Prototypentheorie und Flexionsmorphologie

This article presents an application of the theory of prototypes to the field of inflectional morphology and especially to the treatment of exceptions. From the assumption that the handling of irregular facts is basically ruled by the same principles of categorization as the handling of regular facts, the article shows on concrete examples of German nouns - weak masculine nouns, feminine nouns with inflected e-plural and er-plural - that the principle of the motivation of inflection by other properties of lexical items (phonological, semantic, syntactic properties) also works in inflectional classes with few elements. This type of analysis leads to the hypothesis of much more complex categorial structures, which includes subcategories with very few elements, instead of the traditional dichotomy between regular and irregular or a simple continuum prototypical - non prototypical

Modelling the palaeo-evolution of the geodynamo

International audienceAlthough it is known that the geodynamo has been operating for at least 3.2 Ga, it remains difficult to infer the intensity, dipolarity and stability (occurrence of reversals) of the Precam-brian magnetic field of the Earth. In order to assist the interpretation of palaeomagnetic data, we produce models for the long-term evolution of the geodynamo by combining core ther-modynamics with a systematic scaling analysis of numerical dynamo simulations. We update earlier dynamo scaling results by exploring a parameter space, which has been extended in order to account for core aspect ratios and buoyancy source distributions relevant to Earth in the Precambrian. Our analysis highlights the central role of the convective power, which is an output of core thermodynamics and the main input of our updated scalings. As the thermal evolution of the Earth's core is not well known, two end-member models of heat flow evolution at the core–mantle boundary (CMB) are used, respectively, terminating at present heat flows of 11 TW (high-power scenario) and 3 TW (low power scenario). The resulting models predict that until the appearance of the inner core, a thermal dynamo driven only by secular cooling, and without any need for radioactive heating, can produce a dipole moment of strength comparable to that of the present field, thus precluding an interpretation of the oldest palaeomagnetic records as evidence of the inner core presence. The observed lack of strong long-term trends in palaeointensity data throughout the Earth's history can be rationalized by the weakness of palaeointensity variations predicted by our models relatively to the data scatter. Specifically, the most significant internal magnetic field increase which we predict is associated to the sudden power increase resulting from inner core nucleation, but the dynamo becomes deeper-seated in the core, thus largely cancelling the increase at the core and Earth surface, and diminishing the prospect of observing this event in palaeointensity data. Our models additionally suggest that the geodynamo has lied close to the transition to polarity reversals throughout its history. In the Precambrian, we predict a dynamo with similar dipolarity and less frequent reversals than at present times, due to conditions of generally lower convective forcing. Quantifying the typical CMB heat flow variation needed for the geodynamo to cross the transition from a reversing to a non-reversing state, we find that it is unlikely that such a variation may have caused superchrons in the last 0.5 Ga without shutting down dynamo action altogether

Identities for field extensions generalizing the Ohno-Nakagawa relations

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give another proof of the Ohno-Nakagawa relation without appealing to binary cubic forms.Comment: Version 2, 16 pages, to appear in Compositi

Diagnosis of turbulence radiation interaction in turbulent flames and implications for modeling in large Eddy simulation

International audienceAn a priori study of the turbulence radiation interaction (TRI) is performed on numerical data from Direct Numerical Simulation (DNS) of a turbulent flame. The influence of the various correlations that appear in the radiative emission is investigated and their impact is evaluated in the context of Large Eddy Simulation (LES). In LES, only filtered quantities are computed, where the filter is the grid. The radiative emission is reconstructed first from the exact, then filtered solution variables and the sensitivity to the filter size is evaluated. Three approaches are used to take into account the subgrid scale correlations: the no-TRI, partial TRI and full TRI approaches. Results show that the full TRI is exact compared to the reference emission and that the partial TRI performs worse than the no-TRI for the studied configuration. This indicates that in the studied case, the TRI must be considered in LES in a full formulation

Développement d'un code éléments finis pour simuler le soudage par ultrasons de matériaux composites = Development of a Finite element code for simulating the ultrasonic welding of composite materials

National audienceLe développement récent des matériaux composites à matrices thermoplastiques c'est accompagné de nouveaux moyens d'assemblages. Nous nous concentrons ici sur le soudage par ultrasons. Afin d'étudier l'influence des paramètres procédé sur la qualité d'une soudure, nous proposons une modélisation puis une simulation du procédé. La modélisation se fait à l'aide de deux problèmes mécaniques et d'un problème thermique. Un code de simulation multiphysique a été développé afin de résoudre ces trois problèmes. L'évolution que subit l'interface est simulé à l'aide d'une méthode de level-set et de contact unilatéral par pénalité. Les simulations en 2D sans modélisation du contact montrent que des porosités sont piégées à l'interface. Ceci est confirmé par les essais de soudage statique (sans mouvement de l'outil). Les simulations avec modélisation du contact permettent de mieux décrire l'écrasement à l'interface mais montrent des lacunes physiques. Le soudage dynamique avec avance de l'outil est un variant du procédé permettant de limiter les porosités à l'interface. La simulation de l'écoulement tridimensionnel qui en résulte est en cours. Elle devrait permettre d'expliquer la meilleure qualité de la soudure

Modélisation du rayonnement dans la simulation aux grandes échelles de la combustion turbulente

La simulation de la combustion turbulente connait un nouvel essor avec l'introduction de la Simulation aux Grandes Échelles (SGE) qui permet de prédire l'évolution in stationnaire de l'écoulement réactif turbulent. Dans ce contexte la prise en compte du rayonnement soulève des questions d'ordre a la fois fondamental et pratique. En effet les processus physiques du rayonnement et de la combustion sont de nature radicalement différente : la combustion est contrôlée par des échanges locaux sur une durée finie, alors que le rayonnement est instantané et fait intervenir des échanges a distance. En premier lieu il convient de s'interroger sur l'impact de la modélisation SGE de la combustion turbulente sur le rayonnement. Cette question est traitée dans le cadre plus général de l'interaction rayonnement-turbulence. A partir d'études théoriques et numériques, il est montre que cette interaction est faible et qu'une solution SGE peut être directement utilisée pour un calcul radiatif, sans modélisation supplémentaire. Il s'agit ensuite de mettre en place de façon pratique le couplage in stationnaire rayonnement-combustion turbulente. Un point clé est la réduction du temps de calcul pour le rayonnement, et diverses stratégies sont proposées. En particulier un nouveau modèle spectral est introduit, utilisant une technique de tabulation et garantissant un niveau de précision suffisant. Le temps de calcul radiatif a ainsi été réduit de deux ordres de grandeur, permettant la réalisation d'un calcul couple sur une configuration de flamme pré-melangée turbulente. ABSTRACT : Simulation of turbulent combustion has gained high potential with the Large Eddy Simulation (LES) approach, allowing to predict unsteady turbulent reactive flows. In this context, taking into account radiation rises new fundamental and practical questions. Indeed the physics involved in radiation and in combustion are completely different : combustion is controlled by local exchanges and finite times whereas radiation is instantaneous and is based on non-local exchanges. In a first step, the impact of LES modelling of turbulent combustion on radiation is regarded. This question is treated in the more general frame of the turbulence-radiation interaction. From theoretical and numerical studies, it is shown that this interaction is weak in the LES context so that LES solutions can be directly coupled to radiative calculations, without further modelling. Then the unsteady coupling of radiation and turbulent combustion is realised. A key point is the reduction of calculation time of radiation, and several strategies are proposed. In particular a new global spectral model is introduced, using a tabulation technique and ensuring a sufficient level of accuracy. The radiative time calculation is finally decreased by two orders of magnitude, enabling the realization of a coupled calculation of a turbulent premixed flam

Analysis of the interaction between turbulent combustion and thermal radiation using unsteady coupled LES/DOM simulations

International audienceRadiation exchanges must be taken into account to improve the prediction of heat fluxes in turbulent combustion. The strong interaction with turbulence and its role on the formation of polluting species require the study of unsteady coupled calculations using Large Eddy Simulations (LESs) of the turbulent combustion process. Radiation is solved using the Discrete Ordinate Method (DOM) and a global spectral model. A detailed study of the coupling between radiative heat transfer and LES simulation involving a real laboratory flame configuration is presented. First the impact of radiation on the flame structure is discussed: when radiation is taken into account, temperature levels increase in the fresh gas and decrease in the burnt gas, with variations ranging from 100 K to 150 K thus impacting the density of the gas. Coupling DOM and LES allows to analyze radiation effects on flame stability: temperature fluctuations are increased, and a wavelet frequency analysis shows changes in the flow characteristic frequencies. The second part of the study focuses on the Turbulence Radiation Interaction (TRI) using the instantaneous radiative fields on the whole computational domain. TRI correlations are calculated and are discussed along four levels of approximation. The LES study shows that all the TRI correlations are significant and must be taken into account. These correlations are also useful to calculate the TRI correlations in the Reynolds Averaged Navier-Stokes (RANS) approach. (C) 2011 Published by Elsevier Inc. on behalf of The Combustion Institute