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On extension of the formalism MPDFA and its application to the analyses of DNS 4096$^3$ conducted by Kaneda and Ishihara

Arimitsu, T (Tsukuba)
Tuesday 30 September 2008, 11:30-12:00

Seminar Room 1, Newton Institute


Our original theoretical framework, named Multi-fractal Probability Density Function Analysis (MPDFA), has been extended successfully in order to make it possible to analyze a series of probability density functions (PDFs), extracted from experiments and numerical simulations, with arbitrarily changed measuring areas or distances for various physical quantities representing intermittent behavior characterizing fully developed turbulence.

MPDFA is a unified self-consistent approach for the systems with large deviations, which has been constructed based on the Tsallis-type distribution function following the assumption raised by Frisch and Parisi that the singularities due to the scale invariance of the Navier-Stokes equation for high Reynolds number distribute themselves multifractal way in real physical space. MPDFA can be said as a generalization of the log-normal model. It was shown that MPDFA derives the log-normal model when one starts with the Boltzmann-Gibbs distribution function instead of Tsallis-type distribution function.

As a test of the validity of the extension, we analyzed the PDFs for energy transfer rates and for energy dissipation rates extracted by Kaneda and Ishihara group at Nagoya University from their DNS 4096$^3$.

In this talk, we will present mainly on the theoretical extension of MPDFA and its validity. The detailed analyses of PDFs out of DNS 4096$^3$ and the physical outcomes from them will be given at our poster presentation of this workshop.

Related Links
  • - Journal of Physics: Conference Series {\bf 7} (2005) 101--120.
  • - Anomalous Fluctuation Phenomena in Complex Systems: Plasma Physics, Bio-Science and Econophysics (Special Review Book for Research Signpost), eds. C.~Riccardi and H.E.~Roman (Transworld Research Network, Kerala, India, 2008) in press.


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