a procedure for the identification of linear and non linear multi degree of freedom systems abstract most of the modern techniques for vibration analysis are based on the modal approach however when the systems under study are not lightly damped so that there are significant cross damping terms in the governing equations when there are closely spaced natural frequencies or when non linearities exist then the modal approach is extremely limited a number of techniques have been proposed to deal with these problems but the methods tend to produce models which are subjective in this paper a generalized non iterative approach in which spectral techniques are used is presented for the identification of multi degree of freedom systems from input output records the method is suitable for the analysis not only of systems with significant cross damping but also of highly coupled non linear systems the implementation of the technique is illustrated with two numerically simulated examples

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

accurate multiscale finite element methods for two phase flow simulations in this paper we propose a modified multiscale finite element method for two phase flow simulations in heterogeneous porous media the main idea of the method is to use the global fine scale solution at initial time to determine the boundary conditions of the basis functions this method provides a significant improvement in two phase flow simulations in porous media where the long range effects are important this is typical for some recent benchmark tests such as the spe comparative solution project m christie m blunt tenth spe comparative solution project a comparison of upscaling techniques spe reser eval eng 4 2001 308 317 where porous media have a channelized structure the use of global information allows us to capture the long range effects more accurately compared to the multiscale finite element methods that use only local information to construct the basis functions we present some analysis of the proposed method to illustrate that the method can indeed capture the long range effect in channelized media

an improved sequentially rejective bonferroni test procedure complexity these procedures can be used whenever the observed levels of significance are available for all individual tests it is shown that both the holm and shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics it is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available the methodology is illustrated with a numerical example

hybrid block amr in cartesian and curvilinear coordinates mhd applications abstract we present a novel hybrid block adaptive scheme for use in solving sets of near conservation laws in general orthogonal coordinate systems the adaptive mesh refinement amr scheme is block based i e individual grids have a pre fixed number of grid cells and is implemented for any dimensionality d its hybrid character relaxes the common approach where a block that needs refinement triggers 2 d subblocks when grids are refined by a factor of 2 this introduces incomplete families in the grid hierarchy but approaches the optimal fit to developing flow features inherent in the original patch based amr strategy our hybrid block amr approach is compared with a patch based amr one both exploiting openmp parallelism the implementation is able to handle general curvilinear coordinates for which restriction and prolongation formulae are presented along with boundary treatments at singular boundaries demonstrative examples cover hydro and magnetohydrodynamic mhd applications including tests on a 2d polar grid a 2 5d spherical and a 3d cylindrical configuration the applications cover classical up to relativistic mhd simulations of particular relevance for astrophysical magnetized jet and stellar wind studies

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

dynamic system change detection using a modification of the transfer entropy recent work has validated the use of transfer entropy for exploring coupling in structural dynamics transfer entropy is a measure of information flow between markov processes using transitional probabilities one can get a quantification of the degree of influence one process has on the dynamics of another previous research included a time lag to assess information exchanges at various time scales without resulting in tremendously burdensome computations however it is more informative to view the transfer entropy using two separate time lags to assess transitional probabilities between both processes this work introduces a second time delay into a linearized version of the transfer entropy to produce a transfer entropy surface this surface allows for a fuller assessment of dynamical coupling between measurements analytical and low order correlation based measures of the transfer entropy were formed and compared to common modal analysis methods to assess their ability to detect linear dynamical changes in structures investigations were conducted on a computational linear oscillator and a simple experimental system the transfer entropy is a much better indicator of dynamical changes than the modal techniques for the structural systems studied the plane of greatest sensitivity in the time delayed transfer entropy surface is along the diagonal and not along one coordinate as was utilized in previous work

output frequency response function of nonlinear volterra systems an expression for the output frequency response function ofrf which defines the explicit analytical relationship between the output spectrum and the system parameters is derived for nonlinear systems which can be described by a polynomial form differential equation model an effective algorithm is developed to determine the ofrf directly from system simulation or experimental data simulation studies demonstrate the significance of the ofrf concept and verify the effectiveness of the algorithm which evaluates the ofrf numerically these new results provide an important basis for the analytical study and design of a wide class of nonlinear systems in the frequency domain

identification of multi degree of freedom non linear systems under random excitations by the reverse path spectral method abstract conventional frequency response estimation methods such as the h 1 and h 2 methods often yield measured frequency response functions which are contaminated by the presence of non linearities and hence make it difficult to extract underlying linear system properties to overcome this deficiency a new spectral approach for identifying multi degree of freedom non linear systems is introduced which is based on a reverse path formulation as available in the literature for single degree of freedom non linear systems certain modifications are made in this article for a multi degree of freedom reverse path formulation that utilizes multiple input multiple output data from non linear systems when excited by gaussian random excitations conditioned h c 1 and h c 2 frequency response estimates now yield the underlying linear properties without contaminating effects from the non linearities once the conditioned frequency response functions have been estimated the non linearities which are described by analytical functions are also identified by estimating the coefficients of these functions identification of the local or distributed non linearities which exist at or away from the excitation locations is possible the new spectral approach is successfully tested on several example systems which include a three degree of freedom system with an asymmetric non linearity a three degree of freedom system with distributed non linearities and a five degree of freedom system with multiple non linearities and multiple excitations

a new derivation of the frequency response function matrix for vibrating non linear systems abstract frequency response function matrices relate the inputs and the outputs of structural dynamic systems if a system is linear the frequency response function matrix is the same for any combination or types of inputs over the entire operating range furthermore the frequency response matrix of a linear vibrating system is a simple combination of temporal and spatial characteristics the modal frequencies modal vectors and modal scale factors when a system is non linear the inputs interact through an exchange of energy between the linear and non linear elements in the system no general combination of the temporal and spatial non linear characteristics has to date been proposed to describe these linear non linear interactions this article introduces a unifying perspective of non linearities as internal feedback forces that act together with the external forces to generate the response of the non linear system this perspective of the non linearities is spatial in nature and leads to two simple but conceptually powerful relationships between the frequency response function matrix of a non linear multiple degree of freedom system and its linear counterpart several single and multiple degree of freedom systems are used to demonstrate the use and interpretation of these relationships the broad implication of the new input output frequency response representation for both linear and non linear systems are also addressed in particular the merits of the spatial perspective of non linear systems and the new frequency response relationships are stated in the context of linear and non linear system characterization and identification one implication is that these relationships suggest there is an input output dependent temporal spatial modal decomposition of the frequency response function matrix for non linear systems

a step up multiple test procedure abstract we consider the problem of simultaneously testing k 2 hypotheses on parameters 1 k in a typical application the s may be a set of contrasts for instance a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean it is assumed that least squares estimators 1 k are available that are jointly normally distributed with a common variance known up to a scalar namely the error variance 2 and a common known correlation an independent 2 distributed unbiased estimator of 2 is also assumed to be available we propose a step up multiple test procedure for this problem which tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs by contrast the step down approach which is usually used starts with the most significant and continues as long as a rejection occurs critical constants required by this step up procedure to co

coupling techniques for nonlinear hyperbolic equations iv well balanced schemes for scalar multi dimensional and multi component laws this series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations the coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations in an earlier work this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations in the present paper we significantly extend this framework and in addition encompass equations in several space variables this new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space our main contributions are on one hand the design and analysis of a well balanced finite volume method on general triangulations and on the other hand a proof of convergence of this method toward entropy solutions extending coquel cockburn and lefloch s theory restricted to a single conservation law without coupling the core of our analysis is first the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and second a proof of convergence toward the entropy solution of the coupling problem

feasibility of identifying non linear vibratory systems consisting of unknown polynomial forms abstract system identification techniques for non linear systems may require a priori knowledge of the nature and mathematical form of the non linearities however for practical systems this is not always possible as a result non linearities are often approximated and questions remain as to whether a reasonably accurate model can be determined concurrently under experimental conditions some means of quantifying the amount of measurement noise present in the identification process must also be obtained to resolve such issues a discrete non linear system problem is formulated in the presence of uncorrelated noise and critically examined from the standpoint of identification coherence functions are introduced which are based on a reverse path spectral approach recently developed by the authors for multi degree of freedom systems these coherence functions as calculated from conditioned spectra indicate the extent of uncorrelated noise present and the accuracy of assumed mathematical models employed for describing non linear systems using several example simulation systems including a system with a continuous non linearity described by a non integer exponent both temporal and spectral identification techniques are employed to study the issues described above

comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one and two dimensional hydrodynamic and magnetohydrodynamic problems two of the schemes ydfct and tvdlf are tested extensively for the first time the results give an insight into the limitations of the methods their relative strengths and weaknesses some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised

scalar hyperbolic pde simulations and coupling strategies we report on grid adaptive multi dimensional simulations for hyperbolic pdes with a deliberate focus on the analytically tractable scalar case motivated by recent efforts towards multi physics simulation strategies we investigate a variety of coupling strategies for numerically solving hyperbolic partial differential equations pdes we use adaptive mesh refinement in combination with shock capturing spatio temporal discretizations and first present accuracy and validation tests on both smooth and shock dominated evolutions to investigate the feasibility of coupling means for multi physics simulations we then introduce new reference tests where spatially different flux prescriptions require coupling strategies across the domains where local advection burgers or nonconvex behavior is imposed for these nonlinear single scalar equations we can illustrate and analytically explain the evolutions obtained when handling cases where fluxes differ in spatially non overlapping regions we discuss both conservative and non conservative ways of coupling across the region boundaries when coupling scalar conservation laws where the characteristic speeds change discontinuously across the regional boundaries these two strategies yield differing but mathematically sound solution behaviors their relevance for multi physics simulations where one couples systems of hyperbolic pdes is discussed

a multi level multi domain method for particle in cell plasma simulations a novel adaptive technique for electromagnetic particle in cell pic plasma simulations is presented here two main issues are identified as regards the development of the algorithm first the choice of the size of the particle shape function in progressively refined grids with the decision to avoid both time dependent shape functions and cumbersome particle to grid interpolation techniques and second the necessity to comply with the strict stability constraints of the explicit pic algorithm the adaptive implementation presented responds to these demands with the introduction of a multi level multi domain mlmd system where a cloud of self similar domains is fully simulated with both fields and particles and the use of an implicit moment pic method as baseline algorithm for the adaptive evolution information is exchanged between the levels with the projection of the field information from the refined to the coarser levels and the interpolation of the boundary conditions for the refined levels from the coarser level fields particles are bound to their level of origin and are prevented from transitioning to coarser levels but are repopulated at the refined grid boundaries with a splitting technique the presented algorithm is tested against a series of simulation challenges

a sequentially rejective test procedure based on a modified bonferroni inequality summary a sharper bonferroni procedure for multiple tests of significance is derived this procedure is an improvement of hochberg s 1988 procedure which contrasts the individual p values with corresponding critical points it is shown that hochberg s original procedure is conservative and can be made more powerful by enlarging the rejection region so that the type one error is exactly at the nominal level it is also shown that the modified procedure retains all the desired properties of the original procedure

frequency domain arx model and multi harmonic frf estimators for non linear dynamic systems abstract non linear dynamic systems respond at frequencies other than the excitation frequency however standard frequency response function estimators for linear systems do not accommodate this harmonic distortion a new multi harmonic frequency response function estimator that utilizes discrete frequency models for non linear systems is introduced here the multi harmonic estimator relates the frequency response at each frequency to the input and output spectra within a given frequency band in the same way that autoregressive exogenous input models relate inputs and outputs at particular samples in the time domain overdetermined least mean squares calculations are used to minimize model error throughout a frequency band rather than at a single frequency as in the corresponding linear estimators the resulting multi harmonic frequency response function models are non parametric e g vary with amplitude when linear functions are used and parametric when non linear functions are used a new sensitive indicator for experimentally characterizing non linearity is introduced

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples