measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

on the transient behaviour in discrete time model reference adaptive control analysis and possible improvement abstract this paper shows that a result recently obtained for arbitrarily improving the zero state transient performance of a continuous time model reference adaptive control scheme does not have a counterpart in discrete time using standard l 1 optimal control theory it is shown that unlike the continuous time case it is not possible to modify the control law to obtain arbitrarily small l gain for the closed loop transfer function from the parameter mismatch to the tracking error nevertheless the control law may be modified to minimize this gain perhaps resulting in improved error transients

projecting low dimensional chaos from spatiotemporal dynamics in a model for plastic instability we investigate the possibility of projecting low dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions we first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations we show that at low applied strain rates there is a one to one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops we then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive lyapunov exponents and lyapunov dimension scale with the system size at low and high strain rates using a modified algorithm for calculating correlation dimension density we show that the stress strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos this is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities which is known to be low dimensionally chaotic however the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands

multi scale asymptotic analysis and computation of the elliptic eigenvalue problems in curvilinear coordinates abstract a novel second order two scale asymptotic method is presented for the eigenvalue problems of the second order elliptic operator in the general composite domain the eigenvalue equation is firstly reformulated in curvilinear coordinates with periodic configuration using proper coordinate transformation and by applying the asymptotic expansion technique the eigenfunctions of the system are expanded to the second order terms using the argument of the so called corrector equations the eigenvalues are expressed in terms of the homogenized eigenfunctions and the cell functions are defined in the representative cell domain the feature of the proposed model is that some homogenized material coefficients and all the microscopic cell functions are dependent on the macroscopic coordinates various reduced expressions of the eigenfunctions and eigenvalues are discussed under specific coordinate transformations and the conditions that the cell functions and homogenized coefficients are decoupled from the macroscopic coordinates are elaborated the finite element algorithm is developed and three numerical experiments are carried out which demonstrate the effectiveness of our proposed method in simulating and predicting the vibration behavior of the composite structures it is also indicated that the second order correctors are of necessity to capture the locally oscillating behavior within a periodicity of the eigenfunctions by the coordinate transformation the asymptotic analysis method can be generalized to more general composite domain with quasi periodic and non periodic configurations

on morse s new adaptive controller parameter convergence and transient performance some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by a s morse proc us italy joint seminar syst models feedback 1992 it is proved that the l sub 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error further if the initial conditions are sufficiently small it is shown that the l sub infinity norm of the tracking error is uniformly bounded by the l sub m2 norm of the reference signal these transient bounds are independent of the signals richness and the adaptation gain making them arguably the strongest transient results available in the literature second excitation conditions for exponential stability a property which is well known to insure some local performance measures are given to this end it is shown that modulo a signal dependent time scale change morse s estimator is equivalent to a normalized gradient plus filtering identifier

multiscale asymptotic analysis and numerical simulation for the second order helmholtz equations with rapidly oscillating coefficients over general convex domains the multiscale asymptotic analysis and numerical simulation for the second order helmholtz equations with rapidly oscillating coefficients over general convex domains are discussed in this paper a multiscale asymptotic analysis formulation for this problem is presented by constructing properly the boundary layer a multiscale numerical algorithm and a postprocessing technique are given finally numerical results show that the method presented in this paper is effective and reliable

transient performance and robustness of direct adaptive control it is shown that a discrete adaptive controller with a fixed gain gradient estimator can be applied to linear systems that are undermodeled provided that the mismatch is small and the estimated parameters are projected into a compact convex set which contains stabilizing control parameters and excludes the possibility of dividing with small numbers the latter implies that the sign and a lower bound for the high frequency gain of the modeled part of the system are known the performance of the adaptive system is related to the size of the external perturbations and the ideal result as these tend to zero is obtained the main conclusion is that while convergence stability and robustness may be achieved the transient performance may not be acceptable and the gradient estimator should probably not be used unless modifications are added design guidelines are established the results extend readily to indirect adaptive laws like pole assignment linear quadratic optimal and predictive controllers

multi scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations abstract a new modal analysis method with second order two scale sots asymptotic expansion is presented for axisymmetric and spherical symmetric structures the symmetric structures considered are periodically distributed with homogeneous and isotropic constituent materials by the asymptotic expansion of the eigenfunctions the homogenized modal equations the effective materials coefficients the first and second order correctors are obtained the derived homogenized constitutive relationships are the same as the ones which serve to homogenize the corresponding static problems the eigenvalues are also expanded to the second order terms and using the so called corrector equation the correctors of the eigenvalues are expressed in terms of the first and second order correctors of the eigenfunctions the anisotropic materials are obtained by homogenization with different properties in the circumferential direction especially for the two dimensional axisymmetric layered structure the one dimensional plane axisymmetric and spherical symmetric structures the homogenized eigenfunctions and eigenvalues as well as their corresponding correctors are all solved analytically the finite element algorithm is established three typical numerical experiments are carried out and the necessity of the second order correctors is discussed based on the numerical results it is validated that the sots asymptotic expansion homogenization method is effective to identify the eigenvalues of the axisymmetric and spherical symmetric structures with periodic configurations and the original eigenfunctions with periodic oscillation can be reproduced by adding the correctors to the homogenized eigenfunctions

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the dirichlet problem for second order elliptic equations in perforated domains in this paper we study the spectral properties of dirichlet problems for second order elliptic equation with rapidly oscillating coefficients in a perforated domain the asymptotic expansions of eigenvalues and eigenfunctions for this kind of problem are obtained and the multiscale finite element algorithms and numerical results are proposed

hidden order in crackling noise during peeling of an adhesive tape we address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive lyapunov exponent in a midrange of traction velocities the results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick slip dynamics

characterization of spatiotemporal chaos from time series the analysis of time series generated by spatiotemporal chaotic systems is discussed we find that a grassberger procaccia algorithm with a suitable normalisation for the correction of systematic errors caused by the shape of the attractor is a reliable method for distinguishing between high dimensional chaos and noise we show that even a quantitative description of the attractor is possible by means of dimension densities the results obtained from the time series are in good agreement with values calculated directly from the generating equations of motion

dynamical approach to the spatiotemporal aspects of the portevin le chatelier effect chaos turbulence and band propagation the analysis of experimental time series obtained from single and polycrystals subjected to constant strain rate tests reports an intriguing dynamical crossover from a low dimensional chaotic state at medium strain rates to an infinite dimensional power law state of stress drops at high strain rates we present the results of an extensive study of all aspects of the portevin char21 le chatelier plc effect within the context of a recent model that reproduces this crossover we characterize the dynamics of this crossover by studying the distribution of the lyapunov exponents as a function of the strain rate with special attention to system size effects the distribution of the exponents changes from a small set of positive exponents in the chaotic regime to a dense set of null exponents in the scaling regime as the latter is similar to the result in a shell model for turbulence we compare the results of our model with that of the shell model interestingly the null exponents in our model themselves obey a power law the study is complimented by visualizing the configuration of dislocations through the slow manifold analysis this shows that while a large proportion of dislocations are in the pinned state in the chaotic regime most of them are pushed to the threshold of unpinning in the scaling regime thus providing insight into the mechanism of crossover we also show that this model qualitatively reproduces the different types of deformation bands seen in experiments at high strain rates where propagating bands are seen the model equations can be reduced to the fisher penalty1000 hskip0ptkolmogorov equation for propagative fronts which in turn shows that the velocity of the propagation of the bands varies linearly with the strain rate and inversely with the dislocation density these results are consistent with the known experimental results we also discuss the connection between the nature of band types and the dynamics in the respective regimes the analysis demonstrates that this simple dynamical model captures the complex spatiotemporal features of the plc effect

estimation of large scale dimension densities we propose a technique to calculate large scale dimension densities in both higher dimensional spatio temporal systems and low dimensional systems from only a few data points where known methods usually have an unsatisfactory scaling behavior this is mainly due to boundary and finite size effects with our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate this straightforward approach is based on rather general assumptions so even weak coherent structures obtained from small spatial couplings can be detected with this method which is impossible by using the lyapunov dimension density we demonstrate the efficiency of our technique for coupled logistic maps coupled tent maps the lorenz attractor and the roessler attractor

second order two scale asymptotic analysis for axisymmetric and spherical symmetric structure with periodic configurations abstract a new second order two scale sots analysis finite element algorithm is developed for the axisymmetric and spherical symmetric elastic problems with small periodic configurations the axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction and the spherical symmetric structure is only periodic in radial direction and homogeneous in other two directions the sots asymptotic expansions for the space problem plane axisymmetric problem and spherical symmetric problem are presented and the main feature is that the anisotropic material is obtained by the homogenization the analytical expressions of the cell functions and homogenized solutions for plane axisymmetric and spherical symmetric problems are obtained and the error estimations of the expansions are established the second order asymptotic analysis finite element algorithm is presented and the numerical examples are solved including the hollow cylinder rotating disk and hollow sphere composed of periodic composite materials the computational results demonstrate the effectiveness and accuracy of the sots asymptotic analysis algorithm and the converging behavior of the asymptotic analysis algorithm agrees well with the theoretical prediction it is also indicated that the stress distributions can be correctly computed only by adding the second order correctors

approximation of nonlinear problems associated with radiating bodies in space this paper presents an efficient and reliable method to approximate the solution of nonlinear boundary value problems describing the temperature distribution in a radiating body in space a variational formulation is constructed for an arbitrary radiation law in t p p geqq 1 an integer the minimizing element of an appropriate functional is shown to coincide with the solution of the initial problem the solution is approximated by the finite element method nonlinear programming techniques are discussed and a new fast and stable iterative method is presented

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

second order two scale finite element algorithm for dynamic thermo mechanical coupling problem in symmetric structure the new second order two scale sots finite element algorithm is developed for the dynamic thermo mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials the axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction the spherical symmetric structure is only periodic in radial direction the dynamic thermo mechanical coupling model is presented and the equivalent compact form is derived then the cell problems effective material coefficients and the homogenized thermo mechanical coupling problem are obtained successively by the second order asymptotic expansion of the temperature increment and displacement the homogenized material obtained is manifested with the anisotropic property in the circumferential direction the explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi static thermoelasticity problems are discussed based on the sots method the corresponding finite element procedure is presented and the unconditionally stable implicit algorithm is established some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration the computational results demonstrate that the second order asymptotic analysis finite element algorithm is feasible and effective in simulating and predicting the dynamic thermo mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures this may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo mechanical coupling response under strong aerothermodynamic environment second order two scale sots expansions for dynamic thermo mechanical coupling problems in symmetric structure are obtained sots finite element algorithm is proposed and unconditional stable implicit scheme is established anisotropic material is obtained by homogenization with enhanced strength and minor thermal expansion in circumferential direction the mutual interaction and simultaneous vibration of the temperature and displacement field are simulated a new computational tool is presented for analyzing thermo mechanical response of composites under strong aerothermodynamic environment

multi scale method for the quasi periodic structures of composite materials in this paper we shall present a new second order and two scale approximate solution of boundary value problems for the linear elasticity systems with quasi periodic structures by multi scale analysis the computation of strain and stress is presented here this idea can apply to the damage computation of composite materials because the computation of the local stress by this method having more precision it can provide some inspiration for construct optimal design finally numerical results show that the method presented in this paper is effective and reliable

crossover from chaotic to self organized critical dynamics in jerky flow of single crystals we report a crossover from chaotic to self organized critical dynamics in the portevin le chatelier effect in single crystals of cu 10 al in tension as a function of the applied strain rate for low and intermediate strain rates we provide an unambiguous support for the existence of chaotic stress drops by showing the existence of a finite correlation dimension and a stable positive lyapunov exponent a surrogate data analysis rules out the possibility that the time series is due to a power law stochastic process as the strain rate is increased the distributions of stress drops and the time intervals between the stress drops change from peaked to power law type with an exponent close to unity reminiscent of self organized critical state a scaling relation compatible with self organized criticality relates the various exponents the absence of a finite correlation dimension and a stable positive lyapunov exponent at the highest strain rate also supports the evidence of crossover s1063 651x 99 11011 0

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains in this paper we will discuss the mixed boundary value problems for the second order elliptic equation with rapidly oscillating coefficients in perforated domains and will present the higher order multiscale asymptotic expansion of the solution for the problem which will play an important role in the numerical computation the convergence theorems and their rigorous proofs will be given finally a multiscale finite element method and some numerical results will be presented