Cascade phenomenology

Lesson

Introduction
The matter of scale
Intermittency
Discrete cascade
- Introduction
- Cascade principle
- β-model
- α-model
- p-model
Other type of cascade
Exercises
To go further
Conclusion

Cascade principle

We show in this slide the principle of construction of cascades. Assuming the studied domain has the dimension corresponds to the biggest structure which has an intensity of . It consist of iterating a scale invariant cascade generator from the largest scale to the smallest one . The ratio of these scale is defined as a resolution

. The first step consist to divide the domain by structure, and to assign to each structure an intensity

. Where is the realization of the structure of the first generation of the cascade of a random variable .

Construction of cascade by n iteration of scale invariance generator | Information^[1]

Construction of cascade by n iteration of scale invariance generator | Information^[1]

Biaou, A. (2004). De la méso-échelle à la micro-échelle: Désagrégation spatio-temporelle multifractale des précipitations (Doctoral dissertation, Paris, ENMP).

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