Intervalle (musique) | EPFL Graph Search

En musique, l'intervalle entre deux notes est l'écart entre leurs hauteurs respectives. Cet intervalle est dit harmonique si les deux notes sont simultanées, mélodique si les deux notes sont émises successivement. En acoustique, l'intervalle entre deux sons harmoniques est le rapport de leurs fréquences. Chaque intervalle d'une échelle musicale, elle-même distinctive d'un type de musique (indienne, occidentale, musique orientale, etc.). La perception des intervalles diffère selon les cultures. Il n'existe pas de système musical universel contenant tous les intervalles de toutes les échelles musicales. . Lorsqu'un ne possède pas de , la pour rendre compte des intervalles et des échelles propres à ce système. Propriétés acoustiques Acoustique musicale Historiquement, l'étude des intervalles a commencé par l'étude des rapports entre fréquences. L’école pythagoricienne a, grâce au monocorde, réussi à construire des micro-intervalles, quasi imperceptibles, par simple s

Architecture, environnement et artefact total : la ville selon Reyner Banham et Oswald Mathias Ungers

Thibaut Jean Bernard Pierron

When looking at the city and the land, current architectural practices face a double limitation. On the one hand, the discipline is asked to react to its own specter: the body of authoritarian spatial devices based on a questionable tradition of which the history is well established. All the usual rules that perpetuate themselves in the name of "the good settlement, one relevant and responsive to any human context" [K. Lynch, 1981]. On the other hand, architecture, as a positive and effective strength, is called upon to demonstrate its ability to resist the most evident threat weighting on the land: can architecture - its knowledge and means - contribute to counter territorial consequences of pervasive and expansive logic of advanced capitalism? In taking up this double-task for the city, is architecture then left with only two lasting dead-ends: the dissolution of its lore within a larger ensemble of social practices or the seclusion of the last parcels of its prerogatives, those that can still be rescued? In order to trace an "other" path, our research simultaneously examines the routes taken on both sides of the Atlantic by two figures of the architecture of the second half of the 20th Century: British historian and critic Reyner Banham (1922-1988) and German architect and theoretician Oswald Mathias Ungers (1926-2007). At first sight, such a choice raises two questions: that of the dissimilitude of their respective work and that of the distance which seems to separate their positions within the intellectual field of their time. One of the goals of our research is to draw closer different modes of comprehending the city and the land. Both protagonists used a wide range of tools available - those of the architectural discipline understood as a set of practices and a collected knowledge - to render, in particular, the state of the world, of the western land, of the city and what it became. The main goal of our research is then to track a possible common ground for their positions about the city, which are contemporary to one another and regarded as being differing. Our parallel study of the works on the city of R. Banham and O. M. Ungers must lead to an actualization of our understanding of a set of trails already opened and to seize the consequences on a historiographical, theoretical and practical level. Therefore, our research tends to verify the existence of such common ground in measuring the proximity of the urban and territorial conception in their work, focusing on an interval starting at the beginning of the 1960s to the end of the 1970s. To achieve it, we formulate three hypotheses regarding the themes at the basis of their convergence: the recognition of the emergence of a new condition of the western land; the will to oppose to urbanism and planning different methods; and the definition of a critical equipment based on images.

EPFL2021

Optimal control of nonmodal disturbances in boundary layers

Peter Corbett

"The optimal control of infinitesimal flow disturbances experiencing the largest transient gain over a fixed time span, commonly termed ""optimal perturbations,"" is undertaken using a variational technique in two- and three-dimensional boundary layer flows. The cost function employed includes various energy metrics which can be weighted according to their perceived importance, simplifying the task of determining which terms are essential for a ""good"" control scheme. In the accelerated boundary layers investigated, disturbance kinetic energy can be typically reduced by about one order of magnitude. However, it seems impossible to suppress perturbations completely over the entire control interval; ""good"" control strategies still permit approximately an order of magnitude growth over the initial energy at some point in the interval. It is shown that the control effort efficiently targets the physical mechanisms behind transient growth."

2001

Analysis and numerical simulation of free surface flows

Alexandre Caboussat

Mathematical and numerical aspects of free surface flows are investigated. On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has to be solved on a space interval with one free extremity. This extremity is unknown and moves in time. An ordinary differential equation for the position of the free extremity of the interval is added in order to close the mathematical problem. Local existence in time and uniqueness results are proved for the problem with given domain, then for the free surface problem. A priori and a posteriori error estimates are obtained for the semi-discretization in space. The stability and the convergence of an Eulerian time splitting scheme are investigated. The same methodology is then used to study free surface flows in two space dimensions. The incompressible unsteady Navier-Stokes equations with Neumann boundary conditions on the whole boundary are considered. The whole boundary is assumed to be the free surface. An additional equation is used to describe the moving domain. Local existence in time and uniqueness results are obtained. On the other hand, a model for free surface flows in two and three space dimensions is investigated. The liquid is assumed to be surrounded by a compressible gas. The incompressible unsteady Navier-Stokes equations are assumed to hold in the liquid region. A volume-of-fluid method is used to describe the motion of the liquid domain. The velocity in the gas is disregarded and the pressure is computed by the ideal gas law in each gas bubble trapped by the liquid. A numbering algorithm is presented to recognize the bubbles of gas. Gas pressure is applied as a normal force on the liquid-gas interface. Surface tension effects are also taken into account for the simulation of bubbles or droplets flows. A method for the computation of the curvature is presented. Convergence and accuracy of the approximation of the curvature are discussed. A time splitting scheme is used to decouple the various physical phenomena. Numerical simulations are made in the frame of mould filling to show that the influence of gas on the free surface cannot be neglected. Curvature-driven flows are also considered.