out of plane vibrations of curved non uniform beams of constant radius the governing differential equations for out of plane vibrations of curved non uniform beams of constant radius are derived two physical parameters are introduced to simplify the analysis the explicit relations between the flexural displacement its first three order derivatives and the torsional displacement are derived with these explicit relations the two coupled governing characteristic differential equations can be decoupled and reduced to a sixth order ordinary differential equation with variable coefficients in the torsional displacement it is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms of spatial variable then exact solutions for the out of plane vibrations of the beam can be obtained the derived explicit relations can also be used to reduce the difficulty in experimental measurements finally the influence of taper ratio center angle and arc length on the first two natural frequencies of the beams is illustrated

the equations of motion of curved pipes conveying fluid abstract the non linear differential equations of motion of a fluid conveying pipe the no flow configuration of which is in the shape of a one dimensional line arbitrarily curved and twisted in space are derived by making use of the newtonian approach the extensible dynamics of the beam is based on the timoshenko beam theory some significant differences with the equations available in the open literature are discussed the stressed by flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe fluid systems

the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

time variant channel estimation using discrete prolate spheroidal sequences we propose and analyze a low complexity channel estimator for a multiuser multicarrier code division multiple access mc cdma downlink in a time variant frequency selective channel mc cdma is based on orthogonal frequency division multiplexing ofdm the time variant channel is estimated individually for every flat fading subcarrier assuming small intercarrier interference the temporal variation of every subcarrier over the duration of a data block is upper bounded by the doppler bandwidth determined by the maximum velocity of the users slepian showed that time limited snapshots of bandlimited sequences span a low dimensional subspace this subspace is also spanned by discrete prolate spheroidal dps sequences we expand the time variant subcarrier coefficients in terms of orthogonal dps sequences we call slepian basis expansion this enables a time variant channel description that avoids the frequency leakage effect of the fourier basis expansion the square bias of the slepian basis expansion per subcarrier is three magnitudes smaller than the square bias of the fourier basis expansion we show simulation results for a fully loaded mc cdma downlink with classic linear minimum mean square error multiuser detection the users are moving with 19 4 m s using the slepian basis expansion channel estimator and a pilot ratio of only 2 we achieve a bit error rate performance as with perfect channel knowledge

on channel estimation and detection for multicarrier signals in fast and selective rayleigh fading channels time domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency selective rayleigh fading channel as a consequence of the time varying channel the orthogonality between subcarriers is destroyed in conventional frequency domain approaches resulting in interchannel interference which increases an irreducible error floor in proportion to the normalized doppler frequency an important feature of the proposed technique is the ability to exploit the time selective channel as a provider of time diversity this enables us to achieve performance superior to any other structure without increasing bandwidth or incorporating redundancy in order to reduce the complexity of the estimator we apply the theory of optimal low rank approximation to a minimum mean squared error channel estimator and present a theoretical calculation of mean squared error and simulations to confirm that the estimator is robust to changes in channel characteristics

joint channel estimation equalization and data detection for ofdm systems in the presence of very high mobility this paper is concerned with the challenging and timely problem of joint channel estimation equalization and data detection for uplink orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization sage technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference ici cancelation in order to reduce the computational complexity of the algorithm band limited discrete cosine orthogonal basis functions are employed to represent the rapidly time varying fading channel by the discrete cosine serial expansion coefficients it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal in this way the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity the proposed sage joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel leading to a receiver structure that also incorporates ici cancelation computer simulations show that the cosine transformation represents the time varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm resulting in substantial reduction of the computational complexity

zero relaxation limit to centered rarefaction waves for a rate type viscoelastic system abstract we study a rate type viscoelastic system proposed by i suliciu 1990 internat j engrg sci 28 827 841 which is a 3 3 hyperbolic system with relaxation as the relaxation time tends to zero this system convergences to the well known p system formally in the case where the initial data are the riemann data such that the corresponding solutions of the p system are centered rarefaction waves we show that if the wave strength is suitably small then the solution for the relaxation system exists globally in time and converges to the solution of the corresponding rarefaction waves uniformly as the relaxation time goes to zero except for an initial layer the jump discontinuities in the solutions are decaying exponentially fast as time tends to infinity

new fluid velocity expression in an extensible semi circular pipe conveying fluid a new expression for fluid velocity is presented for a fluid conveying semi circular pipe with an extensible centreline the proposed fluid velocity expression is obtained from the material derivative while the previous velocity expressions are from love s kinematical relations in order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions the equations of in plane motion derived with the new expression are compared to the equations derived with the previous expressions furthermore the equilibrium positions natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed

the dynamics of a piping system with internal unsteady flow abstract the dynamics of a pipeline conveying one dimensional unsteady flow is considered the dynamics of the fluid pipe system is represented by a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow the vibration equations of the pipeline are derived by use of newton s law of motion while the fluid equations are derived based on the concept of a deformable moving control volume the equations are fully coupled to each other and thus can be applied to various fluid pipe interaction problems which can be generated by the diverse operations of valves and pumps attached to the pipeline the equations are applied to a simply supported inclined straight pipeline to investigate the stabilities and dynamic responses of the pipeline the stability analysis is conducted by use of bolotin s method the dynamic responses are numerically investigated for both stable and unstable conditions it is observed that unstable regions in the stability chart expand as the flow velocity and the mass density of the fluid increase and that natural frequencies of the pipeline increase as the fluid friction acting on the inner surface of pipeline increases

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

low complexity equalization of ofdm in doubly selective channels orthogonal frequency division multiplexing ofdm systems may experience significant inter carrier interference ici when used in time and frequency selective or doubly selective channels in such cases the classical symbol estimation schemes e g minimum mean squared error mmse and zero forcing zf estimation require matrix inversion that is prohibitively complex for large symbol lengths an analysis of the ici generation mechanism leads us to propose a novel two stage equalizer whose complexity apart from the fft is linear in the ofdm symbol length the first stage applies optimal linear preprocessing to restrict ici support and the second stage uses iterative mmse estimation to estimate finite alphabet frequency domain symbols simulation results indicate that our equalizer has significant performance and complexity advantages over the classical linear mmse estimator in doubly selective channels

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

a discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws abstract we present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities under a suitable multidimensional generalization of the whitham relaxation subcharacteristic condition we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

stable numerical methods for conservation laws with discontinuous flux function abstract we develop numerical methods for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients using a relaxation approximation the nonlinear equation is transformed to a semilinear diagonalizable problem with linear characteristic variables eulerian and lagrangian methods are used for the advection stage while an implicit explicit scheme solves the relaxation stage the main advantages of this approach are neither riemann problem solvers nor linear iterations are required during the solution process moreover the characteristic based relaxation method is unconditionally stable such that no cfl conditions are imposed on the selection of time steps numerical results are shown for models on traffic flows and two phase flows

new non linear modelling for vibration analysis of a straight pipe conveying fluid abstract a new non linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends using the euler bernoulli beam theory and the non linear lagrange strain theory from the extended hamilton s principle the coupled non linear equations of motion for the longitudinal and transverse displacements are derived these equations of motion are discretized by using the galerkin method after the discretized equations are linearized in the neighbourhood of the equilibrium position the natural frequencies are computed from the linearized equations on the other hand the time histories for the displacements are also obtained by applying the generalized time integration method to the non linear discretized equations the validity of the new modelling is provided by comparing results from the proposed non linear equations with those from the equations proposed by paidoussis

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

channel estimation for ofdma uplink a hybrid of linear and bem interpolation approach we consider the channel estimation for the subband orthogonal frequency division multiple access ofdma uplink the channel for each subband is modeled by combing the linear and fourier basis expansion functions based on this mode a two dimensional interpolation approach is proposed for the channel estimation which is carefully investigated in terms of estimation error and pilot placement

composite scheme using localized relaxation with non standard finite difference method for hyperbolic conservation laws non standard finite difference methods nsfdm introduced by mickens non standard finite difference models of differential equations world scientific singapore 1994 are interesting alternatives to the traditional finite difference and finite volume methods when applied to linear hyperbolic conservation laws these methods reproduce exact solutions in this paper the nsfdm is first extended to hyperbolic systems of conservation laws by a novel utilization of the decoupled equations using characteristic variables in the second part of this paper the nsfdm is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws the original nsfdms introduced by mickens 1994 were not in conservation form which is an important feature in capturing discontinuities at the right locations mickens construction and analysis of a non standard finite difference scheme for the burgers fisher equations journal of sound and vibration 257 4 2002 791 797 recently introduced a nsfdm in conservative form this method captures the shock waves exactly without any numerical dissipation in this paper this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks as a remedy to this defect we use the strategy of composite schemes r liska b wendroff composite schemes for conservation laws siam journal of numerical analysis 35 6 1998 2250 2271 in which the accurate nsfdm is used as the basic scheme and localized relaxation nsfdm is used as the supporting scheme which acts like a filter relaxation schemes introduced by jin and xin the relaxation schemes for systems of conservation laws in arbitrary space dimensions communications in pure and applied mathematics 48 1995 235 276 are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi linear system with a stiff relaxation term the relaxation parameter is chosen locally on the three point stencil of grid which makes the proposed method more efficient this composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme as demonstrated by the test cases together with comparisons with popular numerical methods like roe scheme and eno schemes

numerical methods for hyperbolic conservation laws with stiff relaxation i spurious solutions the author considers the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed uniform spatial grid it is conjectured that certain a priori criteria ensure that the numerical method does not produce spurious solutions as the relaxation time vanishes one criterion is that the limits of vanishing relaxation time and vanishing viscosity commute for the viscous regularization of the hyperbolic system a second criterion is that a certain subcharacteristic condition be satisfied by the hyperbolic system this conjecture is supported with analytical and numerical results for a specific example the solution of generalized riemann problems of a model system of equations with a fractional step scheme in which godunov s method is coupled with the backward euler method similar ideas are applied to the numerical solution of stiff detonation problems

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

nondata aided joint channel estimation and equalization for ofdm systems in very rapidly varying mobile channels this paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization maximum a posteriori probability sage map technique which is particularly well suited to multicarrier signal formats the algorithm is implemented in the time domain which enables one to use the gaussian approximation of the transmitted ofdm samples consequently the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate ser performance based on this gaussian approximation the exact bayesian cramer rao lower bound crlb as well as the convergence rate of the algorithm are derived analytically to reduce the computational complexity of the algorithm discrete legendre orthogonal basis functions are employed to represent the rapidly time varying fading channel it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal the computational complexity of the algorithm is shown to be o nl per detected data symbol and per sage map algorithm cycle where is the number of ofdm subcarriers and is the number of multipath components

numerical passage from kinetic to fluid equations a numerical way to pass from the bhatnagar gross krook model of the boltzmann equation to compressible euler equations is presented in order to do so a stable discretization of the kinetic equati

non linear vibration of a flexible spinning disc with angular acceleration non linear dynamic responses are analyzed for a flexible spinning disc with angular acceleration based on the kirchhoff plate theory and the von karman strain theory non linear equations of motion are derived which are coupled equations between the radial tangential and transverse displacements the equations of motion are discretized by using the galerkin method from the discretized equations the dynamic responses are computed by the generalized time integration method the analysis results show the effects of angular acceleration on the dynamic responses

a kinetic construction of global solutions of first order quasilinear equations on considere le probleme de cauchy pour des equations quasilineaires d ordre 1 de type conservation dans la region t 0 u t i 1 u a i u x i 0 u x o u o x ou x x 1 x n u u x t et a i i 1 n sont des fonctions continument differentiables a valeurs reelles d une seule variable reelle

dynamic stability of a semi circular pipe conveying harmonically oscillating fluid the dynamic stability of a semi circular pipe conveying harmonically oscillating fluid is investigated in this study for analysis harmonically oscillating flow is regarded as a parametrically excited system with time varying coefficients considering the extensibility and nonlinearity of the semi circular pipe the equations of motion and the associated boundary conditions are obtained by using the extended hamilton principle applying floquet theory to the derived equations the stability of the pipe is analyzed for variations of the amplitude and oscillating frequency of the fluid velocity the effects of the mean value for the fluid velocity on the stability are also analyzed it is found that the semi circular pipe may become unstable when the fluctuation frequency approaches some multiples or sum of the out of plane natural frequencies furthermore it is observed that the instability regions increase with the mean value of the velocity the results obtained via the stability analysis are verified by time responses computed by using a direct time integration method

frequency selective fading channel estimation with a polynomial time varying channel model a rectangular windowed least squares estimator using a polynomial model of the time varying channel taps is proposed for estimating the impulse response of a frequency selective fading channel this method provides a significant improvement in mean square identification error msie over the conventional least mean squares lms and the exponentially weighted recursive least squares ew rls algorithms without a polynomial model a detailed study of the effects of channel parameters such as the fading rate and the signal to noise ratio on the proposed method is carried out the performance of the method depends on the window size of the least squares estimator and the polynomial order being used algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well

orthogonal frequency division multiplexing with index modulation in this paper a novel orthogonal frequency division multiplexing ofdm scheme called ofdm with index modulation ofdm im is proposed for operation over frequency selective and rapidly time varying fading channels in this scheme the information is conveyed not only by m ary signal constellations as in classical ofdm but also by the indices of the subcarriers which are activated according to the incoming bit stream different low complexity transceiver structures based on maximum likelihood detection or log likelihood ratio calculation are proposed and a theoretical error performance analysis is provided for the new scheme operating under ideal channel conditions then the proposed scheme is adapted to realistic channel conditions such as imperfect channel state information and very high mobility cases by modifying the receiver structure the approximate pairwise error probability of ofdm im is derived under channel estimation errors for the mobility case several interference unaware aware detection methods are proposed for the new scheme it is shown via computer simulations that the proposed scheme achieves significantly better error performance than classical ofdm due to the information bits carried by the indices of ofdm subcarriers under both ideal and realistic channel conditions

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

vibration analysis of a flexible rotating disk with angular misalignment abstract the dynamic characteristics and responses of a flexible rotating disk are analyzed when the disk has angular misalignment that is defined by the angle between the rotation and symmetry axes based on the von karman strain theory and the kirchhoff plate theory three equations of motion are derived for the transverse radial and tangential displacements when the disk has angular misalignment the derived equations are fully coupled partial differential equations through the transverse radial and tangential displacements in particular the equation of transverse motion is non linear while the others are linear after these partial differential equations and the associated boundary conditions are transformed into a weak form the weak form is discretized to a non linear matrix vector equation by using the finite element method the non linear equation is linearized in the neighbourhood of a dynamic equilibrium position and then the natural frequencies and mode shapes are computed in addition the dynamic time responses are obtained by applying the generalized method the effects of angular misalignment on the natural frequencies the mode shapes and the dynamic responses are investigated the analysis shows that the angular misalignment causes the natural frequency split and the out of plane mode with only one nodal diameter and no nodal circle has the largest frequency split it is also found that the angular misalignment yields the amplitude modulations in the transverse radial and tangential dynamic responses