Search results for "geometry."
showing 10 items of 4386 documents
Variable Length Markov Chains, Persistent Random Walks: a close encounter
2020
This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.
Famille à un paramètre de coniques utilisant des courbes de Bézier à poids complexes
2019
The paper deals with conics in a rational Bézier representation based on mass points where the weights are complex numbers here. A special representation of conics using weighted points and vectors offers a calculus flexibility in the handle elementary geometrical transformations as rotations, homotheties and direct similarity transformations. Some examples are proposed to the reader.
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.
Integrable Systems and Factorization Problems
2002
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is…
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…
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.
Orientation of Polar Molecules by Laser Induced Adiabatic Passage
2002
International audience; We show that two overlapping linearly polarized laser pulses of frequencies ω and its second harmonic 2ω can strongly orient linear polar molecules, by adiabatic passage along dressed states. The resulting robust orientation can be interpreted as a laser-induced localization in the effective double well potential created by the fields, which induces a preliminary molecular alignment. The direction of the orientation can be selected by the relative phase of the fields.
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…