Characterization of self-similarity properties of turbulence in magnetized plasmas

Scipioni, A.; Rischette, P.; Bonhomme, G.; Devynck, P.
November 2008
Physics of Plasmas;11/1/2008, Vol. 15 Issue 11, p112303
Academic Journal
The understanding of turbulence in magnetized plasmas and its role in the cross field transport is still greatly incomplete. Several previous works reported on evidences of long-time correlations compatible with an avalanche-type of radial transport. Persistence properties in time records have been deduced from high values of the Hurst exponent obtained with the rescaled range R/S analysis applied to experimental probe data acquired in the edge of tokamaks. In this paper the limitations of this R/S method, in particular when applied to signals having mixed statistics are investigated, and the great advantages of the wavelets decomposition as a tool to characterize the self-similarity properties of experimental signals are highlighted. Furthermore the analysis of modified simulated fractional Brownian motions (fBm) and fractional Gaussian noises (fGn) allows us to discuss the relationship between high values of the Hurst exponent and long range correlations. It is shown that for such simulated signals with mixed statistics persistence at large time scales can still reflect the self-similarity properties of the original fBm and do not imply the existence of long range correlations, which are destroyed. It is thus questionable to assert the existence of long range correlations for experimental signals with non-Gaussian and mixed statistics just from high values of the Hurst exponent.


Related Articles

  • On the infinite divisibility of squared Gaussian processes. Eisenbaum, Nathalie // Probability Theory & Related Fields;2003, Vol. 125 Issue 3, p381 

    We show that fractional Brownian motions with index in (0,1] satisfy a remarkable property: their squares are infinitely divisible. We also prove that a large class of Gaussian processes are sharing this property. This property then allows the construction of two-parameters families of processes...

  • Scanning Brownian processes. Adler, Robert J.; Pyke, Ron // Advances in Applied Probability;Jun97, Vol. 29 Issue 2, p295 

    Describes how a Gaussian random field is obtained by associating a random field with the value of a set-indexed Brownian motion on the translate of some scanning set. Definition of quadratic variation; Examination of the validity of assumptions made; Application of convex polygons.

  • Non-Gaussian density processes arising from non-poisson... Feldman, Raisa E.; Iyer, Srikanth K. // Journal of Applied Probability;Mar1998, Vol. 35 Issue 1, p213 

    Studies a Gaussian distribution-valued process, the Brownian density process. How the appropriate change in the initial distribution of the infinite particle system, the limiting density is non-Gaussian; Results of the study.

  • Multiple points of trajectories of multiparameter fractional Brownian motion. Talagrand, Michel // Probability Theory & Related Fields;1998, Vol. 112 Issue 4, p545 

    Consider 0<α<1 and the Gaussian process Y(t) on ℝ[sup N] with covariance E(Y(s)Y(t))=|t|[sup 2α] +|s|[sup 2α] -|t-s|[sup 2α] , where |t| is the Euclidean norm of t. Consider independent copies X[sup 1] ,…,X[sup d] of Y and␣the process X(t)=(X[sup 1] (t),…,X[sup...

  • Stochastic analysis, rough path analysis and fractional Brownian motions. Coutin, Laure; Qian, Zhongmin // Probability Theory & Related Fields;2002, Vol. 122 Issue 1, p108 

    In this paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we furthermore obtain a Skohorod integral...

  • A Special Case of Wealth Motion. Stoynov, P. // Journal of Mathematical Sciences;Jun2004, Vol. 121 Issue 5, p2692 

    Considers a simple model for wealth change, called the Homogeneous General Wealth Motion Model. Formulation and proof of a result about the boundary for the probability of default for the Brownian motion with returns to zero; Other models describing a change in wealth; Determination of the...

  • GEOMETRICAL BROWNIAN MOTION DRIVEN BY COLOR NOISE. Zygadlo, Ryszard // Acta Physica Polonica B;2008, Vol. 39 Issue 5, p1283 

    The geometrical Brownian motion driven by Gaussian or dichotomous color noise is considered. The ordinary Malthusian evolution is observed for long times, however the initial values seem lowered and additionally, in the case of dichotomous noise, the rate of growth is decreased. In the latter...

  • Exit problems associated with affine reflection groups. Doumerc, Yan; Moriarty, John // Probability Theory & Related Fields;Nov2009, Vol. 145 Issue 3/4, p351 

    We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type $${\widetilde{A}}$$ case. The results extend to other...

  • Right inverses of Lévy processes and stationary stopped local times. Evans, Steven N. // Probability Theory & Related Fields;2000, Vol. 118 Issue 1, p37 

    If X is a symmetric Lévy process on the line, then there exists a non-decreasing, càdlàg process H such that X(H(x)) = x for all x >= 0 if and only if X is recurrent and has a non-trivial Gaussian component. The minimal such H is a subordinator K. The law of K is identified and shown to...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics