numerical methods for the estimation of multifractal singularity spectra on sampled data physical variables in scale invariant systems often show chaotic turbulent like behavior commonly associated to the existence of an underlying fractal or multifractal structure however the assessment of multifractality over experimental discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates in this paper we have evaluated the quality of different techniques used for multifractal analysis we have tested four different techniques the moment m method the wavelet transform modulus maxima wtmm method the gradient modulus wavelet projection gmwp method and the gradient histogram gh method which are used to estimate the singularity spectra of multifractal signals the test consists in analyzing synthetic multifractal 1d signals with given multifractal spectrum we have compared the results studying the sensibility of each method to the length of the series size of the ensemble and type of spectrum our results show that gmwp method is the one attaining the best performance providing reliable estimates which can be improved when the statistics is increased all the other methods are affected by problems such as the linearization of the right tail of the spectrum and some of them are very demanding in data

gradual multifractal reconstruction of time series formulation of the method and an application to the coupling between stock market indices and their holder exponents abstract a technique termed gradual multifractal reconstruction gmr is formulated a continuum is defined from a signal that preserves the pointwise holder exponent multifractal structure of a signal but randomises the locations of the original data values with respect to this 0 to the original signal itself 1 we demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual tree complex wavelet transform that is the 0 end of the continuum is realised using the recently proposed iterated amplitude adjusted wavelet transform algorithm keylock 2017 that fully randomises the wavelet phases this is extended to the gmr formulation by selective phase randomisation depending on whether or not the wavelet coefficient amplitudes exceeds a threshold criterion an econophysics application of the technique is presented the relation between the normalised log returns and their holder exponents for the daily returns of eight financial indices are compared one particularly noticeable result is the change for the two american indices nasdaq 100 and s p 500 from a non significant to a strongly significant as determined using gmr cross correlation between the returns and their holder exponents from before the 2008 crash to afterwards this is also reflected in the skewness of the phase difference distributions which exhibit a geographical structure with asian markets not exhibiting significant skewness in contrast to those from elsewhere globally

algorithms for two dimensional cutting stock and strip packing problems using dynamic programming and column generation abstract we investigate several two dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed we first present two dynamic programming based algorithms for the rectangular knapsack rk problem and its variants in which the patterns must be staged the first algorithm solves the recurrence formula proposed by beasley the second algorithm for staged patterns also uses a recurrence formula we show that if the items are not so small compared to the dimensions of the bin then these algorithms require polynomial time using these algorithms we solved all instances of the rk problem found at the or library including one for which no optimal solution was known we also consider the two dimensional cutting stock problem we present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns we propose two strategies to tackle the residual instances we also investigate a variant of this problem where the bins have different sizes at last we study the two dimensional strip packing problem we also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed in this case we solve instances for two three and four staged patterns we report on some computational experiments with the various algorithms we propose in this paper the results indicate that these algorithms seem to be suitable for solving real world instances we give a detailed description a pseudo code of all the algorithms presented here so that the reader may easily implement these algorithms

regularity of solutions to coercive and self controlling viscoplastic problems abstract we prove higher regularity of solutions to viscoplastic problems the main idea is to use the finite difference method which allows us to cancel the monotone nonlinearities our main assumption is that velocity is in l 2 h 1 this is true for all coercive and some special for example linear self controlling non coercive models

two dimensional packing problems a survey we consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste in two dimensional bin packing problems these units are finite rectangles and the objective is to pack all the items into the minimum number of units while in two dimensional strip packing problems there is a single standardized unit of given width and the objective is to pack all the items within the minimum height we discuss mathematical models and survey lower bounds classical approximation algorithms recent heuristic and metaheuristic methods and exact enumerative approaches the relevant special cases where the items have to be packed into rows forming levels are also discussed in detail

synthetic turbulence fractal interpolation and large eddy simulation fractal interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse grained navier stokes equations it is based on synthetically generating a scale invariant subgrid scale field and analytically evaluating its effects on large resolved scales in this paper we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher order structure functions and the non gaussian probability density function of the velocity increments extensive a priori analyses of atmospheric boundary layer measurements further reveal that this multiaffine closure model has the potential for satisfactory performance in large eddy simulations the pertinence of this newly proposed methodology in the case of passive scalars is also discussed

anomalous scaling in homogeneous isotropic turbulence the anomalous scaling exponents n of the longitudinal structure functions sn for homogeneous isotropic turbulence are derived from the navier stokes equations by using field theoretic methods to develop a low energy approximation in which the kolmogorov theory is shown to act effectively as a mean field theory the corrections to the kolmogorov exponents are expressed in terms of the anomalous dimensions of the composite operators which occur in the definition of sn these are calculated from the anomalous scaling of the appropriate class of nonlinear green function using an uv fixed point of the renormalization group which thereby establishes the connection with the dynamics of the turbulence the main result is an algebraic expression for n which contains no adjustable constants it is valid at orders n below g 1 where g is the fixed point coupling constant this expression is used to calculate n for orders in the range n 2 10 and the results are shown to be in good agreement with experimental data key examples being 2 0 7 3 1 and 6 1 8

application of generalized thermostatistics to fully developed turbulence abstract we apply the formalism of non extensive statistical mechanics to fully developed turbulent flows we obtain analytical formulas for probability density functions of velocity differences depending on distance r and reynolds number r which are in very good agreement with turbulence experiments the skewness is taken into account by analysing universal contributions due to higher order correlations of the chaotic dynamics we also calculate the moment scaling exponents m which also agree well with experimental data

self similarity properties of natural images resemble those of turbulent flows we show that the statistics of an edge type variable in natural images exhibits self similarity properties which resemble those of local energy dissipation in turbulent flows our results show that selfsimilarity and extended self similarity hold remarkably for the statistics of the local edge variance and that the very same models can be used to predict all of the associated exponents these results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows the properties we have exhibited are relevant for the modeling of the early visual system they should be included in models designed for the prediction of receptive fields s0031 9007 97 05190 9

log poisson statistics and extended self similarity in driven dissipative systems abstract the bak chen tang forest fire model phys lett a 147 1990 297 was proposed as a toy model of turbulent systems where energy in the form of trees is injected uniformly and globally but is dissipated burns locally we review our previous results on the model phys rev e 62 2000 1613 phys rev lett 86 2000 4215 and present our new results on the statistics of the higher order moments for the spatial distribution of fires we show numerically that the spatial distribution of dissipation can be described by log poisson statistics which leads to extended self similarity phys rev e 48 1993 r29 phys rev lett 73 1994 959 similar behavior is also found in models based on directed percolation this suggests that the concept of log poisson statistics of appropriately normalized variables can be used to describe scaling not only in turbulence but also in a wide range of driven dissipative systems

a generalization of scaling models of turbulence we report on some implications of the theory of turbulence developed by v yakhot phys rev e 57 2 1737 1998 in particular we focus on the expression for the scaling exponents n we show that yakhot s result contains three well known scaling models as special cases namely k41 k62 and the theory by v l vov and i procaccia phys rev e 62 6 8037 2000 the model furthermore yields a theoretical justification for the method of extended self similarity ess

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

comment on the paper on the scaling of three dimentsional homogeneous and isotropic turbulence by benzi et al abstract benzi et al presented experimental data and an analysis to the effect that the well known 2 3 kolmogorov obukhov exponent in the inertial range of local structure in turbulence should be corrected by a small but definitely nonzero amount we reexamine the very same data and show that this conclusion is unjustified the data are in fact consistent with incomplete similarity in the inertial range and with an exponent that depends on the reynolds number and tends to 2 3 in the limit of vanishing viscosity

anomalous scaling in anisotropic turbulence abstract we present a short review of the work conducted by our group on the subject of anomalous scaling in anisotropic turbulence the basic idea that unifies all the applications discussed here is that the equations of motion for correlation functions are always linear and invariant to rotations and therefore the solutions foliate into sectors of the symmetry group of all rotations so 3 we have considered models of passive scalar and passive vector advections by a rapidly changing turbulent velocity field kraichnan type models for which we find a discrete spectrum of universal anomalous exponents with a different exponent characterizing the scaling behavior in every sector generically the correlation functions and structure functions appear as sums over all these contributions with nonuniversal amplitudes which are determined by the anisotropic boundary conditions in addition we considered navier stokes turbulence by analyzing simulations and experiments and reached some interesting conclusions regarding the scaling exponents in the anisotropic sectors the theory presented here clarifies questions like the restoration of local isotropy upon decreasing scales we explain when the local isotropy is fully restored and when the lingering effects of the anisotropic forcing appear for arbitrarily small scales

intermittency and rough pipe turbulence recently by analyzing the measurement data of nikuradze naca tech memo no 1292 1950 it has been proposed n goldenfeld phys rev lett 96 044503 2006 that the friction factor f of rough pipe flow obeys a scaling law in the turbulent regime here we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form thereby relating f to the intermittency exponent ensuremath eta by statistically analyzing the measurement data of f we infer a satisfactory estimate for ensuremath eta ensuremath approx 0 02 the inclusion of which is shown to improve the data collapse curve this provides empirical evidence for intermittency other than the direct measurement of velocity fluctuations

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

statistical uncertainty in the analysis of structure functions in turbulence this rapid communication is about a procedure for the statistical uncertainty estimation of velocity structure functions measured in turbulent flows the proposed method is based on the determination of the number of statistically independent samples calculated by the correlation function of the velocity increments and it is applied to experimental data obtained by hot wire measurements in a turbulent jet flow

extended self similarity in the numerical simulation of three dimensional homogeneous flows we report the statistical analysis of several velocity configurations obtained by performing numerical simulations of three dimensional homogeneous incompressible turbulence this analysis provides full support to the idea recently proposed by benzi et al phys rev e 48 29 1993 that fluid flows exhibit extended self similarity a sort of generalized scale invariance which holds at high as well as at low to moderate reynolds numbers

new perspectives in turbulence scaling laws asymptotics and intermittency intermittency a basic property of fully developed turbulent flow decreases with growing viscosity therefore classical relationships obtained in the limit of vanishing viscosity must be corrected when the reynolds number is finite but large these corrections are the main subject of the present paper they lead to a new scaling law for wall bounded turbulence which is of key importance in engineering and to a reinterpretation of the kolmogorov obukhov scaling for the local structure of turbulence which has been of paramount interest in both theory and applications the background of these results is reviewed in similarity methods in the statistical theory of vortex motion and in intermediate asymptotics and relevant experimental data are summarized

closure approach to high order structure functions of turbulence let t p be the structure function of order p of turbulence first t2 is determined then t3 is derived from t2 and finally t p p 3 are derived from t2 and t3 this closure scheme is realized by a non gaussian statistical model we use it to study the scaling law of t p and we find that the available data on scaling exponents favor kolmogorov s 1941 theory rather than his 1962 theory we also predict the high order universal constants of inertial range scaling

linking eulerian and lagrangian structure functions scaling exponents in turbulence abstract in fully developed turbulence intermittency is classically characterized by e q the eulerian scaling exponent of structure functions the same approach can be used in a lagrangian framework using l q to characterize the temporal intermittency of the velocity of a particle advected by a turbulent intermittent field an interesting question is then to know how to relate the scaling functions and explore the links between l q and e q we first provide different transformations between these functions associated to different transformations linking space and time scales we test these relations using experimental estimates for the two functions for small and medium order of moments they are both close to data for larger moments experimental estimates have still too much scatter to conclude the present paper underlines the need of more precise estimates and provides a methodology for future comparisons of eulerian and lagrangian scaling exponents

scaling property of turbulent flows we discuss a possible theoretical interpretation of the self scaling property of turbulent flows extended self similarity ess our interpretation predicts that even in cases when ess is not observed a generalized self scaling must be observed this prediction is checked on a number of laboratory experiments and direct numerical simulations

computing the scaling exponents in fluid turbulence from first principles the formal setup abstract we propose a scheme for the calculation from the navier stokes equations of the scaling exponents n of the nth order correlation functions in fully developed hydrodynamic turbulence the scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the euler equation it constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents n as a consequence the scaling exponents are determined by solvability conditions and not from power counting it is argued that in order to achieve such a formulation one must recognize that the many point space time correlation functions are not scale invariant in their time arguments the assumption of full scale invariance leads unavoidably to kolmogorov exponents it is argued that the determination of all the scaling exponents n requires equations for infinitely many renormalized objects one can however proceed in controlled successive approximations by successive truncations of the infinite hierarchy of equations clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory to this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the nth order correlation functions and green s function in light of this important result we can safely use finite resummations to construct successive closures of the infinite hierarchy of equations this paper presents the conceptual and technical details of the scheme the analysis of the high order closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with v belinicher

onsager s conjecture almost everywhere in time in recent works by isett holder continuous euler flows in three dimensions with compact support in time pp 1 173 2012 and later by buckmaster et al ann math 2015 iterative schemes were presented for constructing solutions belonging to the holder class c 1 5 e of the 3d incompressible euler equations which do not conserve the total kinetic energy the cited work is partially motivated by a conjecture of lars onsager in 1949 relating to the existence of c 1 3 e solutions to the euler equations which dissipate energy in this note we show how the later scheme can be adapted in order to prove the existence of non trivial holder continuous solutions which for almost every time belong to the critical onsager holder regularity c 1 3 e and have compact temporal support

nonconcave entropies in multifractals and the thermodynamic formalism we discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as legendre fenchel transforms of functions analogous to free energy functions we show that the legendre fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave if the spectrum has no definite concavity then the transform yields the concave envelope of the spectrum rather than the spectrum itself some mathematical and physical examples are given to illustrate this result which lies at the root of the nonequivalence of the microcanonical and canonical ensembles on a more positive note we also show that the impossibility of expressing nonconcave multifractal spectra through legendre fenchel transforms of free energies can be circumvented with the help of a generalized free energy function which relates to a recently introduced generalized canonical ensemble analogies with the calculation of rate functions in large deviation theory are finally discussed

extended self similarity in kinetic surface roughening we show from simulations that a limited mobility solid on solid model of kinetically rough surface growth exhibits extended self similarity analogous to that found in fluid turbulence the range over which scale independent power law behavior is observed is significantly enhanced if two correlation functions of different order such as those representing two different moments of the difference in height between two points are plotted against each other this behavior found in both one and two dimensions suggests that the relative exponents may be more fundamental than the absolute ones

spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence the pseudospectral method in conjunction with a technique for obtaining scaling exponents n from the structure functions sn r is presented as an alternative to the extended self similarity ess method and the use of generalized structure functions we propose plotting the ratio sn r s3 r against the separation r in accordance with a standard technique for analyzing experimental data this method differs from the ess technique which plots sn r against s3 r with the assumption s3 r r using our method for the particular case of s2 r we obtain the result that the exponent 2 decreases as the taylor reynolds number increases with 2 0 679 0 013 as r this supports the idea of finite viscosity corrections to the k41 prediction for s2 and is the opposite of the result obtained by ess the pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces

beyond scaling and locality in turbulence an analytic perturbation theory is suggested in order to find finite size corrections to the scaling power laws in the frame of this theory it is shown that the first order finite size correction to the scaling power laws has following form s r cong cr alpha 0 ln r eta alpha 1 where is a finite size scale in particular for turbulence it can be the kolmogorov dissipation scale using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with 0 0 can describe turbulence statistics in the near dissipation range r where the ordinary power law scaling does not apply for moderate reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions the log corrections apply to finite reynolds number interplay between local and non local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self similarity these results have been also expanded on passive scalar mixing in turbulence overlapping phenomenon between local and non local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed

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

lagrangian statistics in forced two dimensional turbulence we report on simulations of two dimensional turbulence in the inverse energy cascade regime focusing on the statistics of lagrangian tracer particles scaling behavior of the probability density functions of velocity fluctuations is investigated the results are compared to the three dimensional case in particular an analysis in terms of compensated cumulants reveals the transition from a strong non gaussian behavior with large tails to gaussianity the reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles

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

convergence of a monotonisation procedure for a non monotone quasi static model in poroplasticity existence theory to quasi static initial boundary value problem of poroplasticity is studied the classical quasi static biot model for soil consolidation coupled with a nonlinear system of ordinary differential equations is considered this article presents a convergence result for the coercive and monotone approximations to solution of the original non coercive and non monotone problem of poroplasticity such that the inelastic constitutive equation is satisfied in the sense of young measures

infinitesimal elastic plastic cosserat micropolar theory modelling and global existence in the rate independent case in this article we investigate the regularizing properties of generalized continua of cosserat micropolar type in the elasto plastic case we propose an extension of classical infinitesimal elasto plasticity to include consistently non dissipative micropolar effects it is shown that the new model is thermodynamically admissible and allows for a unique global in time solution of the corresponding rate independent initial boundary value problem the method of choice is the yosida approximation and a passage to the limit

application of extended self similarity in turbulence from navier stokes turbulence numerical simulations we show that for the extended self similarity ess method it is essential to take the third order structure function taken with the modulus and called d 3 r rather than the standard third order structure function d3 r itself if this is done we find ess towards scales larger than order 10 eta where eta is the kolmogorov scale if d3 r is used there is no ess we also analyze ess within the batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function the re asymptotic inertial range scaling develops only beyond a taylor reynolds number re lambda 500

dynamical poroplasticity model existence theory for gradient type nonlinearities with lipschitz perturbations abstract in this article we study existence theory to a non coercive fully dynamic model of poroplasticity with the non homogeneous boundary conditions where the constitutive function is a continuous element of class lm it is a sum of a maximal monotone map g and a globally lipschitz map l without any additional growth conditions we are able to prove the existence of a solution such that the inelastic constitutive equation is satisfied in the measure valued sense moreover if g is a gradient of a differentiable convex function then there exists a solution such that the constitutive equation is satisfied almost everywhere

extended universality in moderate reynolds number flows is the kolmogorov viscous scale this form seems to be obeyed on a range of scales that is larger than power law scaling it is shown here that this extended universality stems from the structure of the navier stokes equations and from the property of the locality of interactions the approach discussed here allows us to estimate the range of validity of the universal form in addition we examine the possi bility that the observed deviations from the classical values of

highly turbulent solutions of the lagrangian averaged navier stokes alpha model and their large eddy simulation potential we compute solutions of the lagrangian averaged navier stokes alpha lans alpha model for significantly higher reynolds numbers up to re approximately 8300 than have previously been accomplished this allows sufficient separation of scales to observe a navier stokes inertial range followed by a second inertial range specific to the lans alpha model both fully helical and nonhelical flows are examined up to reynolds numbers of approximately 1300 analysis of the third order structure function scaling supports the predicted l3 scaling it corresponds to a k 1 scaling of the energy spectrum for scales smaller than alpha the energy spectrum itself shows a different scaling which goes as k1 this latter spectrum is consistent with the absence of stretching in the subfilter scales due to the taylor frozen in hypothesis employed as a closure in the derivation of the lans alpha model these two scalings are conjectured to coexist in different spatial portions of the flow the l3 e k approximately k 1 scaling is subdominant to k1 in the energy spectrum but the l3 scaling is responsible for the direct energy cascade as no cascade can result from motions with no internal degrees of freedom we demonstrate verification of the prediction for the size of the lans alpha attractor resulting from this scaling from this we give a methodology either for arriving at grid independent solutions for the lans alpha model or for obtaining a formulation of the large eddy simulation optimal in the context of the alpha models the fully converged grid independent lans alpha model may not be the best approximation to a direct numerical simulation of the navier stokes equations since the minimum error is a balance between truncation errors and the approximation error due to using the lans alpha instead of the primitive equations furthermore the small scale behavior of the lans alpha model contributes to a reduction of flux at constant energy leading to a shallower energy spectrum for large alpha these small scale features however do not preclude the lans alpha model from reproducing correctly the intermittency properties of the high reynolds number flow

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

scaling laws and dissipation scale of a passive scalar in fully developed turbulence abstract the scaling laws of the temperature structure functions and their relation with those of velocity have been experimentally studied the relationship between the dissipative scales for velocity and the temperature is first investigated in agreement with recent numerical simulations of pumir 1994 it is found that for prandtl number close to 1 the dissipation scale for a scalar is smaller than that of velocity thus temperature structure functions present a larger scaling interval than that of the velocity the intermittent corrections of scaling are then analyzed it is shown that as proposed in literature r benzi et al 1992 the second order structure function is affected only by the velocity intermittency this structure function is then used as the reference for testing the applicability of the extended self similarity ess to the passive scalar case ess holds but in a narrower interval than that observed in velocity statistics finally a hierarchy for the temperature structure functions similar to that proposed by she and leveque 1994 for the velocity field is introduced and experimentally tested

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

analysis of turbulence by statistics based on generalized entropies an analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the havrda charvat tsallis hct entropy it is revealed by a self consistent analysis for the observed value 0 220 1 that the formula explains experimental data very well with single value q 0 343 of the index which appears in the measures of the renyi entropy or of the hct entropy the probability density functions of the velocity fluctuation and of the velocity gradient are also presented

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

statistical properties of four dimensional turbulence the energy transfer and small scale intermittency in decaying turbulence in four dimensions 4d are studied by direct numerical simulation and by spectral theory in comparison with three dimensions 3d the energy transfer is more efficient in 4d than in 3d hence the exponent of energy decay is larger the kolmogorov constant is 1 31 which is smaller than 1 72 in 3d the longitudinal third order structure function is confirmed to be governed by a 1 2 law 1 2 epsilonr instead of a 4 5 law in 3d the intermittency is weaker in 4d for the total dissipation rate nu summation operator i j partial differentialu j partial differentialx i 2 and the associated velocity difference spherical velocity difference on scale r than in 3d while it is slightly stronger for the surrogated dissipation rate nu partial differentialu 1 partial differentialx 1 2 and the associated longitudinal velocity difference the scaling exponents of the spherical and longitudinal velocity differences are also evaluated indicating that the spherical velocity difference is less intermittent in 4d while the longitudinal difference is more intermittent in 4d the distribution of the eigenvalues of the strain tensor is also examined it was also found that the normalized variance of the pressure gradient epsilon 3 2 nu 1 2 in 4d is smaller than in 3d the roles of the incompressibility condition the pressure gradient and the intermittency in d dimensional turbulence are examined and the importance of the longitudinal component of turbulent velocity field in the energy transfer toward small scales are discussed burgers turbulence as the asymptote of turbulence in large dimension is suggested

scaling hypothesis leading to extended self similarity in turbulence a scaling hypothesis leading to extended self similarity ess for structure functions the qth order moments of the magnitude of the longitudinal component velocity differences in isotropic homogeneous turbulence is proposed this is done by generalizing the scale variable r to rg r l with a crossover function g by extending the refined self similarity it is shown that the presented scaling also leads to ess for structure functions of the energy dissipation rate fluctuations and to ess bridging relations between velocity and dissipation rate moments extended self similarity on the basis of a universal crossover function g strictly holds toward the outer scale l range only yet we find at least approximate ess toward the viscous inner scale l range furthermore the probability densities for the velocity differences and the energy dissipation rate fluctuations which are compatible with this ess are offered

on a discrete dynamical model for local turbulence works towards an explanation of the observed experimental deviation of k41 exponent law are generally based on an energy cascade process an alternative approach based on the analysis of turbulent sequences allows us to construct a sequence model where this deviation has a dynamical origin we finally show why we were forced to go beyond the markovian model and incorporate into the model the frequent long flights an intermittent effect also present in the experimental data

integer linear programming models for 2 staged two dimensional knapsack problems we are given a unique rectangular piece of stock material s with height h and width w and a list of m rectangular shapes to be cut from s each shape s type i i 1 m is characterized by a height a width a profit and an upper bound ub i indicating the maximum number of items of type i which can be cut we refer to the two dimensional knapsack tdk as the problem of determining a cutting pattern of s maximizing the sum of the profits of the cut items in particular we consider the classical variant of tdk in which the maximum number of cuts allowed to obtain each item is fixed to 2 and we refer to this problem as 2 staged tdk 2tdk for the 2tdk problem we present two new integer linear programming models we discuss their properties and we compare them with other formulations in terms of the lp bound they provide finally both models are computationally tested within a standard branch and bound framework on a large set of instances from the literature by reinforcing them with the addition of linear inequalities to eliminate symmetries

von karman howarth equation for three dimensional two fluid plasmas we derive the von karman howarth equation for a full three dimensional incompressible two fluid plasma in the long time limit and for very large reynolds numbers we obtain the equivalent of the hydrodynamic four fifths law this exact law predicts the scaling of the third order two point correlation functions and puts a strong constraint on the plasma turbulent dynamics finally we derive a simple expression for the 4 5 law in terms of third order structure functions which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges

von karman howarth equation for magnetohydrodynamics and its consequences on third order longitudinal structure and correlation functions a derivation in variable dimension of the scaling laws for mixed third order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation between the velocity and magnetic field with full isotropy homogeneity and incompressibility assumed when close to equipartition between kinetic and magnetic energy the scaling relations involve only structure functions in a manner similar to the frac 4 5 law of kolmogorov

velocity structure functions scaling and transitions in high reynolds number couette taylor flow flow between concentric cylinders with a rotating inner cylinder is studied for reynolds numbers in the range 2 ifmmode times else texttimes fi 10 3 lrl 10 6 taylor reynolds numbers 10l r ensuremath lambda l290 for a system with radius ratio ensuremath eta 0 724 even at the highest reynolds number studied the energy spectra do not show power law scaling i e there is no inertial range and the dissipation length scale is surprisingly large nevertheless the velocity structure functions calculated using extended self similarity exhibit clear power law scaling the structure function exponents ensuremath zeta p fit kolmogorov s log normal model within the experimental uncertainty ensuremath zeta p p 3 1 ensuremath mu 6 3 ensuremath p for pl 10 with ensuremath mu 0 27 these ensuremath zeta p values are close to those found in other flows measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported lathrop et al phys rev a 46 6390 1992 measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest reynolds numbers examined these waves show evidence of a transition at r t 1 3 ifmmode times else texttimes fi 10 4 this transition was observed previously in measurements of torque but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at r t velocity measurements indicate that at r t there is a change in the coherent structures of the core flow this is consistent with our analyses of the scaling of the torque our measurements were made at two aspect ratios and no significant dependence on aspect ratio was observable for rg r t

prandtl reuss dynamical elasto perfect plasticity without safe load conditions abstract in this article we study the existence theory to the prandtl reuss dynamical model of elasto perfect plasticity with non homogeneous mixed boundary conditions by using only the yosida approximation of inelastic constitutive multifunction we are able to prove the existence of solutions without assuming any kind of safe load conditions which are quite common in the theory of elasto perfect plasticity

spatial properties of velocity structure functions in turbulent wake flows in this paper we present experimental evidence that the scaling laws for the velocity structure functions s n r v x r ensuremath v x n n 2 4 6 8 hold in various parts of the flow domain the exponents that characterize the scaling are however a function of the position in the wake that is the local strength and ubiquity of coherent structures this variation is shown to be systematic and considerably exceeds the inaccuracy involved in the determination of the exponents this is an objective indication of the influence that the organized flow structures and inhomogeneity may have on intermittency in the analysis we invoke the concept of the extended self similarity ess

lagrangian single particle turbulent statistics through the hilbert huang transform the hilbert huang transform is applied to analyze single particle lagrangian velocity data from numerical simulations of hydrodynamic turbulence the velocity trajectory is described in terms of a set of intrinsic mode functions c i t and of their instantaneous frequency i t on the basis of this decomposition we define the conditioned statistical moments of the c i modes named q order hilbert spectra hs we show that such quantities have enhanced scaling properties as compared to traditional fourier transform or correlation based structure functions statistical indicators thus providing better insights into the turbulent energy transfer process we present clear empirical evidence that the energylike quantity i e the second order hs displays a linear scaling in time in the inertial range as expected from a dimensional analysis we also measure high order moment scaling exponents in a direct way without resorting to the extended self similarity procedure this leads to an estimate of the lagrangian structure function exponents which are consistent with the multifractal prediction in the lagrangian frame as proposed by biferale et al

inverse statistics and multifractality of exit distances in 3d fully developed turbulence abstract the inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions 1 2 3 4 using taylor s frozen field hypothesis we investigate the statistical properties of the exit distances of empirical 3d fully developed turbulence we find that the probability density functions of exit distances at different velocity thresholds v can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold we show that the inverse structure functions exhibit clear extended self similarity ess the ess exponents p 2 for small p p 3 5 are well described by p 2 p 2 which derives from the observed approximate universality of the distributions of the exit distances for different velocity thresholds v the data is not sufficient to reject the hypothesis that monofractal ess is sufficient to explain the data in contrast a measure taking into account the dependence between successive exit distances at a given velocity threshold exhibits clear multifractality with negative dimensions suggesting the existence of a non trivial dependence in the time series of exit times

a column generation heuristic for the two dimensional two staged guillotine cutting stock problem with multiple stock size abstract we consider a two dimensional cutting stock problem where stock of different sizes is available and a set of rectangular items has to be obtained through two staged guillotine cuts we propose a heuristic algorithm based on column generation which requires as its subproblem the solution of a two dimensional knapsack problem with two staged guillotines cuts a further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem as well as a heuristic procedure based on dynamic programming computational experiments show the effectiveness of the proposed approach which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by cintra et al 3

scaling properties of the streamwise component of velocity in a turbulent boundary layer abstract experimental results concerning the statistics of the streamwise component of velocity in a turbulent boundary layer near a solid wall are presented energy spectra probability density functions and velocity structure functions are investigated as a function of the distance to the wall energy spectra and structure functions display power law scalings which depend on this distance on the other hand the relative behavior of structure functions remains constant in the logarithmic sublayer this behavior exhibits two distinct power laws at small scales relative scaling exponents are relatively close to those usually reported in isotropic and homogeneous turbulence at larger scales where shear effects are dominant relative exponents display larger intermittency corrections

measures of intermittency in driven supersonic flows scaling exponents for structure functions of the velocity density and entropy are computed for driven supersonic flows for rms mach numbers of order unity with numerical simulations using the piecewise parabolic method algorithm on grids of up to 512 3 points the driving is made up of either one or three orthogonal shear waves in all cases studied the compressible component of the velocity in the statistically steady regime is weaker than its solenoidal counterpart by roughly a factor of 6 exponents for the longitudinal component of the velocity are comparable to what is found in the incompressible case and appear insensitive to the presence of numerous shocks scaling exponents of the transverse components of the velocity are comparable to those for the longitudinal component density and entropy structure functions display strong departures from linear scaling finally the scaling of structure functions of the energy transfer is also given and compared with the kolmogorov refined similarity hypothesis

small scale intermittency and bursting in a turbulent channel flow the statistical properties of the streamwise velocity fluctuations in a fully developed turbulent channel flow are studied experimentally by means of single hot wire measurements the intermittency features studied through the scaling of the moments of the velocity structure function computed using the extended selfsimilarity and through the probability density function of the wavelet coefficients are found to be dependent on the distance from the wall the maximum intermittency effects are observed in the region between the buffer layer and the inner part of the logarithmic region where it is known that the bursting phenomenon related to coherent structures such as low speed streaks and streamwise vortices is the dominant dynamical feature an eduction technique based on wavelet transform for identification of organized motion is developed and used to analyze the turbulent signals streamwise velocity conditional averages computed on events educed with the proposed method are reported events responsible for intermittency are found to consist of regions of high velocity gradients and are directly correlated with the observed increase of intermittency close to the wall pacs number s 47 27 nz 01 50 pa i introduction a background

generalized scaling in fully developed turbulence in this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows the limits of a new form of scaling named extended self similarity ess are discussed we show that when a mean shear is absent the self scaling exponents are universal and they do not depend on the specific flow 3d homogeneous turbulence thermal convection mhd in contrast ess is not observed when a strong shear is present we propose a generalized version of self scaling which extends down to the smallest resolvable scales even in cases where ess is not present this new scaling is checked in several laboratory and numerical experiments a possible theoretical interpretation is also proposed a synthetic turbulent signal having most of the properties of a real one has been generated

scaling exponents of the second order structure function of turbulence the kolmogorov equation which is an exact relationship between the second order structure function and the third order structure function is applied to study the relative scaling of against according to the extended self similarity ess method it is found that the relative ess scaling exponent is greater than the real or theoretical inertial range scaling exponent of in the case of normal scaling as well as anomalous scaling when and when therefore the experimental and numerical results favours the kolmogorov 2 3 law rather than anomalous scaling previously the results were interpreted as clear evidence of anomalous scaling based upon the assumption that

the armstrong frederick cyclic hardening plasticity model with cosserat effects abstract we propose an extension of the cyclic hardening plasticity model formulated by armstrong and frederick which includes micropolar effects our micropolar extension establishes coercivity of the model which is otherwise not present we study then existence of solutions to the quasistatic rate independent armstrong frederick model with cosserat effects which is however still of non monotone non associated type in order to do this we need to relax the pointwise definition of the flow rule into a suitable weak energy type inequality it is shown that the limit in the yosida approximation process satisfies this new solution concept the limit functions have a better regularity than previously known in the literature where the original armstrong frederick model has been studied

structure function scaling of bounded two dimensional turbulence statistical properties of forced two dimensional turbulence generated in two different flow domains are investigated by numerical simulations the considered geometries are the square domain and the periodic channel domain both bounded by lateral no slip sidewalls the focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no slip boundaries the scaling exponents of the velocity and the vorticity structure functions are compared to the classical kraichnan batchelor leith kbl theory which assumes isotropy homogeneity and self similarity for turbulence scales between the forcing and dissipation scale our investigation reveals that in the interior of the flow domain turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range but it is weakly intermittent however the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the kbl theory predicts near the walls the turbulence is strongly anisotropic at all flow scales

nelkin scaling for the burgers equation and the role of high precision calculations nelkin scaling the scaling of moments of velocity gradients in terms of the reynolds number is an alternative way of obtaining inertial range information it is shown numerically and theoretically for the burgers equation that this procedure works already for reynolds numbers of the order of 100 or even lower when combined with a suitable extended self similarity technique at moderate reynolds numbers for the accurate determination of scaling exponents it is crucial to use higher than double precision similar issues are likely to arise for three dimensional navier stokes simulations

log poisson cascade description of turbulent velocity gradient statistics the log poisson phenomenological description of the turbulent energy cascade is evoked to discuss high order statistics of velocity derivatives and the mapping between their probability distribution functions at different reynolds numbers the striking confirmation of theoretical predictions suggests that numerical solutions of the flow obtained at low moderate reynolds numbers can play an important quantitative role in the analysis of experimental high reynolds number phenomena where small scales fluctuations are in general inaccessible from direct numerical simulations

normal and anomalous scaling of turbulence a non gaussian model of the probability density function pdf of ensuremath delta u r is proposed to study how the scaling exponents s p of the structure function ensuremath delta u r p of finite reynolds number turbulence depends upon the taylor microscale reynolds number r ensuremath lambda here ensuremath delta u r is the longitudinal velocity difference across a distance r and is the statistical average the model not only predicts anomalous scaling s p lp 3 for pg3 observed in experiments at a finite reynolds number but also predicts that s p approaches normal scaling p 3 while r ensuremath lambda is very high hence in contrast to the prevailing multiscaling models the non gaussian pdf model suggests a completely different picture of scaling of isotropic turbulence the anomalous scaling observed in experiments is a finite reynolds number effect and the normal scaling is valid in the real kolmogorov inertial range corresponding to an infinite reynolds number

intermittency in the isotropic component of helical and nonhelical turbulent flows we analyze the isotropic component of turbulent flows spanning a broad range or reynolds numbers the aim is to identify scaling laws and their reynolds number dependence in flows under different mechanical forcings to this end we applied an so 3 decomposition to data stemming from direct numerical simulations with spatial resolutions ranging from 64 3 to 1024 3 grid points and studied the scaling of high order moments of the velocity field the study was carried out for two different flows obtained forcing the system with a taylor green vortex or the arn old beltrami childress flow our results indicate that helicity has no significant impact on the scaling exponents as obtained from the generalized structure functions intermittency effects increase with the reynolds number in the range of parameters studied and in some cases are larger than what can be expected from several models of intermittency in the literature the observed dependence of intermittency with the reynolds number decreases if extended self similarity is used to estimate the exponents

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

a first regularity result for the armstrong frederick cyclic hardening plasticity model with cosserat effects abstract the purpose of this article is to prove the holder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic rate independent armstrong frederick cyclic hardening plasticity model with cosserat effects this model is of non monotone and non associated type in the case of two space dimensions we use the hole filling technique of widman and morrey s dirichlet growth theorem

revisiting rainfall clustering and intermittency across different climatic regimes 1 one of the vexing questions in rainfall research is the role of intermittency and its nonuniversal signature in anomalous scaling functions whether this lack of universal behavior is due to the bursting patterns in rainfall intensity or the alternation between long dry periods and highly clustered wet phases or both remains an open issue to progress on a narrower scope of this problem the effects of intermittency originating from rainfall occurrence are first separated from rainfall intermittency induced by intensity variability across five climatic regimes considered here it was shown that the rainfall occurrence process op exhibits 1 a near constant spectral slope 2 a near constant clustering exponent and 3 a probability density function of dry phases displaying a power law behavior with an exponent 1 5 consistent with other studies for timescales commensurate with frontal and storm systems also for the op the scaling exponents of the normalized higher order structure functions reveal an extensive monofractal scaling at all five climatic regimes when taken together these intersite results are suggestive that rainfall intensity modulations are the main cause of the nonuniversal anomalous scaling and not the clustering properties associated with the support the nature of these modulations is markedly different when comparing rainfall to a familiar and often interrelated process such as scalar turbulence in the case of turbulence amplitude variability of scalar dissipation rates appear to mitigate the intermittency effects connected with anomalous scaling while for rainfall series intensity fluctuations seem to amplify them

inertial range and the finite reynolds number effect of turbulence the kolmogorov law which is the unique exact relationship of inertial range statistics is applied to investigate the finite reynolds number effect in particular to study how the width of the inertial range of finite reynolds number turbulence changes with the taylor microscale reynolds number mathrm r ensuremath lambda it is found that there is no inertial range when mathrm r ensuremath lambda ensuremath leqslant 2000 and within tolerance of 1 error mathrm r ensuremath lambda should be higher than 10 4 in order to have an inertial range wider than one decade the so called inertial range found in experiments and simulations is just a scaling range and is not the same as kolmogorov s inertial range the finite reynolds number effect cannot be neglected within such a scaling range and should be considered in comparing experiments or simulations with theories of the inertial range statistics

towards a nonperturbative theory of hydrodynamic turbulence fusion rules exact bridge relations and anomalous viscous scaling functions in this paper we address nonperturbative aspects of the analytic theory of hydrodynamic turbulence of paramount importance for this theory are the fusion rules that describe the asymptotic properties of n point correlation functions when some of the coordinates tend toward one other we first derive here on the basis of two fundamental assumptions a set of fusion rules for correlations of velocity differences when all the separations are in the inertial interval using this set of fusion rules we consider the standard hierarchy of equations relating the n mathrm th order correlations originating from the viscous term in the navier stokes equations to n 1 mathrm th order originating from the nonlinear term and demonstrate that for fully unfused correlations the viscous term is negligible consequently the hierarchic chain of equations is decoupled in the sense that the correlations of n 1 mathrm th order satisfy a homogeneous equation that may exhibit anomalous scaling solutions using the same hierarchy of equations when some separations go to zero we derive on the basis of the navier stokes equations a second set of fusion rules for correlations with differences in the viscous range the latter includes gradient fields we demonstrate that every n mathrm th order correlation function of velocity differences mathcal f n r 1 r 2 dots exhibits its own crossover length ensuremath eta n to dissipative behavior as a function of say r 1 this length depends on n and on the remaining separations r 2 r 3 dots when all these separations are of the same order r this length scales as ensuremath eta n r ensuremath sim ensuremath eta frac r l x n with x n frac ensuremath zeta n ensuremath ensuremath zeta n 1 ensuremath zeta 3 ensuremath ensuremath zeta 2 2 ensuremath ensuremath zeta 2 with ensuremath zeta n being the scaling exponent of the n mathrm th order structure function we derive a class of exact scaling relations bridging the exponents of correlations of gradient fields to the exponents ensuremath zeta n of the n mathrm th order structure functions one of these relations is the well known bridge relation for the scaling exponent of dissipation fluctuations ensuremath mu 2 ensuremath ensuremath zeta 6

a note on third order structure functions in turbulence starting from the navier stokes equation we rigorously prove that a modified third order structure function stilde3 r asymptotically equals 4 over 3 r is the dissipation rate in an inertial regime from this result we rigorously confirm the kolmogorov four fifths law without the kolmogorov assumption on isotropy our definition of the structure function involves a solid angle averaging over all possible orientations of the displacement vector y besides space time averaging direct numerical simulation for a highly symmetric flow for a taylor reynolds number of up to 155 shows that the flow remains significantly anisotropic and that without solid angle averaging the resulting structure functions approximately satisfy these scaling relations over some range of r l y l for some orientation of y but not for another

statistics of turbulent fluctuations in counter rotating taylor couette flows the statistics of velocity fluctuations of turbulent taylor couette flow are examined the rotation rates of the inner and outer cylinders are varied while keeping the taylor number fixed to 1 49 10 12 o re 10 6 the azimuthal velocity component of the flow is measured using laser doppler anemometry for each experiment 5 10 6 data points are acquired and carefully analyzed using extended self similarity benzi et al phys rev e 48 r29 1993 the longitudinal structure function exponents are extracted and are found to weakly depend on the ratio of the rotation rates for the case where only the inner cylinder rotates the results are in good agreement with results measured by lewis and swinney phys rev e 59 5457 1999 using hot film anemometry the power spectra show clear 5 3 scaling for the intermediate angular velocity ratios o i 0 6 0 8 1 0 roughly 5 3 scaling for o i 0 2 0 3 0 4 2 0 and no clear scaling law can be found for 0 i 0 inner cylinder rotation only the local scaling exponent of the spectra has a strong frequency dependence we relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

the multifractal structure of contrast changes in natural images from sharp edges to textures we present a formalism that leads naturally to a hierarchical description of the different contrast structures in images providing precise definitions of sharp edges and other texture components within this formalism we achieve a decomposition of pixels of the image in sets the fractal components of the image such that each set contains only points characterized by a fixed strength of the singularity of the contrast gradient in its neighborhood a crucial role in this description of images is played by the behavior of contrast differences under changes in scale contrary to naive scaling ideas where the image is thought to have uniform transformation properties field 1987 each of these fractal components has its own transformation law and scaling exponents a conjecture on their biological relevance is also given

intermittency and the slow approach to kolmogorov scaling from a simple path integral involving a variable volatility in the velocity differences we obtain velocity probability density functions with exponential tails resembling those observed in fully developed turbulence the model yields realistic scaling exponents and structure functions satisfying extended self similarity but there is an additional small scale dependence for quantities in the inertial range which is linked to a slow approach to kolmogorov 1941 scaling occurring in the large distance limit

double scaling and intermittency in shear dominated flows the re ned kolmogorov similarity hypothesis is a valuable tool for the description of intermittency in isotropicconditions for ows in presence of a substantial mean shear the nature of intermittency changes since the process ofenergy transfer is a ected by the turbulent kinetic energy production associated with the reynolds stresses in theseconditions a new form of re ned similarity law has been found able to describe the increased level of intermittencywhich characterizes shear dominated ows ideally a length scale associated with the mean shear separates the tworanges i e the classical kolmogorov like inertial range below and the shear dominated range above however the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observedindividually in the present letter we give evidence of the coexistence of the two regimes and support the conjecture thatthe statistical properties of the dissipation eld are practically insensible to the mean shear this allows for atheoretical prediction of the scaling exponents of structure functions in the shear dominated range based on theknown intermittency corrections for isotropic ows the prediction is found to closely match the available numericaland experimental data

exponents of the structure functions in a low temperature helium experiment abstract we report new measurements of longitudinal structure function exponents in fully developed turbulence the measurements are performed in low temperature helium for a wide range of microscale reynolds numbers from 150 to 5040 using large velocity records up to 1010 points for the largest one i e 3 106 integral time scales exponents of the longitudinal structure function of the velocity denoted by p are determined in general up to tenth order and in one case up to twelfth order they are slightly smaller than previously reported values and it is safe to say that within the accuracy of the present measurements they do not seem to evolve significantly with the reynolds number high order values of p obtained by extrapolating the distributions of the velocity increments are determined for the largest record they are found to decrease with p above p 18