adaptive spectral methods with application to mixing layer computations this paper reports some experiments on the use of adaptive chebyshev pseudospectral methods for compressible mixing layer computations different functionals measuring the optimality of the polynomial approximation are discussed and compared in particular we address the problem of the practical computation of the various functionals the utility of the self adaptive method is then demonstrated by some examples from compressible mixing layer calculations

three dimensional simulations of compressible mixing layers visualizations and statistical analysis the effects of compressibility on the planar mixing layer are investigated by means of visualization and statistical analysis of the flowfield quantities computed using three dimensional temporally evolving inviscid simulations the levels of compressibility studied range from relative mach numbers of mr 0 2 2 4 the objectives of this research are to identify large scale structures present in the mixing layer at different levels of compressibility as well as to examine the statistical description of the flowfield in order to gain understanding of the physical entrainment and mixing processes three dimensional simulation visualizations of both the passive scalar and pressure fields show the nature of the large scale structure present in the planar mixing layer to change from nearly two dimensional and spanwise at low compressibility to highly three dimensional and oblique at increased compressibility statistical analysis of the flowfield quantities shows that the shear layer width reynolds shear stress and transverse turbulence intensity decrease with increasing compressibility levels whereas the streamwise turbulence intensity remains nearly constant and the spanwise turbulence intensity increases these statistics support the increasingly three dimensional nature of the large scale motion of the mixing layer with increasing mr

linear prediction approach for efficient frequency estimation of multiple real sinusoids algorithms and analyses based on the linear prediction property of sinusoidal signals two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed in order to achieve accurate frequency estimation the first algorithm uses a generalized unit norm constraint while the second method employs a monic constraint the weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner for the case of a single real tone with sufficiently large data samples both estimators provide nearly identical frequency estimates and their performance approaches crame spl acute r rao lower bound crlb for white gaussian noise before the threshold effect occurs algorithms for closed form single tone frequency estimation are also devised computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the crlb for different frequencies observation lengths and signal to noise ratio snr conditions

comparison of confined compressible spatially developing mixing layers with temporal mixing layers the spatially developing mixing layer is investigated using both linear stability theory and numerical simulations temporal and spatial linear stability solutions are compared and it is found that the temporal and spatial wave numbers are equal the temporal frequency is a function of the spatial frequency and the temporal and spatial growth rates have a one to one correspondence numerical simulations of the euler equations are performed for the spatially developing mixing layer using a linear stability forcing function spatially developing simulations of the supersonic supersonic and supersonic subsonic acoustic instabilities and the kelvinhelmholtz instability are compared to temporally developing simulations and found to be in agreement

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

properties and characteristics of the srivastava khairnar more integral operator abstract in the present paper we derive various properties and characteristics of the srivastava khairnar more integral operator such results as inclusion relationships integral preserving properties inequality properties convolution properties subordination and superordination properties and sandwich type results are obtained relevant connections of the results presented here with those obtained in earlier works are also pointed out

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

differential subordination and superordination results for cho kwon srivastava operator making use of the concepts of differential subordination and superordination many subordination and superordination results are obtained for analytic functions in the open unit disk using the cho kwon srivastava operator by investigating appropriate classes of admissible functions sandwich type results are also obtained

temporal linear stability analysis of three dimensional compressible binary shear layers temporal linear stability analysis is performed on the three dimensional compressible binary shear layer for density ratios ranging from 1 to 32 and convective mach numbers up to 2 comparison is made with the results of spatial theory some stability properties are shared by both approaches for example the independence of the direction of propagation of the most unstable modes from the freestream density ratio but other features are different a single secondary mode appears instead of two at high compressibility an empirical model is proposed for the wave length and phase speed of the most amplified waves direct numerical simulations show good agreement with linear inviscid theory for initial reynolds numbers greater than 400

bayesian detection and estimation of cisoids in colored noise the problem of estimating the number of cisoids in colored noise is addressed it is assumed that the noise can be modeled by an autoregression whose order has also to be estimated a new criterion is proposed for estimating the number of cisoids and the autoregressive model order as well as a new algorithm for estimating the cisoidal frequencies in the derivation a bayesian methodology and subspace decomposition are employed the proposed criterion significantly outperforms the popular mdl and aic as applied in a paper by nagesha and kay in addition an algorithm that reduces the computational complexity of the solution is developed computer simulations that demonstrate the performance of the criterion are included

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure making use of the familiar convolution structure of analytic functions in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order among the various results obtained here for each of these function classes we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the class introduced here

neighborhoods of certain p valent analytic functions with complex order in this paper the authors prove several coefficient bounds distortion inequalities of the class s g n p l b b of p valent analytic functions of complex order by making use of the familiar concept of neighborhoods of p valent analytic functions they obtained several inclusion relations associated with the n p n d neighborhood of this class and its certain derivatives which is defined by means of a certain non homogeneous cauchy euler differential equations

total least squares approach for frequency estimation using linear prediction the resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal to noise ratio snr of the received signal becomes low this resolution can be improved by using the total least squares tls method in solving the linear prediction lp equation this approach makes use of the singular value decomposition svd of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the lp data matrix simultaneously comparison is made to the principle eigenvector pe method of tufts and kumaresan both on theoretical and experimental grounds the tls algorithm exhibits superior performance over the pe method where low rank approximation is applied to the data matrix only

an unbiased equation error identifier and reduced order approximations the equation error ee identification technique is modified to remove the parameter bias problem induced by uncorrelated measurement errors the modification replaces a monic constraint with a unit norm constraint the asymptotic solution replaces a normal equation with an eigenequation the resulting algorithm is simpler than previous schemes while at the same time preserving the desirable properties of the conventional ee method simplicity of an on line algorithm unimodality of the performance surface and consistent identification in the sufficient order case in the more realistic undermodeled case a robustness result shows that the mean optimal parameter values of both the monic and unit norm ee schemes correspond to a stable transfer function for all degrees of undermodeling and for all stationary output disturbances provided the input sequence satisfies an autoregressive constraint otherwise an unstable model may result model approximation properties for the undermodeled case are exposed in detail for the case of autoregressive inputs although both the monic and unit norm variants provide pade approximation properties the unit norm version is capable of autocorrelation matching properties as as well and yields the optimal solution to a first and second order interpolation problem finally the mismodeling error for the undermodeled case is shown to be a well behaved function of the hankel singular values of the unknown system this modification allows ee methods to be admitted to the class of unbiased identification and approximation techniques

neighborhoods for certain subclasses of multivalently analytic functions defined by using a differential operator in the present investigation by making use of the familiar concept of neighborhoods of analytic and multivalent functions we derive coefficient bounds and distortion inequalities associated inclusion relations for the n d neighborhoods of subclasses of analytic and multivalent functions with negative coefficients which are defined by means of a certain nonhomogenous differential equation several special cases of the main results are mentioned

compressible mixing layer linear theory and direct simulation results from linear stability analysis are presented for a wide variety of mixing layers including low speed layers with variable density and high mach number mixing layers the linear amplification predicts correctly the experimentally observed trends in growth rate that are due to velocity ratio density ratio and mach number provided that the spatial theory is used and the mean flow is a computed solution of the compressible boundary layer equations it is found that three dimensional modes are dominant in the high speed mixing layer above a convective mach number of 0 6 and a simple relationship is proposed that approximately describes the orientation of these waves direct numerical simulations of the compressible navier stokes equations are used to show the reduced growth rate that is due to increasing mach number from consideration of the compressible vorticity equation it is found that the dominant physics controlling the nonlinear roll up of vortices in the high speed mixing layer is contained in an elementary form in the linear eigenfunctions it is concluded that the linear theory can be very useful for investigating the physics of free shear layers and predicting the growth rate of the developed plane mixing layer

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

assessment of total variation diminishing schemes in compressible mixing flow computations numerical simulations of temporally developing mixing layers using high resolution total variation diminishing tvd schemes have been carried out to investigate the effects of grid resolution and inherent scheme dissipation on the solution quality owing to the sensitivity of the turbulence results to grid resolution mixing flow computations generally require high grid density to resolve the shear layer dynamics and to interpret the mean and turbulent flowfield interactions various limiters were tested in examining the numerical dissipation effect for which essentially nonoscillatory eno solution is taken as a benchmark basis the computations performed for scheme evaluation covered a broad spectrum including subsonic transonic and supersonic convective mach numbers among the schemes considered the performance of a minmod and van leer limiters comply more consistently with the eno results for a wide range of convective mach numbers whereas the superbee limiter being the test tvd scheme for subsonic and low transonic mach number flow suffers from overcompression which may lead to nonphysical solutions at high supersonic convective mach numbers the result obtained by each tvd scheme is sensitive to the design of the limiter dissipation introduced by the limiting procedure should be kept as minimal as possible but a nonsmooth minimization should be avoided because it may result in nonphysical overcompression particularly for high convective mach number flows

a numerical study of temporal shallow mixing layers using bgk based schemes a numerical study of the temporal shallow mixing layers is performed the depth averaged shallow water equations are solved by the finite volume method based on the bhatnagar gross krook bgk equation the filtering operation is applied to the governing equations and the well known smagorinsky model for the subgrid scale sgs stress is employed in order to present a large eddy simulation les the roll up and pairing processes are clearly shown and the corresponding kinetic energy spectra are calculated the effects of the froude number and the bottom friction are numerically investigated it is shown that the growth rate of the mixing layer decreases as the froude number increases which is very similar to the compressible mixing layers when considering the effects of the mach number the numerical results also indicate that the increase in bottom friction can enhance the stability of the flows which is physically reasonable and consistent with the theoretical and experimental findings

reformulation of pisarenko harmonic decomposition method for single tone frequency estimation based on the linear prediction lp property of sinusoidal signals a closed form unbiased frequency estimator for a real sinusoid in white noise is proposed the frequency estimator which is derived by minimizing a constrained least squares cost function can be considered as a reformulation of the well known pisarenko harmonic decomposer phd online computation of the frequency estimate can be achieved in a very simple manner and its variance is derived computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the phd maximum likelihood and lp based methods as well as crame spl acute r rao lower bound

a hybrid approach to harmonic retrieval in non gaussian arma noise addresses the harmonic retrieval problem in colored noise as contrasted to the reported studies in which gaussian noise was assumed this paper focuses on additive non gaussian arma noise our approach is hybrid in the sense that third order cumulants are first used to identify the ar part of the non gaussian noise process and then correlation based high resolution methods are used for the filtered process to estimate the number of harmonics and their frequencies simulation examples are presented to demonstrate the high resolution of this approach

a parameter estimation approach to estimation of frequencies of sinusoids it is shown that with uniform sampling a sample of the sum of m sinusoids at time nt can be uniquely expressed as a linear combination of the 2m samples at times n 1 t n 2m t the 2m coefficients of linear combination are also the coefficients of a 2m order polynomial whose roots are e pmj omega i omega i being the frequencies of the sinusoids given the samples of sinusoids plus noise a consistent estimate of the 2m coefficients are obtained by the instrumental variable method of parameter estimation it is also possible to track time varying frequencies by a recursive algorithm that exponentially weighs out the past data simulation examples of one and two sinusoids are given

a high order accurate difference scheme for complex flow fields a high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented the reason for oscillation production in numerical solutions is analyzed it is caused by a nonuniform group velocity of wavepackets a method of group velocity control for the improvement of the shock resolution is presented in numerical simulation the fifth order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible n s equations a sixth order accurate symmetric compact difference relation is used to approximate the viscous terms and a three stage r k method is used to advance in time in order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets