Search results for " Geometry."
showing 10 items of 2189 documents
Points massiques, hyperbole et hyperboloïde à une nappe
2015
National audience; Les courbes de Bézier rationnelles quadratiques jouent un rôle fondamental pour la modélisation d'arcs de coniques propre. Cependant, lorsque les deux points extrémaux de l'arc ne sont pas sur la même branche d'une hyperbole, l'utilisation des courbes de Bézier classiques est impossible. Il suffit de considérer les points massiques, à la place des points pondérés, pour remédier à ce problème. De plus, nous gardons la structure (pseudo)-métrique du plan dans lequel nous nous trouvons et il possible de modéliser une branche d'hyperbole dont les extrémités sont deux vecteurs, non colinéaires, de même norme, définis par les directions des asymptotes. Nous donnons comme applic…
Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension
2020
We compute the minimal number p_min of closed orbits of any Morse-Smale flow on any compact odd-dimensional manifold with boundary in terms of some given homological information. The underlying algorithm is based on optimization theory in network flows and transport systems. Such a number p_min is a lower bound in the general case but we provide, for any initial homological data, a Morse-Smale model for which p_min is attained. We also apply our techniques to the problem of the continuation of Lyapnov graphs to Lyapnov graphs of Smale type.
Snapshot imaging of postpulse transient molecular alignment revivals
2008
Laser induced field-free alignment of linear molecules is investigated by using a single-shot spatial imaging technique. The measurements are achieved by femtosecond time-resolved optical polarigraphy (FTOP). Individual alignment revivals recorded at high resolution in ${\text{CO}}_{2}$, as well as simultaneous observation of several alignment revivals produced within the rotational period of the ${\text{O}}_{2}$ molecule are reported. The data are analyzed with a theoretical model describing the alignment experienced by each molecule standing within the interaction region observed by the detector. The temporal dynamics, intensity dependence, and degree of alignment are measured and compare…
Surface plasmon routing along right angle bent metal strips
2005
International audience; An efficient routing of surface plasmon polaritons (SPP) is of fundamental importance in the development of SPP-based photonics. This paper reports that microgratings acting as Bragg mirrors can guide SPP along metal stripes waveguides featuring 90 degrees bents. The measurement of the mirrors efficiency, performed by means of photon scanning tunneling microscopy, shows that bent losses as low as 1.9 dB can be achieved. Finally, we demonstrate operating SPP beamsplitters obtained by an appropriate design of the Bragg mirrors constituting elements. (c) 2005 American Institute of Physics.
Fractal geometry and urban patterns – from exploring morphology to applications in planning
2014
International audience; Fractal geometry turned out to be a powerful approach in many domains for describing complex structures which have multiscale properties. In particular, fractal analysis allows making evident scaling properties and hence underlying structural order principles which cannot be discovered by other measuring approaches like densities which refer to one unique scale. We present here how this approach helps to analyze the distribution of build-up surface in urban patterns and how it can be used to link these morphologiocal properties to specific contexts of urbanization. Indeed, contemporary urban patterns have usually an irregular shape reminding rather deposits on surfac…
Fractal geometry for modeling and measuring urban patterns
2012
International audience
The role of virtual work in Levi-Civita's parallel transport
2015
International audience; According to current history of science, Levi-Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi-Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport.
Building scenarios for a LUTI model : articulation of spaced based models and an agent based model
2013
International audience
Extension des méthodes de géométrie algorithmique aux structures fractales
2013
Defining shapes by iteration allows us to generate new structures with specific properties (roughness,lacunarity), which cannot be achieved with classic modelling.For developing an iterative modeller to design fractals described by a BCIFS, we developed a set oftools and algorithms that permits one to evaluate, to characterize and to analyse different geometricproperties (localisation, convex hull, volume, fractal dimension) of fractals. We identified properties ofstandard CAD operations (intersection, union, offset, . . . ) allowing us to approximate them for fractalsand also to optimize these approximation algorithms.In some cases, it is possible to construct a CIFS with generalised HUTCH…
Development of Removable Visual Impact Indicator or Polymer Composite Materials
2021
The prototype of removable visual impact indicator for thermoset polymer composite materials is developed, and its characteristics are experimentally determined. The indicator is a fabric tape glued by epoxy to the surface of the polymer composite. The tape is impregnated with a composition that provides a visual response at the place of an impact on the composite surface. Ball-drop tests demonstrated the increase of the magnitude of the visual response with the impact energy at different substrate hardnesses. The shelf-life and mode of the tape storage until commissioning are determined. Peel tests showed the ability to remove a used indicator without damaging the surface of the composite.