lyapunov instabilities of lennard jones fluids recent work on many particle systems reveals the existence of regular collective perturbations corresponding to the smallest positive lyapunov exponents les called hydrodynamic lyapunov modes until now however these modes have been found only for hard core systems here we report results on lyapunov spectra and lyapunov vectors lvs for lennard jones fluids by considering the fourier transform of the coordinate fluctuation density u ensuremath alpha x t it is found that the lvs with ensuremath lambda ensuremath approx 0 are highly dominated by a few components with low wave numbers these numerical results provide strong evidence that hydrodynamic lyapunov modes do exist in soft potential systems although the collective lyapunov modes are more vague than in hard core systems in studying the density and temperature dependence of these modes it is found that when the value of the lyapunov exponent ensuremath lambda ensuremath alpha is plotted as function of the dominant wave number k mathit max of the corresponding lv all data from simulations with different densities and temperatures collapse onto a single curve this shows that the dispersion relation ensuremath lambda ensuremath alpha vs k mathit max for hydrodynamical lyapunov modes appears to be universal for the low density cases studied here despite the wavelike character of the lvs no steplike structure exists in the lyapunov spectrum of the systems studied here in contrast to the hard core case further numerical simulations show that the finite time les fluctuate strongly we have also investigated localization features of lvs and propose a length scale to characterize the hamiltonian spatiotemporal chaotic states

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

on the multivariate asymptotic distribution of sequential chi square statistics the multivariate asymptotic distribution of sequential chi square test statistics is investigated it is shown that a when sequential chi square statistics are calculated for nested models on the same data the statistics have an asymptotic intercorrelation which may be expressed in closed form and which is in many cases quite high and b sequential chi squaredifference tests are asymptotically independent some monte carlo evidence on the applicability of the theory is provided

on robustness of the normal theory based asymptotic distributions of three reliability coefficient estimates this paper studies the asymptotic distributions of three reliability coefficient estimates sample coefficient alpha the reliability estimate of a composite score following a factor analysis and the estimate of the maximal reliability of a linear combination of item scores following a factor analysis results indicate that the asymptotic distribution for each of the coefficient estimates obtained based on a normal sampling distribution is still valid within a large class of nonnormal distributions therefore a formula for calculating the standard error of the sample coefficient alpha recently obtained by van zyl neudecker and nel applies to other reliability coefficients and can still be used even with skewed and kurtotic data such as are typical in the social and behavioral sciences

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

a boundary integral modification of the galerkin least squares formulation for the stokes problem abstract a new boundary integral term is added to the galerkin least squares gls formulation the new formulation compensates for a lack of consistency noted for the traditional gls method when bilinear interpolation is used on quadrilateral elements exact solutions at the nodes are obtained for poiseuille flow and another test problem and the pressure singularity for the driven cavity is better captured

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

power of the likelihood ratio test in covariance structure analysis a procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived the procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified using the noncentral chi square distribution the power of the test is approximated by the asymptotic one for a sequence of local alternatives the procedure is illustrated by an example a monte carlo experiment also shows how good the approximation is for a specific case

a unifying expression for the maximal reliability of a linear composite a formally simple expression for the maximal reliability of a linear composite is provided its theoretical implications and its relation to existing results for reliability are discussed

asymptotic chi square tests for a large class of factor analysis models asymptotic behavior of the test statistics for three types of 2 goodness of fit tests is investigated for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector in particular the limiting 2 result for the three tests is shown to hold for the factor vector and for the error vector with any distribution having finite second order moments provided that the components of the error vector are independent as special cases the result holds for exploratory and confirmatory factor analysis models and for certain non normal structural equation models

equivalence of kinetic theory and random matrix approaches to lyapunov spectra of hard sphere systems abstract in the study of chaotic behaviour of systems of many hard spheres lyapunov exponents of small absolute values exhibit interesting characteristics leading to speculations about connections to non equilibrium statistical mechanics analytical approaches to these exponents so far can be divided into two groups macroscopically oriented approaches using kinetic theory or hydrodynamics and more microscopically oriented random matrix approaches in quasi one dimensional systems in this paper i present an approach using random matrices and weak disorder expansion in an arbitrary number of dimensions correlations between subsequent collisions of a particle are taken into account it is shown that the results are identical to those of a previous approach based on an extended enskog equation i conclude that each approach has its merits and provides different insights into the approximations made which include the stoszahlansatz the continuum limit and the long wavelength approximation the comparison also gives insight into possible connections between lyapunov exponents and fluctuations

perturbed phase space dynamics of hard disk fluids abstract the lyapunov spectrum describes the exponential growth or decay of infinitesimal phase space perturbations the perturbation associated with the maximum lyapunov exponent is strongly localized in space and only a small fraction of all particles contributes to the perturbation growth at any instant of time this fraction converges to zero in the thermodynamic large particle number limit for hard disk and hard sphere systems the perturbations belonging to the smallest of the non vanishing exponents are coherently spread out and form orthogonal periodic structures in space the lyapunov modes there are two types of mode polarizations transverse and longitudinal the transverse modes do not propagate but the longitudinal modes do with a speed about one third of the sound speed we characterize the symmetry and the degeneracy of the modes in the thermodynamic limit the lyapunov spectrum has a diverging slope near the intersection with the abscissa no positive lower bound exists for the positive exponents the mode amplitude scales with the inverse square root of the particle number as expected from the normalization of the perturbation vectors

origin of the hydrodynamic lyapunov modes recent studies of the lyapunov spectrum of the hard sphere fluid reveal that there are hydrodynamic lyapunov exponents corresponding to collective perturbations in phase space we show that these collective perturbations are due to the conservation of certain quantities during collisions these new conservation laws generate new hydrodynamic fields just as the conservation of mass momentum and energy generate the density velocity and temperature fields we then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach this theory predicts several properties of the modes but not all of them this suggests that the underlying idea is correct but a detailed theory must be elaborated in another way the hydrodynamic exponents are not related in a simple way to the transport coefficients

mean comparison manifest variable versus latent variable mean comparisons are of great importance in the application of statistics procedures for mean comparison with manifest variables have been well studied however few rigorous studies have been conducted on mean comparisons with latent variables although the methodology has been widely used and documented this paper studies the commonly used statistics in latent variable mean modeling and compares them with parallel manifest variable statistics our results indicate that under certain conditions the likelihood ratio and wald statistics used for latent mean comparisons do not always have greater power than the hotelling t2 statistics used for manifest mean comparisons the noncentrality parameter corresponding to the t2 statistic can be much greater than those corresponding to the likelihood ratio and wald statistics which we find to be different from those provided in the literature under a fixed alternative hypothesis our results also indicate that the likelihood ratio statistic can be stochastically much greater than the corresponding wald statistic the robustness property of each statistic is also explored when the model is misspecified or when data are nonnormally distributed recommendations and advice are provided for the use of each statistic

latent curve analysis as a method for representing development latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth maximum likelihood parameter estimates and associated asymptotic tests follow directly these procedures may be viewed as an alternative to standard repeated measures anova and to first order auto regressive methods as formulated the model encompasses cohort sequential designs and allow for period or practice effects a numerical illustration using data initially collected by nesselroade and baltes is presented

when can one observe good hydrodynamic lyapunov modes inspired by recent results on differences in fluctuations of finite time lyapunov exponents between hard core and soft potential systems we surmise that partial domination of the oseledec splitting dos with respect to subspaces associated with near zero lyapunov exponents is essential for observing good hydrodynamic lyapunov modes hlms numerical results for coupled map lattices are presented to show the importance of dos for observing good hlms this is achieved by relating splitting parameters to the maximum value of the lyapunov mode structure factor

lyapunov modes of two dimensional many body systems soft disks hard disks and rotors the dynamical instability of many body systems can best be characterized through the local lyapunov spectrum its associated eigenvectors and the time averaged spectrum each local lyapunov exponent describes the degree of instability associated with a well defined direction given by the associated unit vector in the full many body phase space for a variety of hard particle systems it is by now well established that several of the vectors all with relatively small values of the time averaged exponent correspond to quite well defined long wavelength modes we investigate soft particles from the same viewpoint here and find no convincing evidence for corresponding modes the situation is similar no firm evidence for modes in a simple two dimensional lattice rotor model we believe that these differences are related to the form of the time averaged lyapunov spectrum near 0

a review of the hydrodynamic lyapunov modes of hard disk systems a review of the results obtained for hard disk fluids confined to a quasi one dimensional qod system is presented one of the main achievements in recent years has been determining the hydrodynamic lyapunov modes hlms as covariant stable and unstable manifolds defined by k vector analogues of the zero exponent subspace of conserved quantities the tangent space dynamics allows an interpretation of the hlms as reduced hydrodynamic fields over the perturbations and is expanded upon in this paper the time evolution of these modes is governed by the dynamics of conjugate pairs of stable and unstable directions each pair is seen to interact in a subspace almost completely separated from other vectors the modes undergo a rotation until they are collinear with the stable or unstable manifold the angle distributions between these covariant stable and unstable hlms are also determined and tangencies are not observed for a generic chaotic trajectory this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

lyapunov spectra of billiards with cylindrical scatterers comparison with many particle systems the dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high dimensional space with fixed hypercylindrical scatterers with specific orientations and positions in this paper the similarities in the lyapunov exponents are investigated between systems of many particles and high dimensional billiards the billiards contain cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions the dynamics of the isotropic billiards are calculated using a monte carlo simulation and a reorthogonalization process is used to find the lyapunov exponents the results are compared to numerical results for systems of many hard particles as well as the analytical results for the high dimensional lorentz gas the smallest three quarters of the positive exponents behave more like the exponents of hard disk systems than the exponents of the lorentz gas this similarity shows that the hard disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller lyapunov exponents apart from the exponent associated with localization the method of the partial stretching factor is used to calculate these exponents analytically with results that compare well with simulation results of hard disks and hard spheres

effect size power and sample size determination for structured means modeling and mimic approaches to between groups hypothesis testing of means on a single latent construct while effect size estimates post hoc power estimates and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables e g anova such measures and methods have not been articulated for analyses involving latent means the current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and mimic approaches to hypothesis testing about differences among means on a single latent construct these measures are then related to post hoc power analysis a priori sample size determination and a relevant measure of construct reliability

a unified approach to exploratory factor analysis with missing data nonnormal data and in the presence of outliers factor analysis is regularly used for analyzing survey data missing data data with outliers and consequently nonnormal data are very common for data obtained through questionnaires based on covariance matrix estimates for such nonstandard samples a unified approach for factor analysis is developed by generalizing the approach of maximum likelihood under constraints statistical properties of the estimates for factor loadings and error variances are obtained a rescaled bartlett corrected statistic is proposed for evaluating the number of factors equivariance and invariance of parameter estimates and their standard errors for canonical varimax and normalized varimax rotations are discussed numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures

the role of bulk viscosity in stabilized finite element formulations for incompressible flow a review abstract in stabilized finite element methods for incompressible flows like e g galerkin least squares gls formulations a bulk viscosity or penalty like term is sometimes present this paper reviews the appearance of this term and its role in stability accuracy and convergence speed issues

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

from synchronization to lyapunov exponents and back the goal of this paper is twofold in the first part we discuss a general approach to determine lyapunov exponents from ensemble rather than time averages the approach passes through the identification of locally stable and unstable manifolds the lyapunov vectors thereby revealing an analogy with generalized synchronization the method is then applied to a periodically forced chaotic oscillator to show that the modulus of the lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization the analytical calculations are carried out for a model the generalized special flow that we construct as a simplified version of the periodically forced rossler oscillator

alternative test criteria in covariance structure analysis a unified approach in the context of covariance structure analysis a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided the discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal and allows the null and alternative hypothesis to be only approximations of the true model also the equivalent of the information matrix and the asymptotic covariance matrix of the vector of summary statistics are allowed to be singular when the fitting function is not asymptotically optimal test statistics which have asymptotically a chi square distribution are developed as a natural generalization of more classical ones issues relevant for power analysis and the asymptotic theory of a testing related statistic are also investigated

on nonequivalence of several procedures of structural equation modeling the normal theory based maximum likelihood procedure is widely used in structural equation modeling three alternatives are the normal theory based generalized least squares the normal theory based iteratively reweighted least squares and the asymptotically distribution free procedure when data are normally distributed and the model structure is correctly specified the four procedures are asymptotically equivalent however this equivalence is often used when models are not correctly specified this short paper clarifies conditions under which these procedures are not asymptotically equivalent analytical results indicate that when a model is not correct two factors contribute to the nonequivalence of the different procedures one is that the estimated covariance matrices by different procedures are different the other is that they use different scales to measure the distance between the sample covariance matrix and the estimated covariance matrix the results are illustrated using real as well as simulated data implication of the results to model fit indices is also discussed using the comparative fit index as an example

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100