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Concept# Musique classique

Résumé

thumb|250px|Une vingtaine de compositeurs de musique classique, parmi les plus importants couvrant la période du .(De gauche à droite, de haut en bas : — Antonio Vivaldi, Jean-Sébastien Bach, Georg Friedrich Haendel, Wolfgang Amadeus Mozart, Ludwig van Beethoven
— Gioachino Rossini, Felix Mendelssohn, Frédéric Chopin, Richard Wagner, Giuseppe Verdi
— Johann Strauss II, Johannes Brahms, Georges Bizet, Piotr Ilitch Tchaïkovski, Antonín Dvořák
— Edvard Grieg, Edward Elgar, Sergueï Rachmaninov, George Gershwin, Aram Khatchatourian.)
La musique classique désigne, pour le grand public, l'ensemble de la musique occidentale appelée « savante » par distinction avec la musique populaire, à partir de la musique médiévale et jusqu'à nos jours.
Si une ambiguïté persiste dans la définition de ce que représente la musique classique, elle est due à l'usage systématique (et sans doute impropre) de l'adjectif « classique », qui sert également à définir une période spécifique de la musique savante o

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Musique de la période classique

La musique de la période classique recouvre par convention la musique écrite entre la mort de Johann Sebastian Bach soit 1750 et le début de la période romantique, soit les années 1820. Par extension,

Musique de chambre

Une œuvre de musique de chambre est une composition musicale destinée à un petit ensemble de cordes, bois, cuivres ou percussions, qui traditionnellement et avant l'affirmation des concerts publics,

Piano

thumb|Piano à queue français actuel Pleyel
thumb|Intérieur d'un piano droit
Le piano est un instrument de musique polyphonique, à clavier, de la famille des cordes frappées. Le son est produit lors

COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numerical exercises.

PHYS-207(a): General physics : quanta

Ce cours est une introduction à la mécanique quantique. En partant de son développement historique, le cours traite les notions de complémentarité quantique et le principe d'incertitude, le processus de mesure, l'équation de Schrödinger, ainsi que des éléments de physique atomique et moléculaire.

PHYS-201(b): General physics : electromagnetism

Introduction à la mécanique des fluides, à l'électromagnétisme et aux phénomènes ondulatoires

Charles Chadi Ayoubi, Boris Thurm

Why do individuals make different decisions when confronted with similar choices? This paper investigates whether the answer lies in an evolutionary process. Our analysis builds on recent work in evolutionary game theory showing the superiority of a given type of preferences, homo moralis, in fitness games with assortative matching. We adapt the classical definition of evolutionary stability to the case where individuals with distinct preferences in a population coexist. This approach allows us to establish the characteristics of an evolutionarily stable population. Then, introducing an assortment matrix for assortatively matched interactions, we prove the existence of a heterogeneous evolutionarily stable population in 2x2 symmetric fitness games under constant assortment, and we identify the conditions for its existence. Conversely to the classical setting, we find that the favored preferences in a heterogeneous evolutionarily stable population are context-dependent. As an illustration, we discuss when and how an evolutionarily stable population made of both selfish and moral individuals exists in a prisoner's dilemma. These findings offer a theoretical foundation for the empirically observed diversity of preferences among individuals.

2018Analytical solutions to problems of solids mechanics are useful to test the accuracy and the precision of the numerical approaches. Problems such as shear locking or boundary layer can be better understood with the help of analytical solutions. However, it is known that only simple cases can be solved by hand. Furthermore, some cases which are theoretically solvable can also result in rather tedious analysis. Nowadays computer and mathematical software development allow to avoid this problem if they are associated with a suitable formulation. Classical formulations of mechanics of elastic body solve each particular problem by obtaining standard differential equations but generally do not give a unified method to solve them. In this paper a non-standard formulation is applied to find analytical solutions for elastic plates considering shear deformation (Reissner-Mindlin model) using a computer-aided approach. In addition, the results are compared to finite element model predictions. The main advantage of the proposed methodology over classical approaches is that it can be applied to problems of structural mechanics that are radically different using the same matrix framework, similarly to the FEM. Therefore, a computer-aided approach is used to obtain the analytical solution. This unified formulation is described Tassinari et al. [6]. The Reissner-Mindlin model (Reissner [3], Mindlin [4]) takes into account the shear deformation and it is generally recommended for moderately thick plates whereas Love-Kirchhoff model is more suitable for thin plates (Kirchhoff [1], Love [2]). The derivation of the governing equations of the RM plate results in a system of partial differential equations. The Levy solution technique can be used (Timoshenko and Woinowsky-Krieger [7], Szilard [5]) once the boundary conditions on two opposite edges are given. The solution is written as a series of orthogonal functions of the first coordinate multiplied by unknown functions of the second coordinate. The governing system is reduced to a system of ODEs that applies for each unknown term of the series. The application of the unified formulation to the Reissner-Mindlin plate results in a governing system of ODEs written in a matrix canonical form (see Tassinari et al. [6]). This expression is characterized by the state vector, which contains the generalized stresses and displacements, and the system matrix which describes the equilibrium. It is shown that this form can be applied to several problems of structural mechanics, by consistently adapting both system matrix and state vector. In this paper, the case of the Reissner-Mindlin plate problem with simply support on two opposite edges is solved. The analytical solution for a particular load case is presented showing the differences between the Reissner-Mindlin solution and the predictions given by the Love-Kirchhoff model (Kirchhoff [1], Love [2]). Finally, the vertical displacement field obtained analytically for different thickness-to-side ratios is compared with finite element method predictions. The analytical solution carried out shows the effect of the shear deformation in plate with small slenderness. In particular, the magnitude of this effect is significant for the vertical displacement. In general, the other components of the state vector are not significantly influenced in the domain of the plate but exhibits perturbations close to the edges. This edge effect is known as boundary layer and further investigations are needed considering higher-order terms. The results obtained from the proposed analytical method and numerical models presented in this study are comparable. Furthermore, the finite element analysis carried out shows that for a reasonable mesh refinement the numerical models used give excellent approximation of the analytical solution. Keywords: analytical solution, unified formulation, shell, plate, Reissner-Mindlin, Love-Kirchhoff, shear strain, finite element. References [1] Kirchhoff G., Über das Gleichgewicht und die Bewegungen einer elastischen Scheibe. Journal für reine und angewandte Mathematik, 1850; 40; 51–58. [2] Love, A. E. H., A treatise on the matematical theory of elasticity, Dover, 1944. [3] Mindlin R. D., Influence of rotatory inertia and shear on flexural vibration of isotropic, elastic plates. Journal of Applied Mechanics, 1951; 18; 31–38. [4] Reissner E., The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, 1945; 67; A69-A77. [5] Szilard R., Theories and applications of plate analysis: classical, numerical and engineering methods. Wiley, 2004. [6] Tassinari L, Monleon S, Gentilini C, Ubertini F. A unified approach for analytical solution of moderately thick shells and plates. (Paper in preparation). [7] Timoshenko S, Woinowsky-Krieger S. Theory of plates and shells. McGraw-Hill, 1959.

On November the 14th 1974, Jack Cornaz died in Lausanne, the town where he was born in 1886. This study traces the unusual career of this architect – a singular figure in the field of Swiss-French architecture of the twentieth century – whose name, from the 1920s, is associated with a wide range of neo-classical buildings on the shores of Lake Geneva, and analyses its context. Labelled both marginal and a dissident – depending on the standpoint of the critic – Cornaz's production is presented for the first time, through minute exploration of his unpublished archives, extensive information gathered in the course of interviews with numerous protagonists, both near and far, of the "cornazian scene", and comprehensive lateral research. Diversified in terms of quantity, and yet so uniform in terms of typology and program, his production appears consistent enough to express in itself the themes and motives which permit an understanding of both the variety of its expressions and in the unity of its intentions. The analysis of some of its nodal points – types of clients, production under influences, relevance of the old, problematic relationship to the tradition – provides an opportunity to grapple with broader architectural issues, some including ontological dimension : notion of imitation, bound to a style, relations between the architect and his patronage, autobiographical nature of his relation to the object, properties of the settlement... Though considered as a passéiste architect, Cornaz – at least at the start of his career – appreciated a form of modernity, understood as a progressive development of classical and regional types into a new language, which did not reject or betray the heritage of the past. In this respect, his work may be considered as representative of one of those traditionalist tendencies taken into account by the history of architecture over the last two decades. Based on the analytical cataloguing of the architect's archives deposited in the ACM (Archives of Modern Construction, Lausanne), the method applied in this study is a cross-disciplinary approach combining historical research with the principles of anthropological investigation. It is also based upon the interlocking of two propositions : it is a historical inquiry analysing sources as well as an epistemological reflection about cognitive procedures at work in the material in question. Adept at disciplinary nomadism and in mimetic fit with her object, the author applies a "patchwork" method. She is convinced that the effect of contiguity and accumulation is meaningful in itself, and that the interest of this matching of quotations, which leads to admittance for the need of the gaps and interplay of the elements, resides in its unsteadiness, like in a mosaic. The book consists of two closely connected volets. Chapters are thematic in the first one, these theoretical essays are completed with monographs of twenty of J. Cornaz's constructions and catalogue entries for his works.

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