dynamic stability of stiffened laminated composite plates and shells subjected to in plane pulsating forces abstract the dynamic stability of laminated composite stiffened or non stiffened plates and shells due to periodic in plane forces at boundaries is investigated in this paper the 3 d degenerated shell element and 3 d degenerated curved beam element are used to model plates shells and stiffeners respectively the characteristic equations for the natural frequencies buckling loads and their corresponding mode shapes are obtained from the finite element equations of motion then the method of hill s infinite determinants or the method of multiple scales is applied to analyze the dynamic instability regions numerical results are presented to demonstrate the effects of various parameters such as skew angle lamination scheme stiffening scheme in plane force type and the curvature of the cylindrical shells on the dynamic stability of stiffened and non stiffened plates and shells subjected to in plane pulsating forces at boundaries

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

modeling highway traffic headway distributions using superstatistics we study traffic clearance distributions i e the instantaneous gap between successive vehicles and time headway distributions by applying the beck and cohen superstatistics we model the transition from free phase to congested phase with the increase of vehicle density as a transition from the poisson statistics to that of the random matrix theory we derive an analytic expression for the spacing distributions that interpolates from the poisson distribution and wigner s surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow the obtained distribution fits the experimental results for single vehicle data of the dutch freeway a9 and the german freeway a5

superstatistics in hydrodynamic turbulence abstract superstatistics is a statistics of a statistics relevant for driven nonequilibrium systems with fluctuating intensive parameters it contains tsallis statistics as a special case we show that probability density functions of velocity differences and accelerations measured in eulerian and lagrangian turbulence experiments are well reproduced by simple superstatistics models we compare fits obtained for log normal superstatistics and 2 superstatistics tsallis statistics

superstatistical generalization of the work fluctuation theorem abstract we derive a generalized version of the work fluctuation theorem for non equilibrium systems with spatio temporal temperature fluctuations for 2 distributed inverse temperature we obtain a generalized fluctuation theorem based on q exponentials whereas for other temperature distributions more complicated formulae arise since q exponentials have a power law decay the decay rate in this generalized fluctuation theorem is much slower than the conventional exponential decay this implies that work fluctuations can be of relevance for the design of micro or nano structures since the work done on the system is relatively much larger than in the conventional fluctuation theorem

stability of incomplete entropy and incomplete expectation region des pays de la loire of france 2007 6088 science research fund 07bs105 huaqiao university people s republic of china

dynamic stability of stiffened laminated composite plates and shells subjected to in plane pulsating forces the dynamic stability of laminated composite stiffened or non stiffened plates and shells due to periodic in plane forces at boundaries is investigated in this paper a three dimensional 3 d degenerated shell element and a 3 d degenerated curved beam element are used to model plates shells and stiffeners respectively the characteristic equations to find the natural frequencies buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion then the method of hill s infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions numerical results are presented to demonstrate the effects of various parameters such as skew angle lamination scheme stiffened scheme in plane force type and curvature of cylindrical shell on the dynamic stability of stiffened and non stiffened plates and shells subjected to in plane pulsating forces at boundaries

pathway model superstatistics tsallis statistics and a generalized measure of entropy abstract the pathway model of mathai a pathway to matrix variate gamma and normal densities linear algebra appl 396 2005 317 328 is shown to be inferable from the maximization of a certain generalized entropy measure this entropy is a variant of the generalized entropy of order considered in mathai and rathie basic concepts in information theory and statistics axiomatic foundations and applications wiley halsted new york and wiley eastern new delhi 1975 and it is also associated with shannon boltzmann gibbs renyi tsallis and havrda charvat entropies the generalized entropy measure introduced here is also shown to have interesting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure expected value and information content in a scheme particular cases of the pathway model are shown to be tsallis statistics c tsallis possible generalization of boltzmann gibbs statistics j stat phys 52 1988 479 487 and superstatistics introduced by beck and cohen superstatistics physica a 322 2003 267 275 the pathway model s connection to fractional calculus is illustrated by considering a fractional reaction equation

continuum based stiffened composite shell element for geometrically nonlinear analysis a continuum based laminated stiffened shell element is used to investigate the static geometrically nonlinear response of composite shells the element is developed from a three dimensional continuum element based on the incremental total lagrangian formulation the newton raphson method or modified riks method is used to trace the nonlinear equilibrium path a number of sample problems of unstiffened and stiffened shells are presented to show the accuracy of the present element and to investigate the nonlinear response of laminated composite plates and shells inite element analyses of the large displacement the ories are based on the principle of virtual work or the associated principle of stationary potential energy horrigmoe and bergan1 presented classical variational principles for non linear problems by considering incremental deformations of a continuum a survey of various principles in incremental form in different reference configurations such as the total lagran gian and updated lagrangian formulations is presented by wiinderlich 2 in the total lagrangian description all static and kinematic variables are referred to the initial configura tion finite element models based on such formulations have been used in the analysis of arch and shell instability prob lems 3 6 a special numerical technique must be adopted to trace the path of the load deflection curve near the limit point i e critical buckling load and in the postbuckling region because the stiffness matrix in the vicinity of the limit point is nearly singular and the descending branch of the load deflec tion curve in the postbuckling region is characterized by a negative definite stiffness matrix many methods have been proposed to solve limit point problems among these are the simple methods of suppressing equilibrium iterations 7 8 the introduction of artificial spring 3 the displacement control method 7 8 and the constant arc length method of riks 11 12 reviews of these most commonly used techniques are con tained in refs 13 and 14 among these methods the modified riks method appears to be the most effective in conjunction with the finite element method many investigators11 15 have used this method in its original or modified form to determine the pre and postbuckling behavior of various types of struc tures such as arches shells and domes in most of these works only isotropic material was considered very few works of the nonlinear buckling analysis of laminated com posite structures are reported in the literature 16 when solving the problems of shells with stiffeners by the finite element method a beam element whose displacement pattern is compatible with that of the shell is required in analyzing eccentrically stiffened cylindrical shell kohnke and schnobrich17 proposed a 16 deg of free dom dof isotropic beam finite element that has displacements compatible with

a possible classification of nonequilibrium steady states we propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents the stationary probabilities can be represented graph theoretically as directed labelled trees closing a single loop in such a graph leads to a representation of probability currents this classification allows us to identify all choices of transition rates based on a master equation which generate the same nonequilibrium steady state we explore the implications of this freedom e g for entropy production

guidelines for the construction of a generating partition in the standard map abstract the validity of a recently developed procedure to construct a symbolic dynamics for the standard map is accurately investigated the implications of all the stages that involve the determination of homoclinic tangencies and the identification of appropriate symmetry lines are discussed moreover an extension of the method from the strongly to the weakly chaotic regime is presented as a result the general validity of the approach is strengthened although many intermediate steps still have no rigorous justification

generalized superstatistics of nonequilibrium markovian systems abstract the paper is devoted to the construction of the superstatistical description for nonequilibrium markovian systems it is based on kirchhoff s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes the latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually then stationary probability as well as flux distributions are represented as some sums over the channels the latter construction actually forms the superstatistical description which however deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the boltzmann type

on maximum entropy principle superstatistics power law distribution and renyi parameter abstract the equilibrium distributions of probabilities are derived on the basis of the maximum entropy principle mep for the renyi and tsallis entropies new s forms for the renyi and tsallis distribution functions are found which are normalised with corresponding entropies in contrast to the usual z forms normalised with partition functions z the superstatistics based on the gibbs distribution of energy fluctuations gives rise to a distribution function of the same structure that the renyi and tsallis distributions have the long range tail of the renyi distribution is the power law distribution with the exponent s expressed in terms of the free renyi parameter q as s 1 1 q the condition s 0 gives rise to the requirement q q can be uniquely determined with the use of a further extension of mep as the condition for maximum of the difference between the renyi and boltzmann entropies for the same power law distribution dependent on q it is found that the maximum is realized for q within the range from 0 25 to 0 5 and the exponent s varies from 1 3 to 2 in dependence on parameters of stochastic systems

random matrix theory within superstatistics we propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics spectral characteristics of systems with mixed regular chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable we illustrate the method by calculating the level density the nearest neighbor spacing distributions and the two level correlation functions for systems in transition from order to chaos the calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment

analysis of dynamic instability for arbitrarily laminated skew plates the dynamic instability and nonlinear response of rectangular and skew laminated plates subjected to periodic in plane load are studied based on von karman plate theory the large amplitude dynamic equations of thin laminated plates are derived by applying the approach of generalized double fourier series on the assumed mode shape the governing equations are reduced to the mathieu equation using galerkin s method the incremental harmonic balance ihb method is applied to solve the nonlinear temporal equation of motion and the region of dynamic instability is determined in this work calculations are carried out for isotropic angle ply and arbitrarily laminated plates under two cases of boundary conditions the principal region of dynamic instability associated with the effect of the stacking sequence of lamination and the skew angle of plate are also investigated and discussed the results obtained indicated that the instability behavior of the system is determined by the several parameters such as the boundary condition number of the layers stacking sequence in plane load aspect ratio amplitude and the skew angle of plate

nonextensive aspects of small world networks abstract nonextensive aspects of the degree distribution in watts strogatz ws small world networks p sw k have been discussed in terms of a generalized gaussian referred to as q gaussian which is derived by the three approaches the maximum entropy method mem stochastic differential equation sde and hidden variable distribution hvd in mem the degree distribution p q k in complex networks has been obtained from q gaussian by maximizing the nonextensive information entropy with constraints on averages of k and k 2 in addition to the normalization condition in sde q gaussian is derived from langevin equations subject to additive and multiplicative noises in hvd q gaussian is made by a superposition of gaussians for random networks with fluctuating variances in analogy to superstatistics interestingly a single p q k may describe with an accuracy of p sw k p q k 10 2 main parts of degree distributions of sw networks within which about 96 99 of all k states are included it has been demonstrated that the overall behavior of p sw k including its tails may be well accounted for if the k dependence is incorporated into the entropic index in mem which is realized in microscopic langevin equations with generalized multiplicative noises

non gaussian probability distribution functions from maximum entropy principle considerations in this work we develop the recently suggested concept of superstatistics c beck and e g d cohen physica a 322 267 2003 face the problem of devising a viable way for estimating the correct statistics for a system in the absence of sufficient knowledge of its microscopical dynamics and suggest to solve it through the maximum entropy principle as an example we deduce the probability distribution function for velocity fluctuations in turbulent fluids which is slightly different from the form suggested by c beck phys rev lett 87 180601 2001

application of the beck model to stock markets value at risk and portfolio risk assessment abstract we apply the beck model developed for turbulent systems that exhibit scaling properties to stock markets our study reveals that the beck model elucidates the properties of stock market returns and is applicable to practical use such as the value at risk estimation and the portfolio analysis we perform empirical analysis with daily intraday data of the s p500 index return and find that the volatility fluctuation of real markets is well consistent with the assumptions of the beck model the volatility fluctuates at a much larger time scale than the return itself and the inverse of variance or inverse temperature obeys distribution as predicted by the beck model the distribution of returns is well fitted by q gaussian distribution of tsallis statistics the evaluation method of value at risk var one of the most significant indicators in risk management is studied for q gaussian distribution our proposed method enables the var evaluation in consideration of tail risk which is underestimated by the variance covariance method a framework of portfolio risk assessment under the existence of tail risk is considered we propose a multi asset model with a single volatility fluctuation shared by all assets named the single model and empirically examine the agreement between the model and an imaginary portfolio with dow jones indices it turns out that the single model gives good approximation to portfolios composed of the assets with non gaussian and correlated returns

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

velocity probability density functions of high reynolds number turbulence abstract this paper deals with the probability density function pdf of velocity differences between two points separated by distance r measurements of pdfs were made for r lying in the inertial range for two different flows in a jet with r 852 and in a wind tunnel with r 2720 these pdfs have a characteristic non gaussian shape with exponential tails following kolmogorov s general ideas of log normality a new model for the pdf is developed which contains two parameters determined by experiments this empirical model agrees with the experimental results that the tails of the pdf deviate from a truly exponential behaviour in particular for small r in addition the model leads to the general scaling law ln e 2 r r 0 differenr from kolmogorov s third hypothesis ln e 2 ln r r 0 restricted to the inertial range only x is x x we develop also a formalism based on an extremum principle which is consistent with both the log normality of e and the above mentioned power law in this formalism can be interpreted as the codimension of dissipative structures and asymptotically varies as 1 ln r

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

constructing a statistical mechanics for beck cohen superstatistics the basic aspects of both boltzmann gibbs bg and nonextensive statistical mechanics can be seen through three different stages first the proposal of an entropic functional s bg k sigma i p i ln p i for the bg formalism with the appropriate constraints sigma i p i 1 and sigma i p i e i u for the bg canonical ensemble second through optimization the equilibrium or stationary state distribution p i e betae i z bg with z bg sigma j e betae j for bg third the connection to thermodynamics e g f bg 1 beta ln z bg and u bg partial differential partial differential beta ln z bg assuming temperature fluctuations beck and cohen recently proposed a generalized boltzmann factor b e integral infinity 0 dbetaf beta e betae this corresponds to the second stage described above in this paper we solve the corresponding first stage i e we present an entropic functional and its associated constraints which lead precisely to b e we illustrate with all six admissible examples given by beck and cohen

experimental lagrangian acceleration probability density function measurement abstract we report experimental results on the acceleration component probability distribution function at r 690 to probabilities of less than 10 7 this is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55 we compare our probability distribution to those predicted by several models inspired by non extensive statistical mechanics we also look at acceleration component probability distributions conditioned on a velocity component for conditioning velocities as high as three times the standard deviation and find them to be highly non gaussian

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

asymptotics of superstatistics superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable e g the inverse temperature they contain tsallis statistics as a special case we develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics a saddle point approximation is developed which relates this problem to a variational principle several examples are worked out in detail

log amplitude statistics of intermittent and non gaussian time series in studies of hydrodynamic turbulence and nonequilibrium systems it has been demonstrated that the observed non gaussian probability density functions are often described effectively by a superposition of gaussian distributions with fluctuating variances based on this framework we propose a general method to characterize intermittent and non gaussian time series in our approach an observed time series is assumed to be described by the multiplication of gaussian and amplitude random variables where the amplitude variable describes the variance fluctuation it is shown analytically that statistical properties of the log amplitude fluctuations can be estimated using the logarithmic absolute moments of the observed time series this method is applicable to a wide variety of symmetric unimodal distributions with heavy tails in order to quantify the deviation from a gaussian distribution by analyzing random cascade type processes and superstatistical non gaussian models with power law tails we demonstrate that our method can provide detailed characterization in a wide range of non gaussian fluctuations

maximum entropy approach to power law distributions in coupled dynamic stochastic systems statistical properties of coupled dynamic stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach the conditions at which the shannon entropy functional leads to power law statistics are investigated it is demonstrated that from a quite general point of view the power law dependencies may appear as a consequence of global constraints restricting both the dynamic phase space and the stochastic fluctuations as a result at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium

superstatistical random matrix theory approach to transition intensities in mixed systems we study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory which is based on beck and cohen s superstatistics we obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos the obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the porter char21 thomas distribution it agrees with the experimental reduced transition probabilities for the 26 mathrm al nucleus better than the commonly used ensuremath chi 2 distribution

complex networks emerging from fluctuating random graphs analytic formula for the hidden variable distribution in analogy to superstatistics which connects boltzmann gibbs statistical mechanics to its generalizations through temperature fluctuations complex networks are constructed from fluctuating erd os r enyi random graphs using a quantum mechanical method the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the poisson transformation as an example a static scale free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems