Cône (géométrie)

vignette|Illustration à l'article Problemata mathematica... publiée sur les Acta Eruditorum, 1734 En géométrie, un cône est une surface réglée ou bien un solide. Surface Cas général Un cône est une surface réglée définie par une droite (d), appelée génératrice, passant par un point fixe S appelé sommet et un point variable décrivant une courbe (c), appelée courbe directrice. On parle aussi dans ce cas de surface conique. Cône de révolution Cône de révolution Parmi ces surfaces coniques, la plus étudiée est le cône de révolution dans lequel la courbe directrice est un cercle de centre O situé dans un plan perpendiculaire à (SO). Ce cône est appelé de révolution car il peut être généré simplement par la rotation d'une droite (d) passant par S autour d'un axe (Sz) différent de (d). La génératrice du cône fait alors un angle fixe \alpha avec l'axe de rotation. C'est à partir de ce cône de révolution que les mathématiciens (dont Apollonius

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (8)

Publications associées

Chargement

Personnes associées

Chargement

Unités associées

Chargement

Concepts associés (58)

Concepts associés

Chargement

Cours associés (12)

Cours associés

Chargement

Séances de cours associées (44)

Afficher plus

Séances de cours associées

Chargement

Helimagnons and Skyrmion Dynamics in Cu2OSeO3 and Fe/Gd Multilayers Explored by Brillouin Light Scattering and X-ray Microscopy

Ping Che

Spin dynamics in skyrmion hosting materials provide novel functionality in magnonics because of the formation of a novel magnon band structure and the nanoscale sizes of magnetic skyrmions. In this thesis, we explore the spin dynamics in the chiral magnet Cu2OSeO3 locally utilizing the scanning micro-focus Brillouin light scattering (BLS) technique at cryogenic temperature. Taking advantage of the high sensitivity and spatial resolution of BLS, we resolved the one-to-one correspondence between different non-collinear phases, such as helical, chiral soliton, conical and skyrmion phases, in a chiral magnet and their collective spin excitations. We show that the continuous-wave laser in BLS enables the stabilization of metastable phases and creation of skyrmion tracks surrounded by the conical phase. The high sensitivity of BLS allows us to deepen the understanding of coexisting phases in the chiral magnet. The results pave the way for the design of further magnonic devices based on chiral magnets. Furthermore, we explore dipolar skyrmions and domain walls in amorphous Fe/Gd multilayers employing scanning transmission x-ray microscopy. We demonstrate the formation of stripe and square lattices of domains by integrating one-dimensional and two-dimensional nanomagnet arrays, respectively. Dynamics of domain walls, multi-domain boundaries and skyrmions were captured with pump-probe spectroscopy. In a skyrmion pair, a magnon wavelength down to 239 nm at 0.33 GHz was observed and compared to the electromagnetic wave whose wavelength is 0.9 m at the same frequency. The extreme wavelength conversion underlines the potential of skyrmion hosting materials concerning miniaturization of information technology and microwave devices.

EPFL2021

Chargement

Enhancement of Second Harmonic Signal in Nanofabricated Cones

Fabrizia Dutto, Martin Heiss, Oriol López Sánchez, Andrea Lovera, Aleksandra Radenovic

Geometrical effects in optical nanostructures on nanoscale can lead to interesting phenomena such as inhibition of spontaneous emission,(1,2) high-reflecting omnidirectional mirrors, structures that exhibit low-loss-waveguiding,(3) and light confinement.(4,5) Here, we demonstrate a similar concept of exploiting the geometrical effects on nanoscale through precisely fabricating lithium niobate (LiNbO3) nanocones arrays devices. We show a strong second harmonic generation (SHG) enhancement, shape and arrangement dependent, up to 4 times bigger than the bulk one. These devices allow below diffraction limited observation, being perfect platforms for single molecule fluorescence microscopy(6) or single cell endoscopy.(7) Nanocones create a confined illumination volume, devoid from blinking and bleaching, which can excite molecules in nanocones proximity. Illumination volume can be increased by combining the SH enhancement effect with plasmon resonances, excited thanks to a gold plasmonic shell deposited around the nanostructures. This results in a local further enhancement of the SH signal up to 20 times. The global SH enhancement can be rationally designed and tuned through the means of simulations.

American Chemical Society2013

Chargement

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

Elia Iseli, Jürg Alexander Schiffmann

The dynamic behavior of spiral-grooved gas bearing supported four degrees-of-freedom (DOF) rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space representation, which couples the equations of motion with the compressible thin-film fluid equation. The linearized method is based on the perturbation analysis around a given eccentric shaft position e, allowing to compute the static and linear dynamic bearing force coefficients at different excitation frequencies. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of K = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-grooved journal bearings (HGJBs) have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1), the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1), the stability region decreases, and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of

2021

Chargement

MATH-126: Geometry for architects II

Ce cours traite des 3 sujets suivants : la perspective, la géométrie descriptive, et une initiation à la géométrie projective.

MATH-329: Continuous optimization

This course introduces students to continuous, nonlinear optimization. We study the theory of optimization with continuous variables (with full proofs), and we analyze and implement important algorithms to solve constrained and unconstrained problems.

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant la situation et appliquant les lois de la physique.

Géométrie

La géométrie est à l'origine la branche des mathématiques étudiant les figures du plan et de l'espace (géométrie euclidienne). Depuis la fin du , la géométrie étudie également les figures appartenan

Cylindre

vignette|Un cylindre quelconque. vignette|Divers cylindres droits (le premier est un cylindre circulaire droit). Un cylindre est une surface réglée dont les génératrices sont parallèles, c'est-à-dire

Ellipse (mathématiques)