extended precise integration method for consolidation of transversely isotropic poroelastic layered media a new numerical method for calculating the consolidation behavior of the stratified transversely isotropic and poroelastic material is presented by combining the extended precise integration algorithm with the integral transformation techniques starting with the governing partial differential equations of a saturated medium with transversely isotropic skeleton and compressible fluid constituents an ordinary differential matrix equation is deduced with the aid of a laplace hankel transform an extended precise integration method for internal loading situations is proposed to solve the ordinary differential matrix equation in the transformed domain and the actual solution is recovered by a numerical inverse transformation numerical examples are also provided to prove the feasibility of this method

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

r s analysis of reaction time in neuron type test for human activity in civil aviation abstract human factors become the most serious problem leading to accidents of civil aviation which stimulates the design and analysis of neuron type test ntt system to explore the intrinsic properties and patterns behind the behaviors of professionals and students in civil aviation in the experiment normal practitioners reaction time sequences collected from ntt exhibit log normal distribution approximately we apply the 2 test to compute the goodness of fit by transforming the time sequence with box cox transformation to cluster practitioners the long term correlation of different individual practitioner s time sequence is represented by the hurst exponent via rescaled range analysis also named by range standard deviation r s analysis the different hurst exponent suggests the existence of different collective behavior and different intrinsic patterns of human factors in civil aviation

establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes stochastic fractal signals can be characterized by the hurst coefficient h which is related to the exponents of various power law statistics characteristic of these processes two techniques widely used to estimate h are spectral analysis and detrended fluctuation analysis dfa this paper examines the analytical link between these two measures and shows that they are related through an integral transform numerical simulations confirm this relationship for ideal synthesized fractal signals their performance as estimators of h is compared based on a mean square error criterion and found to be similar dfa measures are derived for physiological signals of heartbeat r ensuremath r intervals through the integral transform of a spectral density estimate these agree with directly calculated dfa estimates indicating that the relationship holds for signals with nonideal fractal properties it is concluded that dfa and spectral measures provide equivalent characterizations of stochastic signals with long term correlation

theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average we present a bottom up derivation of fluctuation analysis with detrending for the detection of long range correlations in the presence of additive trends or intrinsic nonstationarities while the well known detrended fluctuation analysis dfa and detrending moving average dma were introduced ad hoc we claim basic principles for such methods where dfa and dma are then shown to be specific realizations the mean squared displacement of the summed time series contains the same information about long range correlations as the autocorrelation function but has much better statistical properties for large time lags however the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities we therefore define the fluctuation function as mean squared displacement with weighting kernel we require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal which is only achieved if the weighting kernel implies detrending we show how dfa and dma satisfy these requirements and we extract their kernel weights

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

nonlocal models for damage and fracture comparison of approaches abstract the paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes of quasibrittle materials a number of nonlocal formulations found in the literature are classified according to the type of variable subjected to nonlocal averaging analytical and numerical solutions of a simple one dimensional localization problem are presented it is shown that some of the formulations inevitably lead to residual stresses even at very late stages of the deformation process and consequently they are not capable of modeling complete separation in a widely open macroscopic crack the mechanisms leading to this specific type of stress locking are explained based on a theoretical analysis of the nonlocal constitutive equations it is also pointed out that the nonlocal approach distorts the shape of the stress strain diagram which has to be taken into account when designing an appropriate local softening law

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

long range correlations and trends in colombian seismic time series abstract we study long range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of colombia the long range correlations are detected by the calculation of the hurst exponents for the time series of interevent intervals separation distances depth differences and magnitude differences by using a modification of the classical r s method that has been developed to detect short range correlations in time series we find the existence of persistence for all the time series considered except for magnitude differences we find also by using the d f a until the third order that the studied time series are not influenced by trends additionally an analysis of the hurst exponent as a function of the number of events in the time and the maximum window size is presented

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

levels of complexity in scale invariant neural signals many physical and physiological signals exhibit complex scale invariant features characterized by 1 f scaling and long range power law correlations indicating a possibly common control mechanism specifically it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to 1 f scaling and scale invariance two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1 f scaling they still may belong to different complexity classes our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics gait time series exhibit less complex close to monofractal behavior further we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features these findings are of interest because they underscore the limitations of traditional two point correlation methods in fully characterizing physiological and physical dynamics in addition these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1 f scaling

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

finite element analysis of bifurcation in nonlocal strain softening solids progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise e g ill posedness and multiple bifurcation points this characteristics behavior favours spurious strain localization in numerical analyses and calls for the implementation of localization limiters for instance nonlocal damage constitutive relations the issue of possible stable or unstable equilibrium paths multiple localization zones and of the detection of bifurcation points has however never been addressed in the context of nonlocal constitutive laws we extend here the eigenmode analysis and perturbation method proposed by de borst to the study of the bifurcation and post bifurcation response of discrete nonlocal strain softening solids numerical applications on beams show that bifurcation and instability may occur in the post peak regime as opposed to the case of local constitutive relations the number of possible solutions at a bifurcation point is restricted due to the constraint introduced by the localization limiter and these solutions are shown to be mesh independent

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

a taylor galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua abstract this paper presents a taylor galerkin algorithm formulated in terms of velocities and stresses which can be applied to solid dynamics problems requiring good resolution of small wavelengths such as propagation of shocks the proposed model is both fast as it uses simple linear elements triangles in 2d and tetrahedra in 3d and accurate it mitigates locking and mesh alignment problems and therefore can be applied to localized failure computations without the limitations exhibited by the classical displacement formulations

illusion of persistence in nba 1995 2018 regular season data abstract among the sports fans beliefs about hot hands and winning streaks are widely spread while the scientific debate about these effects is still ongoing recently in a paper by ferreira 2018 detrended fluctuation analysis was applied to the nba teams win records it was shown that 28 considered nba teams exhibit persistence in the win record time series in this paper we take the same data set and compare the obtained results against various random models we find that the empirical results are consistent with the results obtained from various simple random models

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

an embedded strong discontinuity model for cracking of plain concrete abstract a numerical model formulated within the framework of a nonsymmetric strong discontinuity approach for fracture simulations of plain concrete is presented the model is based on the fixed crack concept and makes use of the concept of the elements with embedded discontinuities discontinuity segments of individual elements are considered to form a c0 continuous path enforcement of continuity of the crack path across adjacent elements is established by a partial domain crack tracking algorithm orientation of individual crack segments is derived from a nonlocal strain field the capabilities of the model are shown by means of numerical examples

mixed linear linear simplicial elements for incompressible elasticity and plasticity this paper exploits the concept of orthogonal sub grid scales to stabilize the behaviour of mixed linear linear simplicial elements triangles and tetrahedra in incompressible or nearly incompressible situations both incompressible elastic and j2 plastic constitutive behaviours have been considered the different assumptions and approximations used to derive the method are exposed implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure and that the results obtained compare favourably with those obtained with the q1p0 quadrilateral

comparative analysis on turbulent regime a self affinity study in fluid flow by using openfoam cfd abstract we investigate the self affinity of a fluid velocity time series in turbulent regime we use the cfd openfoam library to simulate the flow of fluid in a duct with two obstacles injecting vorticity downstream we calculated the fluid velocity in three sections in of the structure the simulation presented more turbulences in sections further away from obstacles we assess the self affinity of properties of those sections by using the detrended fluctuation analysis method this scaling method presented two behaviors first a persistent behavior after passing through obstacles second a sub diffusive behavior in turbulent sections presenting a long range correlation exponent ranging between 1 0 and 1 5 the findings suggest that chaotic states tend to follow a sub diffusive process

effect of extreme data loss on long range correlated and anticorrelated signals quantified by detrended fluctuation analysis detrended fluctuation analysis dfa is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations to better identify the intrinsic correlation properties of real world signals where a large amount of data is missing or removed due to artifacts we investigate how extreme data loss affects the scaling behavior of long range power law correlated and anticorrelated signals we introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long range correlations the surrogate signals we generate are characterized by four parameters i the dfa scaling exponent alpha of the original correlated signal u i ii the percentage p of the data removed from u i iii the average length mu of the removed or remaining data segments and iv the functional form p l of the distribution of the length l of the removed or remaining data segments we find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90 in contrast the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost these observations are confirmed on two examples of real world signals human gait and commodity price fluctuations we further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales we find that for anticorrelated signals even 10 of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior in contrast positively correlated signals show no observable changes in the local scaling for up to 65 of data loss while for larger percentage of data loss the local scaling shows overestimated regions with higher local exponent at small scales followed by underestimated regions with lower local exponent at large scales finally we investigate how the scaling is affected by the average length probability distribution and percentage of the remaining data segments in comparison to the removed segments we find that the average length mu r of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value interestingly the scales where the maximum deviation occurs follow a power law relationship with mu r whereas the percentage of data loss determines the extent of the deviation the results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss

generalized viscoelastic models their fractional equations with solutions recently fractional calculus fc has encountered much success in the description of complex dynamics in particular fc has proved to be a valuable tool to handle viscoelastic aspects in this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models especially the maxwell the kelvin voigt the zener and the poynting thomson model to this end we introduce a fractional element in addition to the standard purely elastic and purely viscous elements as we proceed to show many of the fractional differential equations which we obtain by this construction method admit closed form analytical solutions in terms of fox h functions of the minag leffler type

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

consolidation of multilayered half space with anisotropic permeability and compressible constituents abstract this paper presents analytical solutions of consolidation for poroelastic and multilayered half space and anisotropy of the permeability and the compressibility of the pore fluid are considered state vector method together with laplace hankel transform techniques are used to solve the basic governing equations and obtain the transfer matrix in a clearly arranged way forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for the multilayered half space a numerical inversion scheme of crump s method is adopted to obtain time domain solution numerical results are presented for a single homogeneous soil layer and a multilayered half space and they illustrate the influences of the anisotropy of permeability and the compressibility of the pore fluid on the consolidation of the soils

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

long range correlations in heart rate variability during computer mouse work under time pressure abstract the aim of this study was to investigate the influences of time pressure on long range correlations in heart rate variability hrv the effects of relaxation on the cardiovascular regulation system and the advantages of detrended fluctuation analysis dfa over the conventional power spectral analysis in discriminating states of the cardiovascular systems under different levels of time pressure volunteer subjects n 10 male female 5 5 participated in a computer mouse task consisting of five sessions i e baseline session bss which was free of time pressure followed by sessions with 80 ss80 100 ss100 90 ss90 and 150 ss150 of the baseline time electrocardiogram ecg and task performance were recorded throughout the experiments two rest sessions before and after the computer mouse work i e rs1 and rs2 were also recorded as comparison hrv series were subsequently analyzed by both conventional power spectral analysis and detrended fluctuation analysis dfa the long term scaling exponent 2 by dfa was significantly lower in ss80 than that in other sessions it was also found that short term release of time pressure had positive influences on the cardiovascular system i e the 2 in rs2 was significantly higher than that in ss80 ss100 and ss90 no significant differences were found between any two sessions by conventional power spectral analysis our results showed that dfa performed better in discriminating the states of cardiovascular autonomic modulation under time pressure than the conventional power spectral analysis

fluctuation analysis of electric power loads in europe correlation multifractality vs distribution function multifractality abstract we analyzed the timeseries of power loads of 35 separate countries which publicly share hourly data through the entso e platform for more than 5 years moreover we applied multifractal detrended fluctuation analysis for the demonstration of the multifractal nature autocorrelation and the distribution function fundamentals additionally we improved the basic method described by kantelhardt et al using uniform shuffling and surrogation of the datasets in order to prove the robustness of the results with respect to the non linear effects of the processes all the datasets exhibited multifractality in the distribution function as well as in the autocorrelation function the basic differences between individual states are manifested in the width of the multifractal spectra and in the location of the maxima we present the hypothesis concerning the production portfolio and the export import dependencies

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

hurst exponent of very long birth time series in xx century romania social and religious aspects abstract the hurst exponent of very long birth time series in romania has been extracted from official daily records i e over 97 years between 1905 and 2001 included the series result from distinguishing between families located in urban u or rural r areas and belonging ox or not nox to the orthodox religion four time series combining both criteria u r and ox nox are also examined a statistical information is given on these sub populations measuring their xx th century state as a snapshot however the main goal is to investigate whether the daily production of babies is purely noisy or is fluctuating according to some non trivial fractional brownian motion in the four types of populations characterized by either their habitat or their religious attitude yet living within the same political regime one of the goals was also to find whether combined criteria implied a different behavior moreover we wish to observe whether some seasonal periodicity exists the detrended fluctuation analysis technique is used for finding the fractal correlation dimension of such 9 signals it has been first necessary due to two periodic tendencies to define the range regime in which the hurst exponent is meaningfully defined it results that the birth of babies in all cases is a very strongly persistent signal it is found that the signal fractal correlation dimension is weaker i for nox than for ox and ii or u with respect to r moreover it is observed that the combination of u or r with nox or ox enhances the unox uox and rox fluctuations but smoothens the rnox signal thereby suggesting a stronger conditioning on religiosity rituals or rules

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

low order variability diagrams for short range correlation evidence in financial data bgl usd exchange rate dow jones industrial average gold ounce price a method to sort out short range correlations and decorrelations in financial data is tested on three typical sets the bulgarian lev usa dollar bgl usd exchange rate the dow jones industrial average the gold ounce price the method makes use of the so called variability diagram technique three toys are used as models in order to understand features our findings indicate that some predictability can be found at short range time intervals c 1999 elsevier science b v all rights reserved

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

scaling features of texts images and time series in the given paper we consider the scaling features of long letter sequences like human writings discretized images and discretized 3nancial data using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate di5erent scalings for large and small 6uctuations we discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency dax future data c 2001 elsevier science b v all rights reserved

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

exact stiffness method for quasi statics of a multi layered poroelastic medium abstract a method is presented to study the three dimensional quasi static response of a multi layered poroelastic half space with compressible constituents the system under consideration consists of n layers of different thickness and material properties overlying a homogeneous half space fourier expansion laplace transforms and hankel transforms with respect to the circumferential time and radial coordinates respectively are used in the formulation laplace hankel transforms of displacements and pore pressure at layer interfaces are considered as the basic unknowns exact stiffness matrices describing the relationship between generalized displacement and force vectors of a finite layer and a half space are derived explicitly in the transform space the global stiffness matrix of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces the time histories of displacements stresses and pore pressure are obtained by solving the stiffness equation system for discrete values of laplace and hankel transform parameters and using numerical quadrature schemes for laplace and hankel transform inversions selected numerical results for different layered systems are presented to portray the influence of layering and poroelastic material properties the advantage of the present method is that for an n layered system it yields a numerically stable symmetric stiffness matrix of order 4 n 4 n when compared to the unsymmetric and numerically unstable coefficient matrix of order 8 n 8 n associated with the conventional method based on the determination of layer arbitrary coefficients

fractional derivative modeling for axisymmetric consolidation of multilayered cross anisotropic viscoelastic porous media abstract this paper presents a fractional derivative modeling for axisymmetric consolidation of multilayered cross anisotropic viscoelastic porous media the elastic solution for multilayered porous media is acquired by the extended precise integration method the flexibility coefficient of the fractional merchant viscoelastic model is deduced in the laplace transformed domain and the viscoelastic solution of the problem is further obtained by the elastic viscoelastic correspondence principle the numerical results are compared with those of published literatures to verify the proposed method and the influences of fractional derivative order viscoelasticity of solid skeleton and layering of materials on the axisymmetric consolidation of multilayered viscoelastic porous media are investigated by several examples

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

3d modelling of strong discontinuities in elastoplastic solids fixed and rotating localization formulations this paper is concerned with the incorporation of displacement discontinuities into a continuum theory of elastoplasticity for the modelling of localization processes such as cracking in brittle materials based on the strong discontinuity approach sda computational mechanics 1993 12 277 296 mesh objective 2d and 3d finite element formulations are developed using linear and quadratic 2d elements as well as 8 noded 3d elements in the formulation of the finite element model proposed in the paper the analogy with standard formulations is emphasized the parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique this approach results in linearized constitutive equations formally identical to continuum models therefore the standard return mapping algorithm is used to solve the non linear equations in analogy to concepts used in continuum smeared crack models a rotating formulation of the sda is proposed in addition to the standard concept of fixed discontinuities it is shown that the rotating localization approach reduces locking effects observed in analyses based on fixed localization directions the applicability of the proposed sda finite element model as well as its numerical performance is investigated by means of a three dimensional ultimate load analysis of a steel anchor embedded in a concrete block subjected to a shear force copyright 2003 john wiley sons ltd

stabilization of incompressibility and convection through orthogonal sub scales in finite element methods two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper the first of them is the stabilization through the pressure gradient projection which consists of adding a certain least squares form of the difference between the pressure gradient and its l2 projection onto the discrete velocity space in the variational equations of the problem the second is a sub grid scale method whose stabilization effect is very similar to that of the galerkin least squares gls method for the stokes problem it is shown here that the first method can also be recast in the framework of sub grid scale methods with a particular choice for the space of sub scales this leads to a new stabilization procedure whose applicability to stabilize convection is also studied in this paper

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

improving stability and accuracy of reissner mindlin plate finite elements via algebraic subgrid scale stabilization abstract stabilized finite element methods for the solution of reissner mindlin type plate problems are presented the formulations are based on previously described mixed formulations like the assumed natural strain ans or mitc concept or the discrete shear gap dsg method in particular the algebraic subgrid scale asgs formulation is used for the stabilization term the essential idea is to obtain stable elements and improve coarse mesh accuracy at the same time it is shown how this can be achieved by a proper choice of stabilization parameters on the basis of physical insight into the mechanical behavior of shear deformable plates in this context there is a strong relationship to concepts that have been developed long before stabilization techniques appeared in finite element technology particularly the residual bending flexibility or deflection matching technique

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

finite element approximation of the three field formulation of the stokes problem using arbitrary interpolations the stress displacement pressure formulation of the elasticity problem may suffer from two types of numerical instabilities related to the finite element interpolation of the unknowns the first is the classical pressure instability that occurs when the solid is incompressible whereas the second is the lack of stability in the stresses to overcome these instabilities there are two options the first is to use different interpolation for all the unknowns satisfying two inf sup conditions whereas there are several displacement pressure interpolations that render the pressure stable less possibilities are known for the stress interpolation the second option is to use a stabilized finite element formulation instead of the plain galerkin approach if this formulation is properly designed it is possible to use arbitrary interpolation for all the unknowns the purpose of this paper is precisely to present one of such formulations in particular it is based on the decomposition of the unknowns into their finite element component and a subscale which will be approximated and whose goal is to yield a stable formulation a singular feature of the method to be presented is that the subscales will be considered orthogonal to the finite element space we describe the design of the formulation and present the results of its numerical analysis

a regularized xfem framework for embedded cohesive interfaces this work focuses on xfem modeling of elastodamaging interfaces characterized by regularized kinematics after regularization of the displacement discontinuity a process zone of finite width with continuous strain fields emerges the stress fields are independently energy deduced modeled via specific constitutive laws and subsequently introduced within the virtual work principle the methodology can address cohesive interfaces with vanishing and finite thickness in a unified way two dimensional results for a strain localization problem and several delamination tests are discussed in detail and compared with previous numerical experimental results