URI http://ori.unit-c.fr/uid/unit-ori-wf-1-7145 MultiScale Analysis: Fractal (An Introduction to Complex Systems in Environment) fre 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" 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 LOMv1.0 linear LOMv1.0 4 LOMv1.0 texte LOMv1.0 image LOMv1.0 ressource interactive LOMv1.0 author BEGIN:VCARD VERSION:3.0 N:MEZEMATE;Yacine;;; FN:Yacine MEZEMATE EMAIL;TYPE=INTERNET: ORG:Ecole des Ponts ParisTech END:VCARD 2017-04-14 LOMv1.0 author BEGIN:VCARD VERSION:3.0 N:SCHERTZER;Daniel;;; FN:Daniel SCHERTZER EMAIL;TYPE=INTERNET: ORG:Ecole des Ponts ParisTech END:VCARD 2017-04-14 LOMv1.0 publisher BEGIN:VCARD VERSION:3.0 N:Ecole des Ponts ParisTech;;;; FN:Ecole des Ponts ParisTech EMAIL;TYPE=INTERNET: ORG:ENPC END:VCARD 2017-04-14 LOMv1.0 publisher BEGIN:VCARD VERSION:3.0 N:UNIT;;;; FN:UNIT EMAIL;TYPE=INTERNET: ORG:UNIT END:VCARD 2017-04-14 URI http://ori.unit-c.fr/uid/unit-ori-wf-1-7146 LOMv1.0 LOMFRv1.0 SupLOMFRv1.0 text/html https://hmco.enpc.fr/UNIT_ComplexSystems/~gen/6_MultiScaleAnalysis_Fractal/6_MultiScaleAnalysis_Fractal_web.publi/web/co/6_MultiScaleAnalysis_Fractal_web.html LOMv1.0 lecture LOMv1.0 exercise LOMv1.0 medium LOMv1.0 teacher LOMv1.0 learner LOMv1.0 manager LOMv1.0 higher education SupLOMFRv1.0 bac+3 fre LOMv1.0 no LOMv1.0 yes 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). LOMv1.0 ispartof URI https://hmco.enpc.fr/complex-systems/ An Introduction to Complex Systems in Environment LOMv1.0 discipline Classification UNIT 104 Traitements de problèmes d'environnement Classification UNIT 103 Problèmes d'environnement LOMv1.0 discipline CDD 22e éd. 628.1 Techniques sanitaires et urbaines : approvisionnement en eau CDD 22e éd. 628.5 Contrôle de la pollution et techniques d'hygiène industrielle : sites pollués, sols, air CDD 22e éd. 363.7 Déchets, pollutions, polluants, bruit LOMv1.0 security level Projet OCW France tag-ocw Catalogue OCWC home-example unit-cofinance