Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error

Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order 4D-Var prior to the incremental 4D-Var in the full space in order to achieve faster convergence. An application performed in the tropical Pacific Ocean, with assimilation of TAO temperature data, shows the method to be both feasible and efficient. It allows the global cost of the assimilation to be reduced by a factor of 2 without affecting the quality of the solution

Des relations entre les structures musicales et les contextes sociaux dans un répertoire de "sessions" instrumentales irlandaises

La version intégrale de ce mémoire [ou de cette thèse] est disponible uniquement pour consultation individuelle à la Bibliothèque de musique de l’Université de Montréal (www.bib.umontreal.ca/MU)Instants et espaces investis par la musique, les sessions sont actuellement en Irlande un marqueur d’expression culturelle. En surface, celles-ci peuvent être définies en tant que regroupement prévu ou spontané de plusieurs musiciens dans le but de faire de la musique et de passer un agréable moment en communauté. Toutefois, un travail d'enquête réparti sur sept années de recherches dans le nord-ouest irlandais a révélé qu'en profondeur, les sessions représentent un phénomène socioculturel complexe, phénomène social autant que musical, fait musical autant que social, édifice symbolique mixte tissé d'interactions dont la combinatoire à chaque fois renouvelée implique un jeu de relations entre le facteur individuel et les stratégies collectives qui, radicalement, affectent l’ensemble de la structure de l’événement. Comprendre le fonctionnement d'une session revient alors à poser un certain nombre de questions ayant pour finalité de révéler la manière dont les deux pôles du social et du musical se trouvent, en même temps que distincts, inextricablement liés. Les sessions musicales se révèlent ainsi sources d'un certain nombre de problèmes, lesquels, a priori motivés par une connaissance spécifique à notre objet d'étude, conduisent à dépasser le domaine exclusif de l'Irlande pour venir affronter les questionnements plus larges que pose l'ethnomusicologie contemporaine. La présente thèse s'organise en cinq chapitres. Un premier est consacré à une description générale des sessions. L'attention est portée sur les liens dynamiques opérant entre ce qui relève du musical et ce qui procède d'un ordre plus spécifiquement social. Les questions alors soulevées engagent un second chapitre, dont l'organisation est bipartite. Y sont alors exposés, dans un premier temps, les grands axes problématiques sur lesquels cette thèse repose, et dans un second, les réponses méthodologiques impliquées par cette même problématique. Un troisième chapitre consiste à mettre en place l'ensemble des outils nécessaires à la conduite des analyses, à travers une réflexion portant sur les propriétés systématiques de l'ensemble des paramètres sociaux et musicaux caractéristiques de ce que sera notre corpus. L'étape suivante, quatrième chapitre de la thèse, se fonde sur les analyses comparatives d'un corpus de 26 pièces musicales, collectées dans le cadre de 7 situations de sessions distinctes. À travers un cinquième chapitre, le travail se termine enfin par une synthèse fondée sur l'intégralité des résultats analytiques obtenus dans le chapitre précédent.As periods of time and spatial entities invested by music, sessions in Ireland nowadays are a marker of cultural expression. Superficially, those can be defined as a gathering, planned or spontaneous, of several musicians with the prospect to produce music and to share a nice moment together. Yet, a survey pursued over a seven-year research work in north-western Ireland revealed that, in depth, sessions represent complex socio-cultural events, social as much as musical, musical as well as social happening, symbolic entity enriched by interactions whose permanently renewed combination reflects the interplay between individual factors and group strategies, that, radically, affect the whole structure of the event. To understand how a session functions then requires raising a number of questions whose end is to elucidate how the two poles, social and musical, happen to be inextricably linked, though distinct at the same time. Musical sessions thus become a source of problems which, a priori connected to the amount of knowledge specific of our topic, lead to overcome the exclusive domain of Ireland up to facing the broader issues of contemporary ethnomusicology. The present thesis includes five chapters. The first one is a general description of sessions. Attention is paid to the dynamic links operating between what belongs to music and what proceeds from a line more specifically social. Questions then raised trigger a second chapter, whose content is bipartite. First are exposed the major problems on which the thesis rests, and secondly the methodological answers related to the given problematic. A third chapter consists of setting the spectrum of methods required to conduct analyses, through a reflexion bearing on the system properties of the whole range of social and musical parameters that characterize this work. Next step, the fourth chapter is based on the comparative analysis of 26 musical pieces that were collected in the context of seven different situations in distinct sessions. In the fifth chapter, the thesis ends with a synthesis of all analytical results as gathered in the previous chapters

On the complexity of computing Gr\"obner bases for weighted homogeneous systems

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights $W=(w\_{1},\dots,w\_{n})$, $W$-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree $\deg\_{W}(X\_{1}^{\alpha\_{1}},\dots,X\_{n}^{\alpha\_{n}}) = \sum w\_{i}\alpha\_{i}$. Gr\"obner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case. We show that in this case, the complexity estimate for Algorithm~\F5 \left(\binom{n+\dmax-1}{\dmax}^{\omega}\right) can be divided by a factor $\left(\prod w\_{i} \right)^{\omega}$. For zero-dimensional systems, the complexity of Algorithm~\FGLM $nD^{\omega}$ (where $D$ is the number of solutions of the system) can be divided by the same factor $\left(\prod w\_{i} \right)^{\omega}$. Under genericity assumptions, for zero-dimensional weighted homogeneous systems of $W$-degree $(d\_{1},\dots,d\_{n})$, these complexity estimates are polynomial in the weighted B\'ezout bound $\prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}$. Furthermore, the maximum degree reached in a run of Algorithm \F5 is bounded by the weighted Macaulay bound $\sum (d\_{i}-w\_{i}) + w\_{n}$, and this bound is sharp if we can order the weights so that $w\_{n}=1$. For overdetermined semi-regular systems, estimates from the homogeneous case can be adapted to the weighted case. We provide some experimental results based on systems arising from a cryptography problem and from polynomial inversion problems. They show that taking advantage of the weighted homogeneous structure yields substantial speed-ups, and allows us to solve systems which were otherwise out of reach

Prediction of fatigue life improvement in natural rubber using configurational stress

AbstractTo some extent, continua can no longer be considered as free of defects. Experimental observations on natural rubber revealed the existence of distributed microscopic defects which grow upon cyclic loading. However, these observations are not incorporated in the classical fatigue life predictors for rubber, i.e. the maximum principal stretch, the maximum principal stress and the strain energy. Recently, Verron et al. [Verron, E., Le Cam, J.B., Gornet, L., 2006. A multiaxial criterion for crack nucleation in rubber. Mech. Res. Commun. 33, 493–498] considered the configurational stress tensor to propose a fatigue life predictor for rubber which takes into account the presence of microscopic defects by considering that macroscopic crack nucleation can be seen as the result of the propagation of microscopic defects. For elastic materials, it predicts privileged regions of rubber parts in which macroscopic fatigue crack might appear. Here, we will address our interest to a broader context. Rubber is assumed to exhibit inelastic behavior, characterized by hysteresis, under fatigue loading conditions. The configurational mechanics-based predictor is modified to incorporate inelastic constitutive equations. Afterwards, it is used to predict fatigue life. The emphasis of the present work is laid on the prediction of the well-known fatigue life improvement in natural rubber under tension–tension cyclic loading

Inflation of elastomeric circular membranes using network constitutive equations

International audienceThe present paper deals with the use of network-based hyperelastic constitutive equations in the context of thin membranes inflation. The study focus on the inflation of plane circular membranes and the materials are assumed to obey Gaussian and non-Gaussian statistical chains network models. The governing equations of the inflation of axisymmetric thin rubber-like membranes are briefly recalled. The material models are implemented in a numerical tool that incorporates an efficient B-spline interpolation method and a coupled Newton-Raphson/arc-length solving algorithm. Two numerical examples are studied: the homogeneous inflation of spherical balloons and the inflation of initially plane circular membranes. In the second example, the inflation profiles and the distributions of extension ratios along the membrane are extensively analysed during the inflation process. Both examples highlight the need of an accurate modelling of the strain-hardening phenomenon in elastomers

The Importance of Service Elements in Retail Business

This study aims to find out how the external and internal marketing strategic issues of Toko Delima, How is the internal and external analysis of Toko Delima and how is the recommendation of Toko Delima's marketing strategy for 2023. This type of research is a qualitative research with interview data collection methods conducted on Toko Delima owners, Toko Delima consumers and competitor’s store consumers, observation of competitors and documentation studies with secondary data related to Toko Delima. The data analysis method used in this research is by using qualitative analysis methods. The results of this study indicate that in the future Toko Delima will experience changes in STP and its marketing mix, namely in the aspects of price, place and promotion strategies. There is an addition to the service elements of Toko Delima, so that previously using 4P will become 7P. Toko Delima's marketing strategy recommendations for 2023 are promoting using social media namely Instagram, increasing store convenience, adding online sales channels, adding types of promotions and changing product pricing. The results of this study are expected to have a positive impact on the development of science and business in the field of management, especially how to design a marketing strateg