Multifractal analysis of streamflow records of the East River basin (Pearl River), China

Scaling behaviors of the long daily streamflow series of four hydrological stations (Longchuan (1952-2002), Heyuan (1951-2002), Lingxia (1953-2002) and Boluo (1953-2002)) in the mainstream East River, one of the tributaries of the Pearl River (Zhujiang River) basin, were analyzed using multifractal detrended fluctuation analysis (MF-DFA). The research results indicated that streamflow series of the East River basin are characterized by anti-persistence. MF-DFA technique showed similar scaling properties in the streamflow series of the East River basin on shorter time scales, indicating universal scaling properties over the East River basin. Different intercept values of the fitted lines of log-log curve of F_q(s) versus s implied hydrological regulation of water reservoirs. Based on the numerical results, we suggested that regulation activities by water reservoirs could not impact the scaling properties of the streamflow series. The regulation activities by water reservoir only influenced the fluctuation magnitude. Therefore, we concluded that the streamflow variations were mainly the results of climate changes, and precipitation variations in particular. Strong dependence of generalized Hurst exponent h(q) on q demonstrated multifractal behavior of streamflow series of the East River basin, showing ‘universal’ multifractal behavior of river runoffs. The results of this study may provide valuable information for prediction and assessment of water resources under impacts of climatic changes and human activities in the East River basin.     

Multifractal structure in high energy collisions and finite multiplicity corrections

There are established rigorous relations between scaling indices which reveal on one hand the presence of intermittency and on the other hand the presence of multifractal phenomena represented by the frequencyG-moments. In the procedure applied in present paper, also the corresponding intercepts as well as an effective average multiplicity are involved. The last mentioned quantity is introduced by extending the relation which characterizes appearance of the multifractality. It is shown that the relation between scaling indices and corresponding slopes is satisfied with sufficient accuracy by the data available so far on deep-inelastic muon-nucleon scattering at 280 GeV.     

On Multifractal Rigidity

We analyze when a multifractal spectrum can be used to recover the potential. This phenomenon is known as multifractal rigidity. We prove that for a certain class of potentials the multifractal spectrum of local entropies uniquely determines their equilibrium states. This leads to a classification which identifies two systems up to a change of variables.     

Multifractal structure of fully developed hydrodynamic turbulence. I. Kolmogorov's third hypothesis revisited

We discuss intermittency effects in fully developed hydrodynamic turbulence. It is shown that the application of the bounded log-normal distribution to the fluctuations of the local energy dissipation rate resolves some basic difficulties related to Kolmogorov's third hypothesis and gives a good agreement with experiment. The nonlinear interaction of the large-scale and inertial-range turbulent pulsations of the velocities may explain the observable characteristics of the intermittency. We give also a detailed comparison of the results obtained with the use of the bounded log-normal distribution with that obtained in the framework of the homogeneous and random-models, a two-scale Cantor set approximation, and the original unbounded log-normal distribution suggested by Kolmogorov and Obukhov.     

Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence

We present the results of studying the multifractal structure of intermittency in a developed ionospheric turbulence during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is shown, in particular, that the determination of multidimensional structural functions of the energy fluctuations of received signals permits one to obtain the necessary information on multifractal spectra of the studied process of radio-wave scattering in the ionosphere. Experimental data on multifractal spectra of slow fluctuations in the received-signal energy under conditions of a developed small-scale turbulence are compared with the existing concept of the radio-wave scattering within the framework of the statistical theory of radio-wave propagation in the ionosphere. It is inferred that under conditions of a developed ionospheric turbulence, the multifractal structure of the intermittency of slow fluctuations in the received-signal energy is a consequence of the intermittency of small-scale fluctuations in the electron number density of the ionospheric plasma on relatively large spatial scales of about several ten kilometers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 485–493, June 2008.     

On a general concept of multifractality: Multifractal spectra for dimensions,entropies, and Lyapunov exponents. Multifractal rigidity

We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is devoted to the concept of multifractal rigidity. In particular, we use the multifractal spectra to obtain a "physical" classification of dynamical systems. For a class of Markov maps, we show that, if the multifractal spectra for dimensions of two maps coincide, then the maps are differentiably equivalent. (c) 1997 American Institute of Physics.     

Log-Infinitely Divisible Multifractal Processes

 We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson ``product of cylindrical pulses' [7]. Their construction involves some ``continuous stochastic multiplication' [36] from coarse to fine scales. They are obtained as limit processes when the finest scale goes to zero. We prove the existence of these limits and we study their main statistical properties including non-degeneracy, convergence of the moments and multifractal scaling. Received: 8 July 2002 / Accepted: 17 December 2002 Published online: 14 April 2003 Communicated by A. Connes     

Multifractal Statistics of Mesoscopic Systems

A generalization of the Havlin–Bunde multifractal hypothesis is used to obtain a probability distribution corresponding to mesoscopic systems close to the critical regime. Good agreement between results of numerical simulations performed by different authors and this new type of probability distribution is established.     

Multifractal behaviour of n-simplex lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an n-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, β _L, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.     

Multifractal dimension of Lagrangian turbulence

We report experimental measurements of the Lagrangian multifractal dimension spectrum in an intensely turbulent laboratory water flow by the optical tracking of tracer particles. The Legendre transform of the measured spectrum is compared with measurements of the scaling exponents of the Lagrangian velocity structure functions, and excellent agreement between the two measurements is found, in support of the multifractal picture of turbulence. These measurements are compared with three model dimension spectra. When the nonexistence of structure functions of order less than -1 is accounted for, the models are shown to agree well with the measured spectrum.     

Multifractal analysis of infinite products

We construct a family of measures called infinite products which generalize Gibbs measures in the one-dimensional lattice gas model. The multifractal properties of these measures are studied under some regularity conditions. In particular, if the -function is differentiable, we prove a formula which gives the Hausdorff dimension and packing dimension of the set of singularity points of a given order. Mathematical examples include Riesz products,g-measures, andG-measures.     

Multifractal Spectra of Fragmentation Processes

Let (S(t),t0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the fragment that contains x decays exponentially with rate v. We show that there is v _typ>0 such that almost every point x]0,1[ has speed v _typ. Nonetheless, for v in a certain range, the random set _v of points of speed v, is dense in ]0,1[, and we compute explicitly the spectrum vDim( _v ) where Dim is the Hausdorff dimension.     

Multifractal Analysis of Hyperbolic Flows

We establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type. A non-trivial consequence of our results is that for every H?lder continuous function non-cohomologous to a constant, the set of points without Birkhoff average has full topological entropy. Received: 18 November 1999 / Accepted: 3 April 2000