future

Measuring the effect of node aggregation on community detection

Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network. The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence. This is akin to the problem of ecological and atomic fallacies in statistics, or to the Modified Areal Unit Problem in geography. We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure. We illustrate its relevance on real-world examples (mobile phone and Twitter reply-to networks). Our main message is that any node-partitioning analysis performed on aggregated networks should be interpreted with caution, as the outcome may be strongly influenced by the level of the aggregation.Comment: 12 pages, 5 figure

Gear tooth topological modification

The topology of parallel axis gears, such as spur and helical gears is modified to produce quieter and more smoothly operating gear sets with more uniform load distribution. A finite element analysis of the gear in its operating mode is made to produce a plot of radial and tangential deflections of the pinion and gear tooth surfaces which will occur when the gears are loaded during operation. The resultant plot is then inverted to produce a plot, or set of coordinates, which will define the path of travel of the gear tooth grinding wheel, which path is a mirror image of the plot of the finite element analysis. The resulting gears, when subjected to operating loads, will thus be deflected tangentially and radially to their optimum operating, or theoretical true involute, positions so as to produce quieter, smoother, and more evenly loaded gear trains

L’ascension professionnelle et le plafond de verre dans les entreprises privées au Québec

En dépit du consensus social québécois sur l’égalité de fait à atteindre, l’histoire de l’émancipation des femmes reste à parachever. Sur le marché du travail, les échelons supérieurs des organisations, tant privées que publiques, demeurent la prérogative des hommes qui occupent, dans une proportion très élevée, les postes les plus influents dans la majorité des entreprises au Québec et ailleurs. Le présent article s’intéresse au phénomène du plafond de verre et, plus précisément, à la pérennité des facteurs qui contribuent à son édification au sein d’une culture organisationnelle donnée, soit les milieux de la gestion et des finances dans les entreprises privées au Québec. À la suite de l’évolution des valeurs sociétales en matière d’égalité des sexes en Occident, comment peut-on en effet expliquer le maintien de cet effet frontière au cours de la carrière ascendante des femmes cadres? Pour répondre à cette question centrale, les auteures proposent un exposé en quatre temps. Elles tracent d’abord un portrait de la présence des femmes dans les échelons supérieurs des organisations québécoises et canadiennes. Par la suite, elles mettent en évidence les principaux facteurs qui érigent le plafond de verre, puis elles décrivent brièvement les orientations théoriques et méthodologiques qui ont guidé leur étude. Enfin, elles présentent un bref aperçu des résultats préliminaires de recherche et esquissent quelques pistes d’analyse.Despite Quebec’s social consensus on reaching a factual equality, the history of women’s emancipation is yet to be completed. In the work place, staff position within private and public organisations remain men’s prerogative, since they occupy a very high proportion of the influent positions of most enterprises here and abroad. The current article investigates the « glass ceiling » phenomenon, and more precisely the sustainability of the factors contributing to its edification within a given organizational culture in the midst of management and finance in private enterprises of Quebec. Following the evolution of societal values of the Western world in matters of equality between sexes, how can we indeed explain the containment of this frontier effect while the career of leading women is ascending? To answer this crucial question, we propose a four steps analysis. First, we will draw a brief picture of women presence in the higher levels of canadian and quebequer organisation. Second, we will identify the main factors that erect the « glass ceiling » and, third, we will try to understand in which way the gender relations within the organizational culture contribute to the reproduction of theses factors. Finally, we will present and comment our preliminary research results

Towards the generation of industrial bundles through a random process under realistic constraints

International audienceTo get closer to the reality of aeronautics wire harnesses, we propose to represent a bundle as a non-uniform transmission line by discretizing it into several sections. For each section, positions of conductors are randomized. However this procedure is applied with some geometrical constraints thus resulting in a much more realistic bundle profile. Currents and voltages may be determined on each conductor. Then, we use statistical tools to analyze our results. In order to save computation time, we also propose simplified models for simulation studies of the common mode current

Caractérisation de l'activité de la tomatidine et de ses dérivés sur l'ATP synthétase

Il a été démontré dans le laboratoire du professeur François Malouin (Biologie, Université de Sherbrooke) que la tomatidine, un alcaloïde stéroïdien provenant de la famille des Solanacées, possédait une activité antibactérienne contre les small colony variants (SCV) de l’ordre des Bacillales, dont Staphylococcus aureus. Grâce à la collaboration du professeur Éric Marsault (Pharmacologie, Université de Sherbrooke), il a été possible de synthétiser un dérivé de la tomatidine, FC04-100, qui en plus de posséder une activité antibactérienne contre les SCV, ciblait les souches prototypes. Par la suite, des mutants ont été isolés par pression sélective, puis séquencés. Le séquençage a révélé une mutation dans deux gènes, soit une dans le gène ccpA (catabolite carbon protein A) qui conférait un niveau de résistance intermédiaire à la tomatidine et une mutation dans le gène atpE (sous-unité c de l’ATP synthétase) qui est associé à un haut niveau de résistance. Les mutants sélectionnés avec FC04-100 ne possédaient pas une mutation dans le gène ccpA et leur niveau de résistance était limité. Afin de confirmer que la cible ultime était bien l’ATP synthétase, j’ai développé un essai d’inhibition de la production de l’ATP en utilisant des vésicules de membranes inversées pour valider la cible de façon biochimique. Ce test démontre qu’effectivement, la tomatidine et son analogue FC04-100 inhibent la production de l’ATP synthétase chez S. aureus. J’ai aussi démontré que la tomatidine et FC04-100 n’était plus en mesure d’inhiber la production de l’ATP chez les mutants résistants, ce qui confirme que l’ATP synthétase est bien la cible de nos composés. En utilisant des mitochondries de cellules humaines pulmonaires, j’ai de plus démontré que nos molécules inhibitrices étaient beaucoup plus sélectives pour l’ATP synthétase bactérienne que mitochondriale. Ultérieurement, grâce à l’équipe du professeur Marsault et la modélisation moléculaire, il a été possible de trouver une molécule analogue à la tomatidine sans pour autant avoir un squelette stéroïdien. Par les tests d’inhibition et biochimiques, j’ai alors démontré que cette molécule possède les mêmes caractéristiques que la tomatidine ou FC04-100 envers S. aureus et son ATP synthétase. Il sera donc intéressant de poursuivre avec des dérivés de cette nouvelle molécule afin de l’optimiser et éventuellement, d’obtenir une molécule pouvant être utilisée en clinique pour combattre les infections à S. aureus et les Bacillales en général

Crosstalk analysis in complex aeronautical bundle

International audienceAn analysis of crosstalk inside a complex aeronautical bundle from an experimental and from a numerical point of view is proposed. The numerical model is built as a succession of uniform transmission lines generated randomly. Modeling of the geometrical pattern of twisted pairs is included. Crosstalks between these twisted pairs and single wires inside the bundle are measured and computed. In order to save computation time, a simplified model of the bundle is developed and validated