Intermittency of Riemann's non-differentiable function through the fourth-order flatness
| Autor: | Boritchev, Alexandre, Eceizabarrena, Daniel, da Rocha, Victor Vilaça |
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| Rok vydání: | 2019 |
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| Zdroj: | J. Math. Phys. 62 (2021), 093101 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0011569 |
| Popis: | Riemann's non-differentiable function is one of the most famous examples of continuous but nowhere differentiable functions, but it has also been shown to be relevant from a physical point of view. Indeed, it satisfies the Frisch-Parisi multifractal formalism, which establishes a relationship with turbulence and implies some intermittent nature. It also plays a surprising role as a physical trajectory in the evolution of regular polygonal vortices that follow the binormal flow. With this motivation, we focus on one more classic tool to measure intermittency, namely the fourth-order flatness, and we refine the results that can be deduced from the multifractal analysis to show that it diverges logarithmically. We approach the problem in two ways: with structure functions in the physical space and with high-pass filters in the Fourier space. Comment: 17 pages, 2 figures. v2: Major revision. v3: Accepted manuscript |
| Databáze: | arXiv |
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