chaotic features in fractional iterative maps we investigate several properties of the fractional iterative map with two control parameters of and in the range of the fractional value 1 2 the relation between the control parameter at an infinite sequence of period doubling bifurcations and the fractional value is shown for fixed values of the value of is expected to be near four as decreases from 2 to 1 for 1 0 especially the numerical values of are found to show approximately linear decay with decreasing

nonlinear panel flutter by finite element method les equations non lineaires sont calculees a partir de considerations energetiques et la force d etirement non lineaire est formulee en termes de deplacement transversal seul

nonlinear model reduction of von karman plates under quasi steady fluid flow a reduced order model for von karman plates using a method of quadratic components is presented in this paper the method of quadratic components postulates the full kinematics of the plate as consisting of a combination of linear and quadratic components this reduced model is then discretized in space with a galerkin approximation and in time with an implicit integration scheme the plate is coupled with a fluid flowing over it at a supersonic speed using a quasi steady pressure model commonly referred to as piston theory a static loading example is used to validate the model reduction of the plate with respect to other numerical and approximate solutions the limit cycles of the plate coupled with piston theory are calculated via a cyclic method and the results from parameter studies are compared to classical results a previously unexplored regime of the limit cycle amplitudes is investigated a second coexisting limit cycle is found that yields a discontinuity in the limit cycle amplitudes at a critical dynamic pressure

switched multiple sequence excitation model for low bit rate speech compression an apparatus for compressing a speech signal into a compressed speech signal that is represented by a plurality of parameters a time varying digital filter is used to model the vocal tract a number of lpc coefficients specify the transfer function of the filter updated on frame basis an excitation signal is input to the filter analyzed on sub frame basis this excitation signal includes either an adaptive vector quantiser code or a first pulse sequence followed by a second pulse sequence selection logic is used to determine whether the adaptive vector quantiser code or the first pulse sequence better represents the speech signal based thereon a switch selects either the adaptive vector quantiser code or the first pulse sequence thus the parameters which are transmitted through a channel to a destination decoder include the lpc filter coefficients either the adaptive vector quantiser code or the first pulse sequence the second pulse sequence and one bit indicating the state of the switch

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

on the exploitation of chaos to build reduced order models the present study focuses on the model reduction of non linear systems the proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement these eigenmodes called the proper orthogonal modes are optimal with respect to energy content and are used to build a low dimensional model of the non linear system for this purpose the proper orthogonal modes obtained from a chaotic orbit are considered indeed such an orbit is assumed to cover a portion of the phase space of higher dimension and hence of greater measure this higher dimensional data is further assumed to contain more information about the system dynamics than data of a lower dimensional periodic orbit in an example it is shown that the modes for this particular behaviour are more representative of the system dynamics than any other set of modes extracted from a non chaotic response this is applied to a buckled beam with two permanent magnets and the reduced order model is validated using both qualitative and quantitative comparisons

shape from focus the shape from focus method presented here uses different focus levels to obtain a sequence of object images the sum modified laplacian sml operator is developed to provide local measures of the quality of image focus the operator is applied to the image sequence to determine a set of focus measures at each image point a depth estimation algorithm interpolates a small number of focus measure values to obtain accurate depth estimates a fully automated shape from focus system has been implemented using an optical microscope and tested on a variety of industrial samples experimental results are presented that demonstrate the accuracy and robustness of the proposed method these results suggest shape from focus to be an effective approach for a variety of challenging visual inspection tasks

using aeroelastic modes for nonlinear panel flutter at arbitrary supersonic yawed angle it is commonly accepted that six in vacuo natural modes are needed for converged limit cycle oscillations of isotropic rectangular plates exposed to supersonic flow at zero yaw angle to the principle panel length for isotropic or orthotropic rectangular plates under an arbitrary nonzero yawed supersonic flow then 36 or 6 x 6 natural modes are needed for laminated anisotropic rectangular plates even at zero yaw angle 36 or fewer natural modes are needed to deal with such a large number of modes is computationally costly for flutter analysis causing complexity and difficulty in designing controllers for flutter suppression a thorough examination and understanding of the panel limit cycle behavior leads to the use of aeroelastic modes for supersonic nonlinear panel flutter analysis the system equations of motion are formulated first in structural node degrees of freedom aeroelastic modes are selected and determined and the system equations is expressed in the aeroelastic modal coordinates limit cycle amplitudes are then determined using numerical integration examples show that the number of modes could be greatly reduced by using aeroelastic modes for determining limit cycle oscillations of isotropic or anisotropic composite rectangular plates at zero or an arbitrary yawed flow angle only two aeroelastic modes are needed but six to seven aeroelastic modes are needed for designing controllers for flutter suppression

proper orthogonal decomposition pod of a class of vibroimpact oscillations abstract this study employs the method of proper orthogonal decomposition pod also known as the karhunen loeve k l method to extract dominant coherent structures modes that approximate the system behavior from time series data these mode shapes can be used in a galerkin reconstruction process to obtain lower dimensional models for the structural systems under consideration the mode shapes and the energies obtained by this process can also be used to predict certain kinds of periodic or non periodic non linear motions the k l method has been applied successfully to fluid dynamical thermal processes and signal processing however only a handful of works exist in the area of vibration analysis and structural mechanics an extensive k l analysis is performed numerically for two vibroimpacting systems a beam and a rotor lower dimensional models are created and used to study non linear energy transmission from low to higher k l modes extensive reconstructions are also performed to prove the efficacy of the k l method to provide accurate low dimensional dynamical models in addition experimental investigations are presented for the case of the overhung impacting rotor and qualitative comparisons with the theoretical analysis are presented

an adaptive proper orthogonal decomposition method for model order reduction of multi disc rotor system abstract the proper orthogonal decomposition pod method is a main and efficient tool for order reduction of high dimensional complex systems in many research fields however the robustness problem of this method is always unsolved although there are some modified pod methods which were proposed to solve this problem in this paper a new adaptive pod method called the interpolation grassmann manifold igm method is proposed to address the weakness of local property of the interpolation tangent space of grassmann manifold itgm method in a wider parametric region this method is demonstrated here by a nonlinear rotor system of 33 degrees of freedom dofs with a pair of liquid film bearings and a pedestal looseness fault the motion region of the rotor system is divided into two parts simple motion region and complex motion region the adaptive pod method is compared with the itgm method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the itgm method the comparisons of the responses are applied to verify the accuracy and robustness of the adaptive pod method as well as the computational efficiency is also analyzed as a result the new adaptive pod method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter

nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow abstract the high imperfection sensitivity of cylindrical shells under static compressive axial loads is a well known phenomenon in structural stability on the other hand less is known of the influence of imperfections on the nonlinear vibrations of these shells under harmonic axial loads the aim of this work is to study the simultaneous influence of geometric imperfections and an axial fluid flow on the nonlinear vibrations and instabilities of simply supported circular cylindrical shells under axial load the fluid is assumed to be non viscous and incompressible and the flow to be isentropic and irrotational the behavior of the thin walled shell is modeled by donnell s nonlinear shallow shell equations it is subjected to a static uniform compressive axial pre load plus a harmonic axial load a low dimensional modal expansion which satisfies the relevant boundary and continuity conditions and takes into account all relevant nonlinear modal interactions observed in the past in the nonlinear vibrations of cylindrical shells with and without flow is used together with the galerkin method to derive a set of eight coupled nonlinear ordinary differential equations of motion which are in turn solved by the runge kutta method the shell is considered to be initially at rest in a position corresponding to a pre buckling configuration then a harmonic excitation is applied and conditions for parametric instability and dynamic snap through are sought the results clarify the marked influence of geometric imperfections and fluid flow on the dynamic stability boundaries bifurcations and basins of attraction

proper orthogonal decomposition method for analysis of nonlinear panel flutter with thermal effects in supersonic flow abstract the proper orthogonal decomposition pod method for analysis of nonlinear panel flutter subjected to supersonic flow is presented optimal pod modes are extracted from a chaotic galerkin mode responses the aeroelastic equations of motion are constructed using von karman plate theory first order piston theory and quasi steady thermal stress theory a simply supported plate with thermal loads from a uniformly distributed temperature is considered many types of panel behaviors including stable flat dynamically stable buckled limit cycle oscillation nonharmonic periodic motion quasi periodic motion and chaotic motion are observed our primary focus is on chaos and the route to chaos it is found that a sudden transition from the buckled state to chaos occurs time history phase portrait poincare map bifurcation diagram and lyapunov exponent are employed to study chaos the pod chaotic results obtained are compared with the traditional galerkin solutions it is shown that the pod method can obtain accurate chaotic solutions using fewer modes and less computational effort than the galerkin mode approach additionally the pod method converges faster in the analysis of chaotic transients effects of length to width ratios and thermal loads are presented it is found that a smaller width for fixed length will produce more stable flutter response while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions the numerical simulations show that the robustness of the pod modes depends on the dynamic pressure but not on temperature

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

methods for dimension reduction and their application in nonlinear dynamics abstract we compare linear and nonlinear galerkin methods in their efficiency to reduce infinite dimensional systems described by partial differential equations to low dimensional systems of ordinary differential equations both concerning the effort in their application and the accuracy of the resulting reduced system important questions like the choice of the form of the ansatz functions modes the choice of the number m of modes and finally the construction of the reduced system are addressed for the latter point both the linear or standard galerkin method making use of the karhunen loeve proper orthogonal decomposition ansatz functions and the nonlinear galerkin method using approximate inertial manifold theory are used in addition also the post processing galerkin method is compared with the other approaches

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

linearity inside nonlinearity exact solutions to the complex ginzburg landau equation abstract systems of two linear partial differential equations pdes with constant coefficients define a natural basis of elementary functions to build some exact solutions to nonlinear pdes for the one dimensional complex ginzburg landau equation the usual representations of the complex field re a or a are multivalued which makes difficult the search for exact solutions in this manner fortunately the painleve analysis naturally introduces an elementary single valued like representation of a by two fields z grad respectively complex abd real uniquely defined by an explicit expression for and a ze i another important feature is the invariance by parity on a which increases the class of expected solutions this allows to retrieve quite easily the four famous solutions of nozaki and bekki represented by the constant coefficients of two linear partial differential equations and a finite set of constants

fluctuation of mean lyapunov exponent for turbulence abstract lyapunov exponent for the systems described by the complex ginzburg landau equation is studied through its statistics the probability distribution function for the finite time average lyapunov exponent is given its functional form is the same as the systems described by the kuramoto sivashinsky equation that expresses the weak turbulence it is predicted that many kinds of turbulence have the same characteristics concerning their statistics of lyapunov exponent

quantitative characterization of spatiotemporal chaos abstract in this paper one way to characterize spatiotemporal chaos is shown a coupled map lattice is used as a model for the spatiotemporal chaos the local expansion rate is defined for the coupled map lattice in the extension of the low dimensional temporal chaos it is shown that the local expansion rate is closely related to the spatiotemporal pattern of the spatiotemporal chaos the thermodynamic formalism is applied to the local expansion rate the thermodynamic functions describing fluctuations of the local expansion rate are shown the spatiotemporal pattern that fluctuates is shown at the same time it is shown clearly that the thermodynamic functions characterize the spatiotemporal chaos

the use of the karhunen loegve procedure for the calculation of linear eigenfunctions abstract it is shown that the karhunen loeve decomposition may be used to determine the eigenfunctions of a general class of linear operators from an ensemble of realizations that are derived from that system given a moderate size data set either numerical or experimental from a linear system good approximations to the eigenfunctions that characterize the underlying equations can be computed by performing the karhunen loeve procedure two numerical examples are presented the vibration of a thin membrane in a rectangular domain and in a stadium these are used to determine the convergence and accuracy of the method it is found that this method yields accurate results for the first few eigenfunctions with relatively few realizations eigenfunctions with less energy are accurately resolved as the size of the ensemble increase the method is shown to be an efficient and practical procedure for determining the eigenfunctions of systems in complex geometries and in cases where the governing equations are not known a priori the effect of random noise contamination of the data set is also investigated and it is found that the karhunen loeve procedure can still achieve accurate results despite the presence of substantial background noise

nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow abstract in the present study the geometrically nonlinear vibrations of circular cylindrical shells subjected to internal fluid flow and to a radial harmonic excitation in the spectral neighbourhood of one of the lowest frequency modes are investigated for different flow velocities the shell is modelled by donnell s nonlinear shell theory retaining in plane inertia and geometric imperfections the fluid is modelled as a potential flow with the addition of unsteady viscous terms obtained by using the time averaged navier stokes equations a harmonic concentrated force is applied at mid length of the shell acting in the radial direction the shell is considered to be immersed in an external confined quiescent liquid and to contain a fluid flow in order to reproduce conditions in previous water tunnel experiments for the same reason complex boundary conditions are applied at the shell ends simulating conditions intermediate between clamped and simply supported ends numerical results obtained by using pseudo arclength continuation methods and bifurcation analysis show the nonlinear response at different flow velocities for i a fixed excitation amplitude and variable excitation frequency and ii fixed excitation frequency by varying the excitation amplitude bifurcation diagrams of poincare maps obtained from direct time integration are presented as well as the maximum lyapunov exponent in order to classify the system dynamics in particular periodic quasi periodic sub harmonic and chaotic responses have been detected the full spectrum of the lyapunov exponents and the lyapunov dimension have been calculated for the chaotic response they reveal the occurrence of large dimension hyperchaos

optimal model reduction by empirical spectral methods via sampling of chaotic orbits abstract proper orthogonal decomposition pod coupled with the galerkin method is applied to the one dimensional model of a tubular reactor with external heat recycle which exhibits periodic and chaotic solutions the effect of the cooling medium temperature on the system dynamics is considered the issue of the optimal construction of the pod basis is addressed by sampling of the chaotic orbits with the aim of constructing a global basis for a reduced order model rom to demonstrate that such orbits are the most appropriate because they incorporate the maximum amount of information about the system behavior the entropy of the orbit is calculated sampling of the chaotic solutions allows for the determination of the pod basis to be employed in the pod galerkin method the accuracy of the roms is compared by means of the hausdorff distance computed between the asymptotic regime of the reference solution and each of the rom reconstructed asymptotic attractors a norm computed on the sampled time series is employed to compare transient solutions the pod based roms work well even for values of the parameter for which the model behavior is far from chaotic i e periodic orbits or fixed points moreover the pod based roms successfully compare with a classic orthogonal collocation method

galerkin free model reduction for fluid structure interaction using proper orthogonal decomposition abstract a galerkin free model reduction approach for fluid structure interaction fsi is presented in this article the reduced order model rom is based on proper orthogonal decomposition pod where a reduced basis is formed using energy dominant pod modes the reduced basis also consists of characteristics pod time modes that are derived from the pod time modes coefficients by using their periodicity in addition to flow variables the solution state vector comprises the mesh deformation taking into account the structural deformation in fsi a rom solution is obtained by performing a linear interpolation of the reduced basis for changing operating control parameters the proposed galerkin free pod rom approach is demonstrated in terms of two test cases a canonical case study of vortex induced vibration viv of a cylinder at reynolds number r e 100 where simulations are performed for various structural to fluid mass ratios and a shock wave boundary layer induced panel flutter for the second case we use previously computed high fidelity simulations considering only the effect of panel thickness on the aeroelastic coupling between the flexible panel and shock wave boundary layer interaction swbli the inflow is at mach 2 and reynolds number based on panel length r e a 50000 the presented galerking free rom procedure is clean and robust for large mesh deformations in addition to a significantly lower cost of computation compared to the fsi high fidelity simulations

nonlinear panel flutter using high order triangular finite elements a 54 degree of freedom high order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems the finite element formulation is based on kirchhoffs theory of thin plates the quasisteady aerodynamic theory is used numerical solution procedures are presented the limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped respectively the effects of in plane compressive force mass ratio and in plane edge stress free condition are considered stress distributions for the limit cycle oscillation of a two dimensional panel are plotted for the case of panels under static pressure differential the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels respectively the effect of biaxial in plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region dynamically stable buckled region and the limit cycle oscillation region are found alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part i stability abstract the study presented is an investigation of the non linear dynamics and stability of simply supported circular cylindrical shells containing inviscid incompressible fluid flow non linearities due to large amplitude shell motion are considered by using the non linear donnell s shallow shell theory with account taken of the effect of viscous structural damping linear potential flow theory is applied to describe the fluid structure interaction the system is discretiszd by galerkin s method and is investigated by using a model involving seven degrees of freedom allowing for travelling wave response of the shell and shell axisymmetric contraction two different boundary conditions are applied to the fluid flow beyond the shell corresponding to i infinite baffles rigid extensions of the shell and ii connection with a flexible wall of infinite extent in the longitudinal direction permitting solution by separation of variables they give two different kinds of dynamical behaviour of the system as a consequence of the fact that axisymmetric contraction responsible for the softening non linear dynamical behaviour of shells is not allowed if the fluid flow beyond the shell is constrained by rigid baffles results show that the system loses stability by divergence

computationally efficient model for flow induced instability of cnt reinforced functionally graded truncated conical curved panels subjected to axial compression abstract as a first endeavor the aeroelastic responses of functionally graded carbon nanotube reinforced composite fg cntrc truncated conical curved panels subjected to aerodynamic load and axial compression are investigated the nonlinear dynamic equations of fg cntrc conical curved panels are derived according to green s strains and the novozhilov nonlinear shell theory the aerodynamic load is estimated in accordance with the quasi steady krumhaar s modified supersonic piston theory by taking into account the effect of the panel curvature matrix transform method along with the harmonic differential quadrature method hdqm are employed to solve the nonlinear equations of motion of the fg cntrc truncated conical curved panel the advantage of the matrix transform method is that we only need to discretize the meridional direction effects of semi vertex angle of the cone subtended angle of the panel boundary conditions geometrical parameters volume fraction and distribution of cnt and mach number on the aeroelastic characteristics of the fg cntrc conical curved panel are put into evidence via a set of parametric studies and pertinent conclusions are outlined the results prove that the panels with different fg distributions have different critical dynamic pressure it is found that the semi vertex and subtended angles play a pivotal role in changing the critical circumferential mode number of the flutter instability besides the research shows that the superb efficiency of proposed method with few grid points which requires less cpu time are attributed to the matrix transform method and the higher order harmonic approximation function in the hdqm

stacking sequence design of flat composite panel for flutter and thermal buckling in this paper we formulate the stacking sequence design of laminated composite flat panels for maximum supersonic flutter speed and maximum thermal buckling capacity the design is constrained to have stable limit cycle oscillation in the vicinity of the flutter boundary for the purpose of comparison we consider both linear and nonlinear panel flutter analyses because of manufacturing constraints the stacking sequence of the laminate is selected from a discrete set of orientation angles the plate is modeled using von karman plate equations and assumed to be subjected to uniform temperature differential the aerodynamic load on the plate is computed using third order piston theory the plate equations of motion are derived using hamilton s principle and discretized using the rayleigh ritz method the nonlinear panel flutter analysis is performed using an approximate perturbation approach the pareto fronts describing the trade off between thermal buckling and flutter are generated for different panel aspect ratios it is observed that optimal designs obtained for both linear and nonlinear flutter analyses are similar with only the predicted flutter speeds different this suggests that for the purpose of preliminary stacking sequence design linear flutter analysis is sufficient

the effect of temperature on the large amplitude vibrations of curved beams the thermoelastic geometrically nonlinear vibrations of isotropic straight and curved beams are studied using p version hierarchical finite elements first order shear deformation theory is followed and both the longitudinal displacements and inertia are taken into account the nonlinear equations of motion are solved in the time domain by newmark s method the influence of parameters like the temperature variation the thickness and the ratio of curvature on the beams nonlinear dynamics is studied periodic and non periodic motions are found

system identification guided basis selection for reduced order nonlinear response analysis reduced order nonlinear simulation is often times the only computationally efficient means of calculating the extended time response of large and complex structures under severe dynamic loading this is because the structure may respond in a geometrically nonlinear manner making the computational expense of direct numerical integration in physical degrees of freedom prohibitive as for any type of modal reduction scheme the quality of the reduced order solution is dictated by the modal basis selection the techniques for modal basis selection currently employed for nonlinear simulation are ad hoc and are strongly influenced by the analyst s subjective judgment this work develops a reliable and rigorous procedure through which an efficient modal basis can be chosen the method employs proper orthogonal decomposition to identify nonlinear system dynamics and the modal assurance criterion to relate proper orthogonal modes to the normal modes that are eventually used as the basis functions the method is successfully applied to the analysis of a planar beam and a shallow arch over a wide range of nonlinear dynamic response regimes the error associated with the reduced order simulation is quantified and related to the computational cost

variational learning for switching state space models we introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes this model combines and generalizes two of the most widely used stochastic time series models hidden markov models and linear dynamical systems and is closely related to models that are widely used in the control and econometrics literatures it can also be derived by extending the mixture of experts neural network jacobs jordan nowlan hinton 1991 to its fully dynamical version in which both expert and gating networks are recurrent inferring the posterior probabilities of the hidden states of this model is computationally intractable and therefore the exact expectation maximization em algorithm cannot be applied however we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward and backward recursions for hidden markov models and the kalman filter recursions for linear dynamical systems we tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea the results suggest that variational approximations are a viable method for inference and learning in switching state space models

dynamics of phase singularities in two dimensional oscillating systems abstract we study the dynamics of vortices that arise in two dimensional nonequilibrium systems above a hopf bifurcation to uniform temporal oscillations evolution equations for the vortex positions and for a global phase field are derived and used to study vortex interactions we suggest that the interactions need not be purely attractive or repulsive bound vortex pairs can exist which either precess around fixed points in the plane or drift in directions perpendicular to the inter vortex axes

quantitative characterization of spatiotemporal chaos ii dynamic aspects and anomalous scaling abstract spatiotemporal chaos is characterized quantitatively the characterization of a special model for coupled map lattices has been carried out successfully yet the dynamic aspects of this model are discussed in the present paper anomalous scaling of the probability distribution function for the local lyapunov exponent is shown the characteristics of one model for spatiotemporal chaos are given statistically

characterization of a system described by kuramoto sivashinsky equation with lyapunov exponent abstract the characteristics of a system described by kuramoto sivashinsky equation are obtained through the statistics of a mean lyapunov exponent this mean lyapunov exponent takes large values and fluctuates large when the system is disordered temporally and spatially this behavior of the spatially extended system is captured clearly by the probability distribution function for the time averaged one of the mean lyapunov exponent

an investigation of methods for determining depth from focus the concept of depth from focus involves calculating distances to points in an observed scene by modeling the effect that the camera s focal parameters have on images acquired with a small depth of field this technique is passive and requires only a single camera the most difficult segment of calculating depth from focus is deconvolving the defocus operator from the scene and modeling it most current methods for determining the defocus operator employ inverse filtering the authors reveal some fundamental problems with inverse filtering inaccuracies in finding the frequency domain representation windowing effects and border effects a general matrix based method using regularization is presented which eliminates these problems the new method is confirmed experimentally with the results showing an rms error of 1 3

analysis of photometric properties of occluding edges by the reversed projection blurring model this paper analyzes photometric properties of occluding edges and proves that an object surface behind a nearer object is partially observable beyond the occluding edges we first discuss a limitation of the image blurring model using the convolution and then present an optical flux based blurring model named the reversed projection blurring rpb model unlike the multicomponent blurring model proposed by nguyen et al the rpb model enables us to explore the optical phenomena caused by a shift variant point spread function that appears at a depth discontinuity using the rpb model theoretical analysis of occluding edge properties are given and two characteristic phenomena are shown 1 a blurred occluding edge produces the same brightness profiles as would be predicted for a surface edge on the occluding object when the occluded surface radiance is uniform and 2 a nonmonotonic brightness transition would be observed in blurred occluding edge profiles when the occluded object has a surface edge experimental results using real images have demonstrated the validity of the rpb model as well as the observability of the characteristic phenomena of blurred occluding edges

independent component analysis to enhance performances of karhunen loeve expansions for non gaussian stochastic processes application to uncertain systems abstract in the context of engineering systems an essential step in uncertainty quantification is the development of accurate and efficient representation of the random input parameters for such input parameters modeled as stochastic processes karhunen loeve expansion is a classical approach providing efficient representations using a set of uncorrelated but generally statistically dependent random variables the dependence structure among these random variables may be difficult to estimate statistically and is thus ignored in many practical applications this simplifying assumption of independence may lead to considerable errors in estimating the variability in the system state thus limiting the effectiveness of karhunen loeve expansion in certain cases in this paper independent component analysis is exploited to linearly transform the random variables used in karhunen loeve expansion resulting into a set of random variables exhibiting higher order decorrelation the stochastic wave equation is investigated for numerical illustration whereby the random stiffness coefficient is modeled as a non gaussian stochastic process under the assumption of independence among the random variables used in the karhunen loeve expansion and independent component analysis representations the latter provides more accurate statistical characterization of the output process for the specific cases examined

chaotic vibrations of circular cylindrical shells galerkin versus reduced order models via the proper orthogonal decomposition method abstract the geometric nonlinear response of a water filled simply supported circular cylindrical shell to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency is investigated the response is investigated for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation bifurcation diagrams of poincare maps obtained from direct time integration and calculation of the lyapunov exponents and lyapunov dimension have been used to study the system by increasing the excitation amplitude the response undergoes i a period doubling bifurcation ii subharmonic response iii quasi periodic response and iv chaotic behaviour with up to 16 positive lyapunov exponents hyperchaos the model is based on donnell s nonlinear shallow shell theory and the reference solution is obtained by the galerkin method the proper orthogonal decomposition pod method is used to extract proper orthogonal modes that describe the system behaviour from time series response data these time series have been obtained via the conventional galerkin approach using normal modes as a projection basis with an accurate model involving 16 degrees of freedom dofs validated in previous studies the pod method in conjunction with the galerkin approach permits to build a lower dimensional model as compared to those obtainable via the conventional galerkin approach periodic and quasi periodic response around the fundamental resonance for fixed excitation amplitude can be very successfully simulated with a 3 dof reduced order model however in the case of large variation of the excitation even a 5 dof reduced order model is not fully accurate results show that the pod methodology is not as robust as the galerkin method

comparison between the modal identification method and the pod galerkin method for model reduction in nonlinear diffusive systems this paper presents a comparison between the modal identification method mim and the proper orthogonal decomposition galerkin pod g method for model reduction an example of application on a nonlinear diffusive system is used to illustrate the study the study shows that in both methods the state formulation of the nonlinear diffusive equation may be similar however the ideas behind both methods are completely different the considered example shows that for both methods reducing the order up to 99 5 gives enough accuracy to simulate the dynamic of the original system it is also seen in this example that the reduced model given through the mim are slightly faster and more accurate than the ones given through the pod g method copyright 2006 john wiley sons ltd

fluctuation of mean lyapunov exponent for a coupled map lattice model abstract fluctuation of mean lyapunov exponent for the coupled map lattice of logistic map is studied theorem by gallavotti and cohen for many particle systems is applied to the coupled map lattice model it is shown that the fluctuation of mean lyapunov exponent for the model satisfies the extended form of the fluctuation theorem by them the concept of the mean lyapunov exponent introduced in this paper turns out to be realistic as well as the one for many particle systems as a result the relation between mean lyapunov exponent and entropy production rate is derived

low dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition in formulating mathematical models for dynamical systems obtaining a high degree of qualitative correctness i e predictive capability may not be the only objective the model must be useful for its intended application and models of reduced complexity are attractive in many cases where time consuming numerical procedures are required this paper discusses the derivation of discrete low dimensional models for the nonlinear vibration analysis of thin cylindrical shells in order to understand the peculiarities inherent to this class of structural problems the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed this choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads geometric nonlinearities due to finite amplitude shell motions are considered by using donnell s nonlinear shallow shell theory a perturbation procedure validated in previous studies is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the galerkin method using modal expansions for the displacements that

single image refocusing and defocusing in this paper we present a postprocessing method to tackle the single image refocusing and defocusing problem the proposed method can accomplish the tasks of focus map estimation and image refocusing and defocusing given an image with a mixture of focused and defocused objects we first detect the edges and then estimate the focus map based on the edge blurriness which is depicted explicitly by a parametric model the image refocusing problem is addressed in a blind deconvolution framework where the image prior is modeled by using both global and local constraints in particular we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a local prior to ensure the sharpness of the refocused image experimental results demonstrate that the proposed method performs well in producing visually plausible images with different focus effects from a single input

a horizontal fluid conveying cantilever spatial coherent structures beam modes and jumps in stability diagram the proper orthogonal decomposition method is used to obtain a low dimensional model for the planar non linear dynamics of a horizontal fluid conveying cantilever undergoing a limit cycle oscillation the finite dimensional approximation of the non linear partial differential equation pde describing the oscillation is carried out by a galerkin projection scheme using both the cantilever beam modes and proper orthogonal modes coherent structures as projection bases which leads to a finite set of coupled ordinary differential equations the proper orthogonal modes are obtained semi analytically using the cantilever beam modes as a basis a systematic study is then carried out focusing on the jumps in the linear stability diagram of a horizontal fluid conveying cantilever vis a vis the order of the finite dimensional model obtained using either the beam modes or the proper orthogonal modes depending on the mass ratio of the cantilever while the order of the finite dimensional model using the beam mode basis increases steadily up to 10 the corresponding order when the proper orthogonal modes are used to span the solution of the pde remains unaltered only two

chaotifing a linear hyperbolic system of partial differential equations by means of nonlinear boundary reflection abstract we introduced a hyperbolic linear system of partial differential equations with nonlinear boundary conditions and proved strictly that it is chaotic under some simple assumptions this can be understood as chaotifing a hyperbolic linear system of partial differential equations with nonlinear boundary conditions several examples of simulation are presented the numerical simulation fits the theoretical analysis well

theory and experiments for large amplitude vibrations of empty and fluid filled circular cylindrical shells with imperfections abstract the large amplitude response of perfect and imperfect simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated donnell s non linear shallow shell theory is used and the solution is obtained by the galerkin method several expansions involving 16 or more natural modes of the shell are used the boundary conditions on the radial displacement and the continuity of circumferential displacement are exactly satisfied the effect of internal quiescent incompressible and inviscid fluid is investigated the non linear equations of motion are studied by using a code based on the arclength continuation method a series of accurate experiments on forced vibrations of an empty and water filled stainless steel shell have been performed several modes have been intensively investigated for different vibration amplitudes a closed loop control of the force excitation has been used the actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model several interesting non linear phenomena have been experimentally observed and numerically reproduced such as softening type non linearity different types of travelling wave response in the proximity of resonances interaction among modes with different numbers of circumferential waves and amplitude modulated response for all the modes investigated the theoretical and experimental results are in strong agreement

real time modelling of diastolic filling of the heart using the proper orthogonal decomposition with interpolation abstract in this research a reduced order method rom called the proper orthogonal decomposition with interpolation podi is used to drastically reduce computation time of highly complex and non linear problems as encountered in simulating the heart the idea behind this method is to first construct a database of pre computed full scale solutions using the element free galerkin method efg and then project a selected subset of these solutions to a low dimensional space using the moving least square method an interpolation is carried out for the problem at hand before the resulting coefficients are projected back to the original high dimensional solution space computations are carried out on a bi ventricle model to investigate the performance and accuracy varying the material parameters and to determine the sensitivity with respect to the parametric values the podi calculations are completed within 1 25 s on a normal desktop machine with the relative l2 error norm not exceeding 2 5 10 3 hence it is demonstrated that real time modelling of the heart can be successfully carried out at acceptable error levels

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

nonlinear flutter of composite panels under yawed supersonic flow using finite elements a finite element formulation is presented for the effects of arbitrary flow direction on the large amplitude supersonic flutter of composite panels the von karman large deflection plate theory is used to account for large amplitude limit cyde oscillations quasisteady first order piston theory aerodynamics is employed for aerodynamic loading and first order shear deformation theory is used for laminated composite panels an efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations a modal participation is defined and the minimum number of linear modes for accurate and converged limit cycle response can be ensured examples are given for isotropic and composite panels at yawed supersonic flow

proper orthogonal decomposition and its applications part ii model reduction for mems dynamical analysis abstract proper orthogonal decomposition pod methods are popular tools for data analysis aimed at obtaining low dimensional approximate descriptions of a high dimensional process in many engineering fields the applications of pod methods to model reduction for microelectromechanical systems mems are reviewed in this paper in view of the fact that existing pod methods in the model reduction for dynamic simulation of mems dealt with only noise free data this paper proposes a neural network based method that combines robust principal component analysis pca neural network model with galerkin procedure for dynamic simulation and analysis of non linear mems with noisy data simulations are given to show the performance of the proposed method in comparison with the existing method compared with the standard pca neural network model the robust pca neural network model has a number of numerical advantages such as the stability and robustness to noise injected data and the faster convergence of iterations in the training stages than the existing neural network technique the macro model generated by using the eigenvectors extracted from the proposed method as basis functions shows its flexibility and efficiency in the representation and simulation of the original non linear partial differential equations

nonlinear model reduction via a locally weighted pod method summary in this article we propose a new approach for model reduction of parameterized partial differential equations pdes by a locally weighted proper orthogonal decomposition lwpod method the presented approach is particularly suited for large scale nonlinear systems characterized by parameter variations instead of using a global basis to construct a global reduced model lwpod approximates the original system by multiple local reduced bases each local reduced basis is generated by the singular value decomposition of a weighted snapshot matrix compared with global model reduction methods such as the classical proper orthogonal decomposition lwpod can yield more accurate solutions with a fixed subspace dimension as another contribution we combine lwpod with the chord iteration to solve elliptic pdes in a computationally efficient fashion the potential of the method for achieving large speedups while maintaining good accuracy is demonstrated for both elliptic and parabolic pdes in a few numerical examples copyright 2016 john wiley sons ltd

supersonic flutter analysis of stiffened laminated plates subject to thermal load abstract flutter analysis of stiffened laminated plates has been performed the purpose of this study is to analyze the flutter characteristics of stiffened plates subject to thermal load the first order shear deformable plate and timoshenko beam theories are used for the finite element modelling of a skin panel and stiffeners respectively the von karman non linear strain displacement relation is used to account for large deflections first order piston theory is used for modelling aerodynamic loads the newton raphson iteration method and complex eigenvalue solver with the lum ntf approximation method are used to obtain the postbuckled deflection and flutter information respectively the guyan reduction method and mode tracing procedure are employed for an efficient analysis the effects of various parameters such as the stiffening scheme lamination angle boundary conditions and temperature gradient on flutter characteristics are investigated through some numerical examples from these examples it can be shown that the selection of a proper stiffening scheme results in great improvements of flutter characteristics of laminated panels without introducing considerable weight penalty

statistics of phase turbulence ii abstract the system described by the kuramoto sivashinsky equation skse is shown to have a short and a long time regimes the probability distribution function pdf for the absolute value of the solution is subjected to different scaling laws in the two time regimes the local expansion rate ler and its two time correlation function are calculated the time regime where the correlation for the ler remains is shorter than the one for the absolute value of the solution for the skse the fluctuation in the ler becomes small as the damping constant is increased the pdf for the ler is also given in this paper

hybrid proper orthogonal decomposition formulation for linear structural dynamics abstract hybrid proper orthogonal decomposition podh formulation is a pod based reduced order modeling method where the continuous equation of the physical system is projected on the pod modes obtained from a discrete model of the system the aim of this paper is to evaluate the hybrid pod formulation and to compare it with other pod formulations on the simple case of a linear elastic rod subject to prescribed displacements in the perspective of building reduced order models for coupled fluid structure systems in the future in the first part of the paper the hybrid pod is compared to two other formulations for the response to an initial condition an approach based on the discrete finite elements equation of the rod called the discrete pod podd and an analytical approach using the exact solution of the problem and consequently called the analytical pod poda this first step is useful to ensure that the podh performs well with respect to the other formulations the podh is therefore used afterwards for the forced motion response where a displacement is imposed at the free end of the rod the main contribution of this paper lies in the comparison of three techniques used to take into account the non homogeneous dirichlet boundary condition with the hybrid pod the first method relies on control functions the second on the penalty method and the third on lagrange multipliers finally the robustness of the hybrid pod is investigated on two examples involving firstly the introduction of structural damping and secondly a nonlinear force applied at the free end of the rod

finite element modal formulation for hypersonic panel flutter analysis with thermal effects a finite element time domain modal formulation for analyzing nonlinear flutter of panels subjected to hypersonic airflow has been developed von karman large deflection plate theory is used for description of the structural nonlinearity and third order piston theory is employed to consider the aerodynamic nonlinearity the thermal loadings of uniformly distributed surface temperatures and temperature gradients through the panel thickness are considered by the application of the modal truncation technique the number of governing equations of motion is reduced dramatically so that the computational costs are reduced significantly all possible types of panel behavior including flat and stable buckled but dynamically stable limit cycle oscillation lco periodic motion and chaotic motion were observed examples of the applications of the proposed methodology were flutter responses of isotropic and composite panels special emphasis was placed on the boundary between lco and chaos and on the route to chaos time history phase plane plot poincare map bifurcation diagram and lyapunov exponent are employed in the chaos study it is found that at low or moderately high dynamic pressures the fluttering panel typically takes a period doubling route to evolve into chaos whereas at high dynamic pressures the route generally involves bursts of chaos and rejuvenations of periodic motions

finite element time domain modal formulation for nonlinear flutter of composite panels a finite element time domain modal approach is presented for determining the nonlinear flutter characteristics of composite panels at elevated temperatures the von karman large deflection strain displacement relations quasisteady first order piston theory aerodynamics and quasisteady thermal stress theory are used to formulate the nonlinear panel flutter finite element equations of motion in nodal displacements a set of nonlinear modal equations of motion of much smaller degrees of freedom for the facilitation in time numerical integration is then obtained through a modal transformation and reduction all five types of panel behavior flat buckled limit cycle periodic and chaotic motions can be determined

maximum likelihood hidden markov modeling using a dominant sequence of states approximate maximum likelihood ml hidden markov modeling using the most likely state sequence mlss is examined and compared with the exact ml approach that considers all possible state sequences it is shown that for any hidden markov model hmm the difference between the approximate and the exact normalized likelihood functions cannot exceed the logarithm of the number of states divided by the dimension of the output vectors frame length furthermore for gaussian hmms and a given observation sequence the mlss is typically the sequence of nearest neighbor states in the itakura saito sense and the posterior probability of any state sequence which departs from the mlss in a single time instant decays exponentially with the frame length hence for a sufficiently large frame length the exact and approximate ml approach provide similar model estimates and likelihood values

finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow a finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented by using the principle of virtual work the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von karman s large deflection plate theory the first order piston theory aerodynamics and the quasi steady thermal stress theory the system equations of motion can be mathematically separated into two sets of equations and then solved in sequence the first set of equations yields the panel thermal aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit cycle oscillations stability and flutter boundaries can also be obtained from the two sets of system equations finite element large amplitude limit cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing galerkin time integration and other finite element solutions effects of nonuniform temperature distributions panel length to width ratios and boundary conditions on flutter responses of rectangular and triangular panels are presented

fluctuation of mean lyapunov exponent for kuramoto sivashinsky equation abstract the statistical aspect of lyapunov exponent for kuramoto sivashinsky equation is studied fluctuation of mean lyapunov exponent is given by the probability distribution function of its time coarse grained quantity local lyapunov exponent the functional form of the probability distribution function is obtained its form is different from the one obtained from the large deviation statistics also the relation between the damping constant included in kuramoto sivashinsky equation and lyapunov exponent is obtained

quantitative characterization of spatiotemporal patterns ii abstract disorderness of spatiotemporal patterns which are obtained by nonlinear partial differential equations is characterized quantitatively the mean lyapunov exponent for a nonlinear partial differential equation is given the local lyapunov exponent which is a finite time average of the mean lyapunov exponent is shown to have close relation to the spatiotemporal patterns it is suggested that the systems which are described by nonlinear partial differential equations are characterized statistically through the probability distribution function of the local lyapunov exponent

focused image recovery from two defocused images recorded with different camera settings two new methods are presented for recovering the focused image of an object from only two blurred images recorded with different camera parameter settings the camera parameters include lens position focal length and aperture diameter first a blur parameter 0 is estimated using one of our two recently proposed depth from defocus methods then one of the two blurred images is deconvolved to recover the focused image the first method is based on a recently proposed spatial domain convolutioddeconvolution transform this method requires only the knowledge of 7 of the camera s point spread function psf it does not require information about the actual form of the camera s psf the second method in contrast to the first requires full knowledge of the form of the psf as part of the second method we present a calibration procedure for estimating the camera s psf for different values of the blur parameter 0 in the second method the focused image is obtained through deconvolution in the fourier domain using the wiener filter for both methods results of experiments on actual defocused images recorded by a ccd camera are given the first method requires much less computation than the second method the first method gives satisfactory results for up to medium levels of blur and the second method gives good results for up to relatively high levels of blur

proper orthogonal decomposition reduced order model for nonlinear aeroelastic oscillations in this study the proper orthogonal decomposition method in conjunction with a galerkin projection scheme is employed to solve the title problem of a fluttering plate in both two and three dimensions undergoing supersonic flow using von karman s large deflection plate theory and quasi steady supersonic aerodynamic theory proper orthogonal decomposition based reduced order models are constructed by using the responses as snapshots from the conventional galerkin method which also plays a role as a reference method in this paper results for the buckled limit cycle oscillation and chaotic responses of the simply supported plate are presented and compared with the galerkin solutions numerical examples demonstrate that the proper orthogonal decomposition reduced order model permits a much lower dimensional model as compared to that obtainable via the galerkin approach for example for a plate length to width ratio equal to 4 only two proper orthogonal decomposition modes are required to describe the pa

finite element analysis of large amplitude panel flutter of thin laminates the principle of virtual work is used to develop the equations of motion the large deflections are represented by von karman strain displacement relations and the aerodynamic load is represented by the use of the quasisteady first order piston theory the equations of motion are solved by implementing the lineared updated mode with a nonlinear time function lum ntf approximation critical flutter values and limit cycle amplitudes for graphite epoxy and boron epoxy laminates are investigated

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

a comparison of shell theories for large amplitude vibrations of circular cylindrical shells lagrangian approach abstract large amplitude geometrically non linear vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated the lagrange equations of motion are obtained by an energy approach retaining damping through rayleigh s dissipation function four different non linear thin shell theories namely donnell s sanders koiter flugge lur e byrne and novozhilov s theories which neglect rotary inertia and shear deformation are used to calculate the elastic strain energy the formulation is also valid for orthotropic and symmetric cross ply laminated composite shells the large amplitude response of perfect and imperfect simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories numerical responses obtained by using these four non linear shell theories are also compared to results obtained by using the donnell s non linear shallow shell equation of motion a validation of calculations by comparison with experimental results is also performed both empty and fluid filled shells are investigated by using a potential fluid model the effects of radial pressure and axial load are also studied boundary conditions for simply supported shells are exactly satisfied different expansions involving from 14 to 48 generalized co ordinates associated with natural modes of simply supported shells are used the non linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis

reconstructing arbitrarily focused images from two differently focused images using linear filters we present a novel filtering method for reconstructing an all in focus image or an arbitrarily focused image from two images that are focused differently the method can arbitrarily manipulate the degree of blur of the objects using linear filters without segmentation the filters are uniquely determined from a linear imaging model in the fourier domain an effective and accurate blur estimation method is developed the simulation results show that the accuracy and computational time of the proposed method are improved compared with the previous iterative method and that the effects of blur estimation error on the quality of the reconstructed image are very small the method performs well for real images acquired without visible artifacts

lyapunov exponent of partial differential equation abstract the method of calculating numerically the lyapunov exponent of partial differential equations is stated the mean lyapunov exponent and the local lyapunov exponent are introduced in order to characterize the systems described by the partial differential equations it is shown that the mean lyapunov exponent expresses clearly how disordered the spatial patterns are

an object oriented framework for reduced order models using proper orthogonal decomposition pod this work presents an object oriented design for reduced order modeling using the proper orthogonal decomposition pod technique object oriented design attributes such as data encapsulation inheritance and polymorphism are shown to produce efficient implementations that optimize code reuse and maintainability in reduced order models this paper demonstrates how existing finite element libraries can be used to efficiently carry out integration of field quantities and their gradients over complex domains for producing reduced order models that are based on the weak form galerkin method and pod furthermore numerical examples are used to show how reduced order models are computationally feasible for reducing cpu time as long as the computational expense incurred in solving the associated systems of linear equations is significantly higher than the computational expense related to the assembly of the system of equations

spatiotemporal chaos in the one dimensional complex ginzburg landau equation the dynamical behavior of a large one dimensional system obeying the cubic complex ginzburg landau equation is studied numerically as a function of parameters near a supercritical bifurcation two types of chaotic behavior can be distinguished beyond the benjamin feir instability a phase turbulence regime with a conserved phase winding number and no phase dislocations space time defects and a defect regime with a nonzero density of defects the transition between the two can either be continuous or discontinuous hysteretic depending on parameters the spatial decay of the phase correlation function is inferred to be exponential in both regimes with a sharp decrease of the correlation length upon entering the defect phase the temporal decay of correlations is exponential in the defect regime

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part ii large amplitude vibrations without flow abstract the non linear response of empty and fluid filled circular cylindrical shells to harmonic excitations is investigated both modal and point excitations have been considered the model is suitable to study simply supported shells with and without axial constraints donnell s non linear shallow shell theory is used the boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied the radial deflection of the shell is expanded by using a basis of seven linear modes the effect of internal quiescent incompressible and inviscid fluid is investigated the equations of motion obtained in part i of this study are studied by using a code based on the collocation method the validation of the present model is obtained by comparison with other authoritative results the effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated clarifying questions open for a long time the results show the occurrence of travelling wave response in the proximity of the resonance frequency the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half wave and limit cycle responses modes with two longitudinal half waves are also investigated

method of speech recognition using variational inference with switching state space models a method is developed which includes 1 defining a switching state space model for a continuous valued hidden production related parameter and the observed speech acoustics and 2 approximating a posterior probability that provides the likelihood of a sequence of the hidden production related parameters and a sequence of speech units based on a sequence of observed input values in approximating the posterior probability the boundaries of the speech units are not fixed but are optimally determined under one embodiment a mixture of gaussian approximation is used in another embodiment an hmm posterior approximation is used

observation of a strange attractor abstract phase space portraits have been constructed and analyzed for noisy nonperiodic data obtained in an experiment on a nonequilibrium homogeneous chemical reaction the phase space trajectories define a limit set that is an attractor following a perturbation the trajectory quickly returns to the attracting set this attracting set is shown to be strange nearby trajectories separate exponentially on the average moreover the poincare sections exhibit the stretching and folding that is characteristic of strange attractors

nonlinear normal modes for damped geometrically nonlinear systems application to reduced order modelling of harmonically forced structures in order to build efficient reduced order models roms for geometrically nonlinear vibrations of thin structures a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities the linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation a special attention is focused on how all the linear modal damping terms are gathered together in order to define a precise decay of energy onto the invariant manifolds also defined as nonlinear normal modes nnms then this time independent formulation is used to reduce the dynamics governing the oscillations of a structure excited by an external harmonic force the validity of the proposed roms is systematically discussed and compared with other available methods in particular it is shown that large values of the modal damping of the slave modes may change the type of nonlinearity hardening softening behaviour of the directly excited master mode two examples are used to illustrate the main features of the method a two degrees of freedom dof system allows presentation of the main results through a simple example then a water filled circular cylindrical shell with external resonant forcing is considered in order to show the ability of the method to substantially reduce the dynamics of a continuous structure 2006 elsevier ltd all rights reserved

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

a curve evolution approach for unsupervised segmentation of images with low depth of field in this paper we describe a novel algorithm for unsupervised segmentation of images with low depth of field dof first of all a multi scale reblurring model is used to detect the object of interest ooi in saliency space then to determine the boundary of ooi an active contour model based on hybrid energy function is proposed in this model a global energy item related with the saliency map is adopted to find the global minimum and a local energy term regarding the low dof image is used to improve the segmentation precision in addition an adaptive parameter is attached to this model to balance the weight of global and local energy furthermore an unsupervised curve initialization method is designed to reduce the number of evolution iterations finally we conduct experiments on various low dof images and the results demonstrate the high robustness and precision of the proposed approach