MultiScale Analysis: Fractal (An Introduction to Complex Systems in Environment)

Auteur(s) : Yacine MEZEMATE, Daniel SCHERTZER    2017-04-14,  2017-04-14  Éditeur(s) : Ecole des Ponts ParisTech   ENPC, UNIT   UNIT;     Description : In meteorology, oceanology, climatology, hydrology and more generally in geophysics, the researches (turbulence, chaos, global climate evolution understanding, tectonic, seismology...), in studies (strategies definition of sampling for the next generation satellite, estimation of extreme fluctuations of fields, cyclones trajectory or pollutants...), faced by a fundamental difficulty : the extreme variability at large scale range in time and space of the measured fields. This variability coming from the non linear interaction not only at different scale but also between different processes. In order to face on this difficulty, without using artifacts, it has been necessary to develop a specific tools, concepts and technical, to achieve both simple theoretical representations and quantitative assessment of this variability which can be repeated in a simple manner at different scales. These tools have been developed either from the analysis of symmetries of evolution equations when these are known, or on simple phenomenological considerations (self-similar models cascade) or even just empirical (spectra, structure functions...). These approaches have led to develop and renew the concepts of scale invariance or fractals, and releasing from the nonlinear variability a unifying issue geophysics. Module 6 of the course set "An Introduction to Complex Systems in Environment" Mots-clés libres : complex systems in environment, environmental engineering, extreme variability, multiscale analysis, Fractal, Hausdorff dimension, Von Koch snowflake, Cantor set, Sierpinski carpet, Box counting, Co-dimension, ingénierie de l'environnement, système complexe Accès à la ressource : https://hmco.enpc.fr/UNIT_ComplexSystems/~gen/6_Mu... Conditions d'utilisation : Cet ensemble de supports pédagogiques est la propriété, à parts égales, d’UNIT et de l'École des Ponts ParisTech. Il est régi par la licence logicielle GPL, dans sa version française CeCILL (http://www.cecill.info/licences/Licence_CeCILL-V1_VF.pdf).

DONNEES PEDAGOGIQUES Type pédagogique : lecture, exercise Granularité : 4 Niveau : higher education, bac+3 Public cible : teacher, learner, manager Langue de l'apprenant : fre Niveau d'interactivité du document : medium DONNEES TECHNIQUES Format : text/html

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