chaotic component obscured by strong periodicity in voice production system the effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two mass model the two mass model assumes the glottal airflow to be laminar nonviscous and incompressible in this model when the asymmetric factor is decreased from 0 65 to 0 35 only 1 1 and 1 2 modes are detectable however with the same parameters four vibratory modes 1 1 1 2 2 4 2 6 are found in the asymmetric composite model using the navier stokes equations to describe the complex aerodynamics in the glottis moreover the amplitude of the waveform is modulated by a small amplitude noiselike series the nonlinear detection method reveals that this noiselike modulation is not random but rather it is deterministic chaos this result agrees with the phenomenon often seen in voice in which the voice signal is strongly periodic but modulated by a small amplitude chaotic component the only difference between the two mass model and the composite model is in their descriptions of glottal airflow therefore the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production including bifurcation and a small amplitude chaotic component obscured by strong periodicity

bifurcations in an asymmetric vocal fold model a two mass model of vocal fold vibrations is analyzed with methods from nonlinear dynamics bifurcations are located in parameter planes of physiological interest subglottal pressure stiffness of the folds it is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes toroidal oscillations and chaos the corresponding attractors are characterized by phase portraits spectra and next maximum maps the relevance of these simulations for voice disorders such as laryngeal paralysis is discussed

harmonic wavelets towards the solution of nonlinear pde in this paper harmonic wavelets which are analytically defined and band limited are studied together with their differentiable properties harmonic wavelets were recently applied to the solution of evolution problems and more generally to describe evolution operators in order to consider the evolution of a solitary profile and to focus on the localization property of wavelets it seems to be more expedient to make use of functions with limited compact support either in space or in frequency the connection coefficients of harmonic wavelets are explicitly computed in the following at any order and characterized by some recursive formulas in particular they are functionally and finitely defined by a simple formula for any order of the basis derivatives

trigonometric wavelet method for some elliptic boundary value problems abstract in this paper we apply trigonometric wavelet method to investigate the numerical solution of elliptic boundary value problem in an exterior unit disk the simple computation formulae of the entries in the stiffness matrix are obtained it shows that we only need to compute 2 2 j 1 elements of one 2 j 2 2 j 2 stiffness matrix moreover the error estimates of the approximation solutions are given and some test examples are presented

the stability of infinite element schemes for transient wave problems the transformation of conjugated infinite elements from the frequency domain to the time domain is described this procedure yields discrete numerical models for transient acoustics which are local in space and time these can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time the conditions under which this is true are investigated in this article a numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied axisymmetric spherical and spheroidal formulations are considered

wavelet solutions for the dirichlet problem a modified classical penalty method for solving a dirichlet boundary value problem is presented this new fictitious domain penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domains it is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast approximate calculation of boundary integral the compact support and orthonormality of the basis are essential for representing the boundary measure numerically and therefore for implementing this methodology

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

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

effect of level difference between left and right vocal folds on phonation physical experiment and theoretical study as an alternative factor to produce asymmetry between left and right vocal folds the present study focuses on level difference which is defined as the distance between the upper surfaces of the bilateral vocal folds in the inferior superior direction physical models of the vocal folds were utilized to study the effect of the level difference on the phonation threshold pressure a vocal tract model was also attached to the vocal fold model for two types of different models experiments revealed that the phonation threshold pressure tended to increase as the level difference was extended based upon a small amplitude approximation of the vocal fold oscillations a theoretical formula was derived for the phonation threshold pressure this theory agrees with the experiments especially when the phase difference between the left and right vocal folds is not extensive furthermore an asymmetric two mass model was simulated with a level difference to validate the experiments as well as the theory the prima

transient wave envelope elements for wave problems a novel family of infinite wave envelope elements is described which can be used in conjunction with conventional finite elements to model the transient wave equation in unbounded regions the elements are obtained by applying an inverse fourier transformation to a mapped wave envelope formulation in the frequency domain the discrete transient equations obtained in this way can be applied to two dimensional and three dimensional problems without restriction being valid over a full range of excitation frequencies the effectiveness and accuracy of the method is demonstrated in application to simple test cases which involve the calculation of transient sound fields generated by pulsating spheres and cylinders excited from rest in an unbounded region test solutions are compared to analytic solutions and to finite element solutions obtained by using large computational grids which extend beyond the region influenced by the transient disturbance

a numerical scheme for solving a class of logarithmic integral equations arisen from two dimensional helmholtz equations using local thin plate splines abstract this paper presents a numerical method for solving logarithmic fredholm integral equations which occur as a reformulation of two dimensional helmholtz equations over the unit circle with the robin boundary conditions the method approximates the solution utilizing the discrete collocation method based on the locally supported thin plate splines as a type of free shape parameter radial basis functions the local thin plate splines establish an efficient and stable technique to estimate an unknown function by a small set of nodes instead of all points over the solution domain to compute logarithm like singular integrals appeared in the method we use a particular nonuniform gauss legendre quadrature rule since the scheme does not require any mesh generations on the domain it can be identified as a meshless method the error estimate of the proposed method is presented numerical results are included to show the validity and efficiency of the new technique these results also confirm that the proposed method uses much less computer memory in comparison with the method established on the globally supported thin plate splines moreover it seems that the algorithm of the presented approach is attractive and easy to implement on computers

a galerkin boundary element method based on interpolatory hermite trigonometric wavelets abstract a galerkin boundary element method based on interpolatory hermite trigonometric wavelets is presented for solving 2 d potential problems defined inside or outside of a circular boundary in this paper in this approach an equivalent variational form of the corresponding boundary integral equation for the potential problem is used the trigonometric wavelets are employed as trial and test functions of the variational formulation the analytical formulae of the matrix entries indicate that most of the matrix entries are naturally zero without any truncation technique and the system matrix is a block diagonal matrix each block consists of four circular submatrices hence the memory spaces and computational complexity of the system matrix are linear scale this approach could be easily coupled into domain decomposition method based on variational formulation finally the error estimates of the approximation solutions are given and some test examples are presented

spatiotemporal analysis of complex signals theory and applications we present a space time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos this permits the introduction of several characteristics of the signal three characteristic energies and entropies one temporal one spatial and one global and a characteristic dimension although the technique is general we concentrate on its applications to hydrodynamic problems specifically the transition to turbulence we consider two cases of application a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk in the latter we show a direct relation between the global entropy and the different instabilities that the flow undergoes as reynolds number increases

a meshless discrete collocation method for the numerical solution of singular logarithmic boundary integral equations utilizing radial basis functions abstract the main intention of the current paper is to describe a scheme for the numerical solution of boundary integral equations of the second kind with logarithmic singular kernels these types of integral equations result from boundary value problems of laplace s equations with linear robin boundary conditions the method approximates the solution using the radial basis function rbf expansion with polynomial precision in the discrete collocation method the collocation method for solving logarithmic boundary integral equations encounters more difficulties for computing the singular integrals which cannot be approximated by the classical quadrature formulae to overcome this problem we utilize the non uniform composite gauss legendre integration rule and employ it to estimate the singular logarithm integrals appeared in the method since the scheme is based on the use of scattered points spread on the analyzed domain and does not need any domain elements we can call it as the meshless discrete collocation method the new algorithm is successful and easy to solve various types of boundary integral equations with singular kernels we also provide the error estimate of the proposed method the efficiency and accuracy of the new approach are illustrated by some numerical examples

a meshless galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions abstract this paper presents a computational scheme to solve nonlinear logarithmic singular boundary integral equations these types of integral equations arise from boundary value problems of laplace s equations with nonlinear robin boundary conditions the discrete galerkin method together with the inverse multiquadric radial basis functions established on scattered points is utilized to approximate the solution the discrete galerkin method for solving boundary integral equations results from the numerical integration of all integrals in the method the proposed scheme uses a special accurate quadrature formula via the nonuniform gauss legendre integration rule to compute logarithm like singular integrals appeared in the scheme since the numerical method developed in the current paper does not require any mesh generations on the boundary of the domain it is meshless and does not depend to the domain form we also investigate the error analysis of the proposed method illustrative examples show the reliability and efficiency of the new scheme and confirm the theoretical error estimates

trigonometric wavelets for hermite interpolation the aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials the pair of scaling functions which span the sample spaces are fundamental functions for hermite interpolation on a dyadic partition of nodes on the interval 0 2 two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions together with the corresponding dual functions these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences consequently this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment

a finite element model of vocal fold vibration a finite element model of the vocal fold is developed from basic laws of continuum mechanics to obtain the oscillatory characteristics of the vocal folds the model is capable of accommodating inhomogeneous anisotropic material properties and irregular geometry of the boundaries it has provisions for asymmetry across the midplane both from the geometric and tension point of view which enables one to simulate certain kinds of voice disorders due to vocal fold paralysis it employs the measured viscoelastic properties of the vocal fold tissues the detailed construction of the matrix differential equations of motion is presented followed by the solution scheme finally typical results are presented and validated using an eigenvalue method and a commercial finite element package abaqus

computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model with the use of an endoscopic high speed camera vocal fold dynamics may be observed clinically during phonation however observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function especially when the laryngeal disease lacks any clear morphological presentation in this study biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three dimensional model until the dynamics of both systems are similar first a mathematical optimization method is presented next model parameters such as pressure tension and masses are adjusted to reproduce vocal fold dynamics and the deduced parameters are physiologically interpreted various combinations of global and local optimization techniques are attempted evaluation of the optimization procedure is performed using 50 synthetically generated data sets the results show sufficient reliability including 0 07 normalized error 96 correlation and 91 accuracy the technique is also demonstrated on data from human hemilarynx experiments in which a low normalized error 0 16 and high correlation 84 values were achieved in the future this technique may be applied to clinical high speed images yielding objective measures with which to document improved vocal function of patients with voice disorders

anterior posterior biphonation in a finite element model of vocal fold vibration in this paper a finite element model is used to simulate anterior posterior biphonation neubauer et al j acoust soc am 110 6 3179 3192 2001 the anterior posterior stiffness asymmetric factor and the anterior posterior shape asymmetric factor describe the asymmetry properties of vocal folds spatiotemporal plot spectral analysis anterior posterior fundamental frequency ratio cross covariation function and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations calculation results show that the anterior posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration when the stiffness asymmetry reaches a certain level the drop in spatial coherence desynchronizes the vibration modes the anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies fa and fp the complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination

numerical solution of hypersingular equation using recursive wavelet on invariant set in this paper we construct the chebyshev recursive wavelets on a unit interval of the first kind the second kind and their corresponding weight functions we apply wavelet collocation method to solve the natural boundary integral equation of the harmonic equation on the lower half plane numerically it is convenient and accurate to generate the stiffness matrix two numerical examples are presented it is shown that the stiffness matrix is highly sparse when the order of the stiffness matrix becomes large current method allows choosing an appropriate weight function to increase the convergence rate and accuracy of the numerical results

irregular vocal fold vibration high speed observation and modeling direct observations of nonstationary asymmetric vocal fold oscillations are reported complex time series of the left and the right vocal fold vibrations are extracted from digital high speed image sequences separately the dynamics of the corresponding high speed glottograms reveals transitions between low dimensional attractors such as subharmonic and quasiperiodic oscillations the spectral components of either oscillation are given by positive linear combinations of two fundamental frequencies their ratio is determined from the high speed sequences and is used as a parameter of laryngeal asymmetry in model calculations the parameters of a simplified asymmetric two mass model of the larynx are preset by using experimental data its bifurcation structure is explored in order to fit simulations to the observed time series appropriate parameter settings allow the reproduction of time series and differentiated amplitude contours with quantitative agreement in particular several phase locked episodes ranging from 4 5 to 2 3 rhythms are generated realistically with the model

galerkin trigonometric wavelet methods for the natural boundary integral equations a simply supported boundary value problem of biharmonic equations in the unit disk is reduced into an equivalent second kind natural boundary integral equation nbie with hypersingular kernel in the sense of hadamard finite part trigonometric hermite interpolatory wavelets introduced by quak math comput 65 1996 683 722 as trial functions are used to its galerkin discretization with 2 j 1 degrees of freedom on the boundary it is proved that the stiffness matrix is a block diagonal matrix and its diagonal elements are some symmetric and block circulant submatrices the simple computational formulae of the entries in stiffness matrix are obtained these show that we only need to compute 2 2 j j 1 elements of a 2 j 2x2 j 2 stiffness matrix the error estimates for the approximation solutions are established finally numerical examples are given

wavelet approximations for first kind boundary integral equations on polygons an elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent first kind boundary integral equation its galerkin discretization with n degrees of freedom on the boundary with spline wavelets as basis functions is analyzed a truncation strategy is presented which allows to reduce the number of nonzero elements in the stiffness matrix from o n 2 to o n log n entries the condition numbers are bounded independently of the meshwidth it is proved that the compressed scheme thus obtained yields in o n log n 2 operations approximate solutions with the same asymptotic convergence rates as the full galerkin scheme in the boundary energy norm as well as in interior points numerical examples show the asymptotic error analysis to be valid already for moderate values of n

time integration for spherical acoustic finite infinite element models in this paper we analyse the numerical time integration of models of exterior acoustics the major challenge lies in the instabilities that may arise from the infinite elements in this paper we consider the special case of spherical infinite elements formulations which have shown their relevance for industrial applications we propose a method that combines crank nicholson s method with a filtering step by the backward euler method the paper is illustrated with an example relevant to industry copyright c 2005 john wiley sons ltd

spatio temporal analysis of irregular vocal fold oscillations biphonation due to desynchronization of spatial modes this report is on direct observation and modal analysis of irregular spatio temporal vibration patterns of vocal fold pathologies in vivo the observed oscillation patterns are described quantitatively with multiline kymograms spectral analysis and spatio temporal plots the complex spatio temporal vibration patterns are decomposed by empirical orthogonal functions into independent vibratory modes it is shown quantitatively that biphonation can be induced either by left right asymmetry or by desynchronized anterior posterior vibratory modes and the term ap anterior posterior biphonation is introduced the presented phonation examples show that for normal phonation the first two modes sufficiently explain the glottal dynamics the spatio temporal oscillation pattern associated with biphonation due to left right asymmetry can be explained by the first three modes higher order modes are required to describe the pattern for biphonation induced by anterior posterior vibrations spatial irregularity is

time series analysis for system identification and diagnostics abstract the problem of construction of dynamical system phase space and estimation of attractor dimension from time series is considered two techniques for improving the phase space construction according to takens theorem are compared the method proposed by broomhead and king and another method based on the works of neymark and co workers the second method is shown to be rather efficient for investigation of systems with essentially inhomogeneous attractors an iterative filtering algorithm that allows the extraction of deterministic components of experimental data is proposed the application of these methods to prediction of the time series model fitting and attractor characteristics calculation is also considered the use of quantitative characteristics of chaotic motion for dynamical system diagnostics is discussed

interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations for normal phonation two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1 1 entrainment the eigenfunctions show some correspondence to theoretical low order normal modes of a simplified three dimensional elastic continuum and to the normal modes of a linearized two mass model the eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations these chaotic oscillations might be understood in terms of a desynchronization of a few of the low order modes and may be related to mechanisms of creaky voice or vocal fry furthermore some of the empirical eigenfunctions captured during complex oscillations correspond to higher order normal modes described in earlier theoretical work the empirical eigenfunctions may also be useful in the design of lower order models valid over the range for which the empirical eigenfunctions remain more or less constant and may help facilitate bifurcation analyses of the biomechanical simulation

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle

galerkin wavelet methods for two point boundary value problems anti derivatives of wavelets are used for the numerical solution of differential equations optimal error estimates are obtained in the applications to two point boundary value problems of second order the orthogonal property of the wavelets is used to construct efficient iterative methods for the solution of the resultant linear algebraic systems numerical examples are given