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Tue, 31 Mar 2020 01:13:57 GMT

Cascade phenomenology (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
Multiplicative cascade processes are frequently used as phenomenological models for the study of a variety of complex systems exhibiting fractal/multifractal behavior. In particular the energy dissipation field of fully developed turbulent flows has been most successfully modeled in such terms, physically motivated by Richardson's poem of energy transfer from large to small scales by random breakups of eddies. Multiplicative cascade models are based on two assumptions: the existence of a scaleindependent and statistical independence of the random weights at one breakup from those of any other breakup.
During this lesson, we will give the principle of cascade and in which context were developed. We introduce three types of models that describe the cascade phenomenology. We finished with two exercises which allows us to play with model and the model.
Module 4 of the course set "An Introduction to Complex Systems in Environment"
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Spectral Analysis (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
We introduce in this lecture the spectral analysis which is based on the Fourier transform. The main objective of using this can of analysis in our studies is to check the scale invariance propriety of the studied field and also to identify the involved processes. The spectral analysis is widely used in fluid dynamics especially in turbulence field. We will show in this lesson that the spectrum of the studied field in loglog plot is characterized by a given slope which allows us to identify the involved process. We will start this lesson by an introduction to the Fourier transform and the discrete Fourier transform, after that we will mention some domain of application of the spectral analysis and we will finish by the identification of some process in geophysics.
Module 5 of the course set "An Introduction to Complex Systems in Environment"
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URL: http://www.supnumerique.gouv.fr/ressourcespedagogiques/notice/view/oai%253Awww.unit.eu%253Aunitoriwf17143 ]]>