twenty five years of multifractals in fully developed turbulence a tribute to giovanni paladin the paper on the multifractal nature of fully developed turbulence and chaotic systems by benzi et al 1984 j phys a math gen 17 3521 has been a starting point of many investigations on the different faces of self similarity and intermittency in turbulent phenomena since then the multifractal model has become a useful tool for the study of small scale turbulence in particular for detailed predictions of different eulerian and lagrangian statistical properties on the occasion of the 50th birthday of our unforgettable friend and colleague giovanni paladin 1958 1996 we review here the basic concepts and some applications of the multifractal model for turbulence

on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

multifractal fluctuations in the survival probability of an open quantum system we predict a multifractal behavior of transport in the deep quantum regime for the opened kicked rotor model our analysis focuses on intermediate and large scale correlations in the transport signal and generalizes previously found parametric mono fractal fluctuations in the quantum survival probability on small scales

cascade structures and scaling exponents in a dynamical model of turbulence measurements and comparison a detailed examination of the cascade statistics and scaling exponents is carried out for a dynamical system model of fully developed turbulence called the goy shell model the convergence in time of the probability density functions and moments of the velocity fluctuations and their scaling exponents is studied with particular care with a large sample size 5 ifmmode times else texttimes fi 10 9 we demonstrate that there exists a finite cutoff for the velocity fluctuations at each inertial range wave number shell and the properties of the cutoff determine the scaling exponents of all moments this cutoff represents the most intermittent structures in the cascade dynamics and exhibits a power law dependence on wave number the accurately determined scaling exponents permit a detailed comparison with various phenomenological models describing the statistics of the energy cascade the consideration of the first and second derivatives of the scaling exponents with respect to the order of the moments p provides the evidence that the hierarchical structure model she and leveque phys rev lett 72 336 1994 predicts the best functional dependence on p of the scaling exponents in the goy shell model

the nilpotent centralizer method for spectrally arbitrary patterns this paper introduces a new criterion for an n n sign pattern respectively zero nonzero pattern a to be spectrally arbitrary that is to have the property that for each monic real polynomial r x of degree n there exists a matrix with sign pattern respectively zero nonzero pattern a that has r x as its characteristic polynomial to date analytic properties of a certain polynomial map associated with a have been used to prove that a is spectrally arbitrary in this paper we derive a method that uses the algebraic structure of a certain nilpotent matrix to show that a sign pattern respectively zero nonzero pattern is spectrally arbitrary

predictability of velocity and temperature fields in intermittent turbulence we discuss the relation between predictability and the sensitive dependence on initial conditions in turbulent flows the dependence on the reynolds number of the maximum lyapunov exponent of the flow is evaluated within the multifractal model the temporal intermittency of the degree of chaos is found to localize on the degrees of freedom corresponding to high wavenumbers we discuss the consequences for the mechanism for the growth of small perturbations we show that intermittency causes long tails in the distribution of the predictability times both in the velocity field and in a passively advected scalar field though there is no simple relation between these two times numerical evidence of this picture is provided within the framework of a cascade model for velocity and temperature fields in fully developed turbulence

on intermittency in a cascade model for turbulence in this note we study the possibility of performing analytic computations of the exponents characterizing the multifractal behaviour of turbulence a simple analytic computation is presented in the framework of the cascade model or shell model

parameter estimation in non extensive thermostatistics abstract equilibrium statistical physics is considered from the point of view of statistical estimation theory this involves the notions of statistical model of estimators and of exponential family a useful property of the latter is the existence of identities obtained by taking derivatives of the logarithm of the partition sum it is shown that these identities still exist for models belonging to generalised exponential families in which case they involve escort probability distributions the percolation model serves as an example a previously known identity is derived it relates the average number of sites belonging to the finite cluster at the origin the average number of perimeter sites and the derivative of the order parameter

new classes of spectrally arbitrary ray patterns an n n ray pattern matrix s is said to be spectrally arbitrary if for every monic nth degree polynomial f with coefficients from c there is a complex matrix in the ray pattern class of s such that its characteristic polynomial is f in this article we give new classes of spectrally arbitrary ray pattern matrices

spectrally and inertially arbitrary sign patterns we introduce some n by n sign patterns which allow for arbitrary spectrum and hence also arbitrary inertia consequently we demonstrate that some known inertially arbitrary patterns are in fact spectrally arbitrary we demonstrate that all inertially arbitrary patterns of order 3 are spectrally arbitrary and classify all spectrally arbitrary patterns of order 3 we illustrate that in general the class of spectrally arbitrary patterns is distinct from the inertially arbitrary patterns and present some observations about inertially arbitrary patterns

nonharmonic fourier series and spectral theory we consider the problem of using functions g x exp ix 1 x to form biorthogonal expansions in the spaces lp 7r sr for various values of p the work of paley and wiener and of levinson considered conditions of the form ix ni a p which insure that g is part of a biorthogonal system and the resulting biorthogonal expansions are pointwise equiconvergent with ordinary fourier series norm convergence is obtained for p 2 in this paper rather than imposing an explicit growth condition we assume that x n is a multiplier sequence on lp t 7t conditions are given insuring that g inherits both norm and pointwise convergence properties of ordinary fourier series further xn and gn are shown to be the eigenvalues and eigenfunctions of an unbounded operator a which is closely related to a differential operator i a generates a strongly continuous group and a2 generates a strongly continuous semigroup half range expansions involving cos x x or sin x n x on 0 7t are also shown to arise from linear operators which generate semigroups many of these results are obtained using the functional calculus for well bounded operators

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

on the f alpha spectrum of one hump maps based on a perturbative procedure developed to solve for the universal parameters of one hump maps the corresponding fractal dimensions dq and the f alpha spectrum are studied

harmonious representation of pdfs reflecting large deviations abstract the framework of multifractal analysis mfa is distilled to the most sophisticated one within this transparent framework it is shown that the harmonious representation of mfa utilizing two distinct tsallis distribution functions one for the tail part of probability density function pdf and the other for its center part explains the recently observed pdfs of turbulence in the highest accuracy superior to the analyses based on other models such as the log normal model and the p model

chaotic cascades with kolmogorov 1941 scaling we define a chaotic deterministic variant of random multiplicative cascade models of turbulence it preserves the hierarchical tree structure thanks to the addition of infinitesimal noise the zero noise limit can be handled by perron frobenius theory just like the zero diffusivity limit for the fast dynamo problem random multiplicative models do not possess kolmogorov 1941 k41 scaling because of a large deviations effect our numerical studies indicate thatdeterministic multiplicative models can be chaotic and still have exact k41 scaling a mechanism is suggested for avoiding large deviations which is present in maps with a neutrally unstable fixed point

local properties of extended self similarity in three dimensional turbulence where the scaling exponent q is some function of q it is shown in numerous experiments and numerical simulations that the range of applicability of the ess is substantially larger than that for ordinary self similarity and the ess can exist even for situations where the ordinary self similarity cannot be observed at all the aim of the present letter is twofold the first is to study local properties of ess defined as h u pi u 3 p r 2 where p r are depending on r the local approach allows to develop some old ideas at past a representation p p 3 p p 3 18 derived from a lognormal model was shown to hold for the values averaged over an inertial interval of certain extension here we will show that the representation holds locally i e with p r and r depending on r in the above defined sense ranging from the dissipative kolmogorov length to integral scale for any observed reynolds number in direct numerical simulations up to r 459 the second aim is to examine the implication of the variation of the local intermittency exponent r it is often mentioned that there is no characteristic length in turbulence so that the structure functions obey a power law in the inertial region and the associated scaling exponents are independent of scale however a recent study of turbulence reveals the existence of the structures 9 a question then naturally arises as to whether there may be any characteristic length ascribed to the structures 10 the peculiar variation of r with respect to r observed in the letter indicates that there is a certain length affecting the ess the she leveque model 11 is also very popular in the last years for this model the local exponent is expressed in a general form

correlations in multifractals we present an analysis of the implicit assumptions that lie at the basis of the scaling relations for fractal measures proposed by cates et al 1 furthermore the scaling relations which have been shown to hold for trivial multifractals like the generalized cantor set 2 are tested numerically for critical wave functions of an incommensurate system

geometrical multifractality of growing structures the authors study the mass distribution of fractal objects growing by subsequent addition of units to the structure it is demonstrated that in the limit of very large sizes such structures generally exhibit multifractal properties without defining a singular measure on the fractal support using the mass as a measure on the fractal for a few simple deterministic processes they give the spectrum of corresponding fractal dimensions exactly according to their results such geometrical multifractals should be very common and consist of parts which have a varying local fractal scaling of mass different from that of the whole object they demonstrate the variation of multifractal properties as a function of the increasing size in this way establishing for the calculation of multifractality an approach common in the studies of fractal properties of growing clusters

extreme values and fat tails of multifractal fluctuations in this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process we also study the heavy power law tail behavior of probability density function associated with such data we show that because of strong correlations the standard extreme value approach is not valid and classical tail exponent estimators should be interpreted cautiously extreme statistics associated with multifractal random processes turn out to be characterized by non self averaging properties our considerations rely upon some analogy between random multiplicative cascades and the physics of disordered systems and also on recent mathematical results about the so called multifractal formalism applied to financial time series our findings allow us to propose an unified framework that accounts for the observed multiscaling properties of return fluctuations the volatility clustering phenomenon and the observed inverse cubic law of the return pdf tails

intermittency as multifractality in history space temporal intermittency in a chaotic dynamical system can be regarded as a manifestation of the multifractal properties of the set of histories the renyi entropies kq which generalize the kolmogorov entropy k1 play a role analogous to the exponents tau q characterising the scaling properties of the moments of the mass distribution the authors introduce the topological entropy h lambda of the subset of histories with the same local expansion parameter they show that kq and h lambda are related to each other by means of a legendre transformation

multiscaling and multifractality abstract a general scaling argument is presented which predicts for the two points correlation function for growth phenomena and critical phenomena a scaling form multiscaling of the type g r r r d d r r a r r where r is the distance from the origin r a characteristic length and a x is an amplitude a connection between multifractality and multiscaling is shown the numerical data of plischke and racz on diffusion limited aggregation and a soluble model for spinodal decomposition are found in agreement with such multiscaling form

dynamical equations for high order structure functions and a comparison of a mean field theory with experiments in three dimensional turbulence two recent papers v yakhot phys rev e 63 026307 2001 and r j hill j fluid mech 434 379 2001 derive through two different approaches that have the navier stokes equations as the common starting point a set of dynamic equations for structure functions of arbitrary order in turbulence these equations are not closed yakhot proposed a mean field theory to close the equations for locally isotropic turbulence and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments and for its behavior for intermediate amplitudes at high reynolds numbers some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure as well as on other aspects predicted by the theory comparison between the theory and the data shows varying levels of agreement and reveals gaps inherent to the implementation of the theory

aquifer operator scaling and the effect on solute mixing and dispersion 1 since aquifer parameters may have statistical dependence structures that are present across a huge range of scales the concepts of fractional brownian motion fbm have been used in both analytic and numerical stochastic settings most previous models have used isotropic scaling characterized by a single scalar hurst coefficient any real world anisotropy has been handled by an elliptical stretching random k field we define a d dimensional extension of fbm in which the fractional order integration may take on different orders in the d primary possibly nonorthogonal scaling directions and the degree of connectivity and long range dependence is freely assigned via a probability measure on the unit sphere this approach accounts for the different scaling found in the vertical versus horizontal directions in sedimentary aquifers and allows very general degrees of continuity of k in certain directions it also allows for the representation of fracture networks in a continuum setting the eigenvectors of the scaling matrix describe the primary fracture scaling directions and discrete weights of fractional integration represent fracture continuity that may be limited to a small number of directions in a numerical experiment the motion of solutes through 2 d operator fractional gaussian fields depends very much on transverse hurst coefficients transverse scaling in the range of fractional gaussian noise engenders greater plume mixing and a transition to a fickian regime higher orders of integration in the range of fractional brownian motion are associated with thicker layering of aquifer sediments and more preferential unmixed transport therefore direct representation of the unique directional scaling properties of an aquifer is important for realistic simulation of transport

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

on the scaling of three dimensional homogeneous and isotropic turbulence abstract in this paper we investigate the scaling properties of three dimensional isotropic and homogeneous turbulence we analyze a new form of scaling extended self similarity recently introduced in the literature we found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low reynolds number and it extends over a much wider range of scales with respect to the inertial range

potentially nilpotent and spectrally arbitrary even cycle sign patterns abstract an n n sign pattern s n is potentially nilpotent if there is a real matrix having sign pattern s n and characteristic polynomial x n a new family of sign patterns c n with a cycle of every even length is introduced and shown to be potentially nilpotent by explicitly determining the entries of a nilpotent matrix with sign pattern c n these nilpotent matrices are used together with a jacobian argument to show that c n is spectrally arbitrary i e there is a real matrix having sign pattern c n and characteristic polynomial x n i 1 n 1 i i x n i for any real i some results and a conjecture on minimality of these spectrally arbitrary sign patterns are given

transverse structure functions in high reynolds number turbulence transverse structure functions are obtained at high reynolds numbers in atmospheric turbulence taylor microscale reynolds numbers between 10 000 and 15 000 these measurements confirm that their scaling exponents are different from those for longitudinal structure functions implications of this conclusion are discussed briefly

multiparticle diffusion limited aggregation with strip geometry abstract two finite density versions of the multiparticle dla model have been investigated on strips of width l lattice units with periodic boundary conditions in model i single particles are added to the deposit at the position in which they first attempt to step onto the deposit and in model ii particles directly and indirectly connected to the deposit via nearest neighbor occupancy are added when they first contact the growing deposit for model i the growth of the deposit mass crosses over from t 1 2 dependence in the low density short time limit to m t in the high density long time limit for model ii a similar crossover is found but as the density approaches the percolation threshold the deposit mass is found to grow according to m t with having a value of about 4 3 these results help to resolve some apparent discrepancies between the results of earlier work on closely related models by voss and by meakin and deutch

novel dynamical scaling in kinetic growth phenomena abstract a novel dynamical scaling characterized by infinitely many growth exponents is presented this new behavior is manifested in the time dependent pair correlation function and therefore is amenable to direct experimental observation an exact analytical solution on the time dependent ginzburg landau model is obtained in the large n limit for a quench at zero temperature which exhibits such multiscaling behavior this new form of behavior reflects a morphological pattern in the growing domains and is expected in other growth phenomena as indicated by preliminary analysis on dla clusters a connection between multiscaling and multifractality is discussed

multifractal behavior of polynomial fourier series abstract we study the spectrum of singularities of a family of fourier series with polynomial frequencies in particular we prove that they are multifractal functions the case of degree two was treated by s jaffard in 1996 higher degrees require completely different ideas essentially because harmonic analysis techniques poisson summation are useless to study the oscillation at most of the points we introduce a new approach involving special diophantine approximations with prime power denominators and fine analytic and arithmetic aspects of the estimation of exponential sums to control the holder exponent in thin cantor like sets

spectrally arbitrary star sign patterns abstract an n n sign pattern s n is spectrally arbitrary if for any given real monic polynomial g x of degree n there is a real matrix having sign pattern s n and characteristic polynomial g x all n n star sign patterns that are spectrally arbitrary and all minimal such patterns are characterized this subsequently leads to an explicit characterization of all n n star sign patterns that are potentially nilpotent it is shown that any super pattern of a spectrally arbitrary star sign pattern is also spectrally arbitrary

spectrally arbitrary patterns abstract an n n sign pattern matrix s is an inertially arbitrary pattern iap if each nonnegative triple n 1 n 2 n 3 with n 1 n 2 n 3 n is the inertia of a matrix with sign pattern s analogously s is a spectrally arbitrary pattern sap if for any given real monic polynomial r x of order n there is a matrix with sign pattern s and characteristic polynomial r x focusing on tree sign patterns consider the n n tridiagonal sign pattern t n with each superdiagonal entry positive each subdiagonal entry negative the 1 1 entry negative the n n entry positive and every other entry zero it is conjectured that t n is an iap by constructing matrices a n with pattern t n it is proved that t n allows any inertia with n 3 0 1 2 n 1 n for all n 2 this leads to a proof of the conjecture for n 5 the truth of the conjecture is extended to n 7 by showing the stronger result that t n is a sap the proof of this latter statement involves finding a matrix a n with pattern t n that is nilpotent further questions about patterns that are saps and iaps are considered

completeness and basis properties of complex exponentials this paper is concerned with what might be termed the fine structure of the completeness and basis properties of complex exponentials we give new criteria for two sequences to have the same excess in the sense of paley and wiener a result that illuminates and supplements a well known completeness criterion of levinson and new examples and counterexamples pertaining to riesz bases

three dimensional synthetic turbulence constructed by spatially randomized fractal interpolation a spatially randomized fractal interpolation algorithm to construct three dimensional synthetic turbulence from original coarse field is reported as in the one dimensional case by ding et al phys rev e 82 036311 2010 during the fractal interpolation positions mapping between large and small scale cubes are chosen randomly and the stretching factors are drawn from a log poisson random multiplicative process a linear combination function defined as the base part in fractal interpolation and a theoretical energy spectrum model for fully developed turbulence are introduced into the procedure statistical analysis shows that the synthetic field displays some properties very close to the direct numeric simulated field such as probability distributions of velocity velocity gradient velocity increment and the anomalous scaling behavior of the longitude velocity structure functions which follows the sl94 model precisely after a short time using direct numeric simulation with the synthetic field as initial data the typical local dynamical structures described by the teardrop shape of the q r plane for empirical turbulence can be reproduced

some results on the behavior and estimation of the fractal dimensions of distributions on attractors the strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation in this paper we first provide a rigorous mathematical framework for the study of dimension focusing on pointwise dimension x and the generalized renyi dimensionsd q and give a rigorous proof of inequalities first derived by grassberger and procaccia and hentschel and procaccia we then specialize to the problem of statistical estimation of the correlation dimension and information dimension it has been recognized for some time that the error estimates accompanying the usual procedures which generally involve least squares methods and nearest neighbor calculations grossly underestimate the true statistical error involved in least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates we then develop an estimation procedure for which corrects for an important bias term the local measure density and provides confidence intervals for the general applicability of this method is illustrated with various numerical examples

a random process for the construction of multiaffine fields abstract we define a random process for the construction of multiaffine fields given the scaling exponents for the structure functions the difference with analogous processes for positive defined multifractal measures is stressed in particular our methods can be used for the study of the scaling laws exhibited by the velocity field in three dimensional fully developed turbulence we also discuss the probability distribution functions for the increments of the signal in the scaling range

universal power law tails for singularity dominated strong fluctuations integrals of the type i t identical to integral integral dxdy delta t h x y are considered where h is a function from an ensemble labelled by parameters i can represent circulation times of fluid particles in the plane orbital periods or semiclassical densities of states for one dimensional hamiltonian systems spectral densities for two dimensional crystals or the strength of a wave pulse produced by propagation of a deformed step discontinuity as h varies over the ensemble i develops strong fluctuations associated with legendre singularities for unrestricted functions h the probability distribution p i describing the fluctuations of i decays according to a universal i 9 law obtained by a scaling argument involving arnold s classification of catastrophes if h is only quadratic in y p varies as i 10 if the integral defining i is one dimensional p varies as i 3 if it is three dimensional i decays no faster than i 48 the probability distribution of i identical to mod delta i delta t mod decays as i 2

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

multifractal wavefunction at the localisation threshold the authors point out that the field theoretical description of the localisation transition exhibits anomalous scaling for the moments of the probability density at the localisation threshold this property hints at a multifractal structure of the wavefunction they attempt an analysis of the corresponding singularity distribution

potentially nilpotent sign pattern matrices abstract a sign pattern is said to be potentially nilpotent if it allows nilpotence in this paper a number of qualitative necessary or sufficient conditions for a sign pattern to allow nilpotence are established the sign patterns that allow nilpotence of index 2 are investigated for orders up to three potentially nilpotent sign patterns are characterized potentially nilpotent tree sign patterns are also explored

multiscaling transformation in dynamical systems and turbulence abstract multiscaling is a scaling law where the exponent is slowing varying with the length scale pseudo algebraic law we discuss its origin as a consequences of multifractility and the existence of a lower cutoff in the calculation of correlation functions in different contexts we derive some exact results in the case of two scale cantor sets which can be extended to other fractal structures such as strange attractors of chaotic systems in fully developed turbulence the cutoff is naturally introduced by the viscosity and our approach leads to the prediction of an intermediate dissipation range which can be tested experimentally

multifractal moving average analysis and test of multifractal model with tuned correlations we address two common major problems in the study of time series characterizing fluctuations in complex systems multifractal analysis and multifractal modeling specifically we introduce a multi fractal centered moving average mf cma analysis which is computationally easier but equivalently performing compared with the well established multi fractal detrended fluctuation analysis mf dfa with linear detrending in addition we study in detail a generalized binomial multi fractal model gb mfm to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long term persistence we use the data generated by this model as well as realistic by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite size effects as well as limitations due to spurious multifractality

non gaussian statistics of atmospheric turbulence and related effects on aircraft loads non gaussian statistical properties of turbulence in the inertial range can be characterized in terms of an exponent k that defines the scaling of velocity increments together with a fractal dimension d that quantifies intermittency a new method of data analysis for measuring k and d i sp resented based on the collapsing of appropriately normalized probability distributions measured at different scales the method is illustrated by its application to records of turbulence measured at low altitudes by a specially instrumented gnat trainer aircraft the resulting multifractal statistical description of velocity increments is consistent with results obtained by previous authors using a different method of analysis based on the scaling of velocity structure functions and with the predictions of recent theoretical models of physical processes in the inertial range it is demonstrated how the results can be applied directly to the estimation of aircraft loads using a new multifractal formulation of statisticaldiscrete gust theory qualitative differences between the resulting estimated loads and the loads predicted by the statistical method prescribed in the current airworthiness regulations the power spectral density method are identified

verification of the scaling relation within mpdft by analyzing pdfs for energy dissipation rates out of 40963 dns abstract the pdfs for energy dissipation rates extracted by kaneda and ishihara from their 40963 dns for fully developed turbulence are analyzed within the framework of multifractal probability density function theory mpdft to a high accuracy mpdft is a statistical mechanical ensemble theory for analyzing intermittent phenomena providing fat tail probability density functions pdfs recently mpdft has been improved by introducing a new scaling relation so as to be able to analyze intermittency through any series of pdfs with arbitrary magnification 1 it was fixed to a unique value 2 since the value of can be determined freely by observers the choice of should not affect observables the validity of the generalized mpdft is verified successfully through the precise analyses of several series of pdfs with different values of in the course of the verification it is revealed that the system of fully developed turbulence has much wider area representing scaling behaviors than the inertial range with the help of mpdft it has become possible to separate the coherent turbulent motion from fluctuations this may benefit the wavelet analysis of turbulence

allow problems concerning spectral properties of sign pattern matrices a survey abstract an n n sign pattern matrix has entries in 0 this paper surveys the following problems concerning spectral properties of sign pattern matrices sign patterns that allow all possible spectra spectrally arbitrary sign patterns sign patterns that allow all inertias inertially arbitrary sign patterns sign patterns that allow nilpotency potentially nilpotent sign patterns and sign patterns that allow stability potentially stable sign patterns relationships between these four classes of sign patterns are given and several open problems are identified

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

multifractality of the feigenbaum attractor and fractional derivatives it is shown that fractional derivatives of the integrated invariant measure of the feigenbaum map at the onset of chaos have power law tails in their cumulative distributions whose exponents can be related to the spectrum of singularities f this is a new way of characterizing multifractality in dynamical systems so far applied only to multifractal random functions frisch and matsumoto j stat phys 108 1181 2002 the relation between the thermodynamic approach vul sinai and khanin russian math surveys 39 1 1984 and that based on singularities of the invariant measures is also examined the theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations