statistical condition estimation for linear systems the standard approach to measuring the condition of a linear system compresses all sensitivity information into one number thus a loss of information can occur in situations in which the standard condition number with respect to inversion does not accurately reflect the actual sensitivity of a solution or particular entries of a solution it is shown that a new method for estimating the sensitivity of linear systems addresses these difficulties the new procedure measures the effects on the solution of small random changes in the input data and by properly scaling the results obtains reliable condition estimates for each entry of the computed solution moreover this approach which is referred to as small sample statistical condition estimation is no more costly than the standard 1 norm or power method 2 norm condition estimates and it has the advantage of considerable flexibility for example it easily accommodates restrictions on or structure associated with allowable perturbations the method also has a rigorous statistical theory available for the probability of accuracy of the condition estimates however it gives no estimate of an approximate null vector for nearly singular systems the theory of this approach is discussed along with several illustrative examples

the boundary condition at an impedance wall in a non uniform duct with potential mean flow the boundary condition at an impedance wall in a duct with a steady mean flow requiring the specification of the normal component of acoustic particle velocity is examined it is found that when implemented in the weak formulation of the finite element method it can be considerably simplified the boundary condition would appear to require data which includes the tangential derivative of the tangential mean flow velocity the normal derivative of the normal component of mean flow velocity and the derivatives of the mean flow density and the boundary admittance along the boundary it is shown that with suitable rearrangement the normal and tangential velocity derivatives can be eliminated as can the derivatives of the mean flow density and admittance the boundary condition becomes only slightly more complicated than the corresponding boundary condition when mean flow is absent and is no more difficult to implement requiring only local values of tangential mean flow velocity density and admittance which are already required as data for the weak formulation of the field equation

on the acoustics of low mach number bulged throated and baffled nozzles abstract the acoustic wave equation for quasi one dimensional propagation along a duct of varying cross section containing a low mach number mean flow is obtained section 2 by using as variables either the potential or the velocity section 2 1 the ray approximation that holds only for wavelengths which are short compared with the length scales of the variation of the cross section and mean flow velocity is used as a factor to reduce the wave equation to a schrodinger form section 2 2 it is shown that the latter reduced form for the potential is the most convenient for studying the acoustics of catenoidal section 2 3 and sinusoidal section 3 1 nozzles it is found that these inherit respectively the filtering properties of catenoidal horns and transparency properties of sinusoidal horns this approach also applies to the exponential nozzle section 3 3 whereas for the gaussian nozzle the sound field can be expressed in terms of hermite functions by using a semi reduced form section 3 2 of the wave equations the exact solutions of the nozzle wave equation section 3 for the four families of ducts are plotted section 4 as amplitude and phase versus distance for several combinations of frequency and low mach number the nozzle families considered include the catenoidal in figures 1 2 6 9 in section 4 1 the sinusoidal figures 3 10 11 and exponential figures 5 12 13 in section 4 2 and the first six eigenfunctions of gaussian nozzles figures 4 14 17 in section 4 3 the various cases presented here are applications of a technique which derives the acoustics of low mach number nozzles from that of the corresponding horns i e ducts of the same cross section but without mean flow

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

weighted scale free networks with variable power law exponents abstract we present a weighted scale free network model in which the power law exponents can be controlled by the model parameters the network is generated through the weight driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links the simplicity of the model enables us to derive analytically the various statistical properties such as the distributions of degree strength and weight the degree strength and degree weight relationship and the dependencies of these power law exponents on the model parameters finally we demonstrate that networks of words coauthorship of researchers and collaboration of actor actresses are quantitatively well described by this model

comments on transfer function synthesis using frequency response data frequency response data constitute a good basis for transfer function synthesis when using appropriate techniques for frequency response approximation not all of the numerous existing methods yield excellent results whitfield 1986 discussed various methods with the aid of examples his statement that the frequency approximation technique of stahl 1984 often yields divergent results is only correct when using the iterative matrix adaptation method in conjunction with the least squares cost function however applying the direct solution method as introduced by stahl 1984 all the approximation results of whitfield 1986 can be improved

effects of attachment preferences on coevolution of opinions and networks abstract in the coevolution of network structures and opinion formation we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures it has been found that a heterogeneous network structure is easier to be reached with more high degree preferential hdp nodes there exists high correlation between the convergence time and the network heterogeneity the heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network with preferential attachment and long time evolvement most of the nodes would become separated and only a few leaders would have immediate neighbors analytical calculations based on mean field theory reveal that both the transition point p t r and the consensus time depend upon the standard deviation of the degree distribution d p t r increases while decreases with the rise of d functions of p t r k k 1 and a n k d 2 k are found theoretical analyses are in accordance with simulation data

multimodal admittance method in waveguides and singularity behavior at high frequencies this work presents a multimodal method for the propagation in a waveguide with varying height and its relation to trapped modes or quasi trapped modes the coupled mode equations are obtained by projecting the helmholtz equation on the local transverse modes to solve this problem we integrate the riccati equation governing the admittance matrix dirichlet to neumann operator for many propagating modes i e at high frequencies the numerical integration of the riccati equation shows that the rule is that this matrix has quasi singularities associated to quasi trapped modes

a study of wave propagation in varying cross section waveguides by modal decomposition part i theory and validation the propagation of acoustic waves in waveguides with variable cross section is considered using multimodal decomposition the approach adopted is to construct two infinite first order differential equations for the components of the pressure and the velocity projected over the normal modes from these an infinite matricial riccati equation is derived for the impedance matrix these equations are ordinary differential equations that can be integrated after truncation at a sufficient number of modes and take into account the coupling between modes the stiffness of the pressure velocity equations induced by the presence of evanescent modes is avoided by first calculating the impedance matrix along the guide the method is checked using different examples where the solutions of the plane wave approximation or the finite element method are known results show the method provides simple and accurate means to obtain the acoustic field with correct boundary conditions in a nonuniform guide with no restriction on the flare

asymptotic behaviour of transfer function synthesis methods this paper presents an analysis of the asymptotic behaviour of the solutions to various iterative linear least squares methods that synthesize transfer functions from frequency response data the methods of sanathanan and koerner and lawrence and rogers are shown to possess asymptotic solutions that do not coincide with the solution to a fundamental non linear least squares criterion several methods with more appropriate asymptotic behaviour are then suggested the analytical tools presented should allow analysis of conditions for the convergence of iterative linear least squares methods

plant rational transfer approximation from input output data a rational transfer function model of the plant is generally desirable in feedback system design when only plan input and output data are available over finite sometimes incomplete time intervals this is especially so in a recent exact design technique for highly uncertain time varying and non linear plants here the plants are replaced rigorously by an equivalent linear time invariant plant set existing numerical techniques were found inadequate especially in the high frequency range which is important in the design of feedback systems with large plant uncertainty a technique was developed with excellent results even for noisy data unstable and non minimum phase plants and severely truncated time intervals the transfer function is calculated directly without derivation of the input output signal transforms the operations involve repeated integrations of the data numerous examples are included

clogging and self organized criticality in complex networks we propose a simple model that aims at describing in a stylized manner how local breakdowns due to imbalances or congestion propagate in real dynamical networks the model converges to a self organized critical stationary state in which the network shapes itself as a consequence of avalanches of rewiring processes depending on the model s specification we obtain either single scale or scale free networks we characterize in detail the relation between the statistical properties of the network and the nature of the critical state by computing the critical exponents the model also displays a nontrivial sudden collapse to a complete network

on linear and non linear wave equations for the acoustics of high speed potential flows the wave equation is derived for the acoustic potential in the following cases a linear non linear sound waves respectively of small large amplitude b medium at rest or steady potential flow the latter either of low mach number or high speed c three dimensional propagation in free space or quasi one dimensional acoustics of ducts of varying cross section thus there are 2 3 2 12 cases for which 34 distinct forms of the wave equations are derived table 1 of these 16 forms of the wave equation in 10 cases appear explicitly in the references given the wave equations are derived from a variational principle for linear sound part 1 and checked by elimination among the equations of potential unsteady flow for non linear acoustics part ii it is shown that the non linear wave equations partly new can be written in a form similar to the linear acoustics ones mostly known by taking into account the self convection of sound by sound this implies replacing the linear local and material derivatives byself convected and non linear extensions of these table 2 which also affect the sound speed

reconstruction of linear and non linear continuous time system models from input output data using the kernel invariance algorithm abstract a new kernel invariance algorithm kia is introduced to determine both the significant model terms and estimate the unknown parameters in non linear continuous time differential equation models of unknown systems

model order reduction for large systems in computational electromagnetics abstract this paper examines classical model order reduction mor strategies in view of the particular properties and needs of computational electromagnetism hereby reduced models are mainly needed for two reasons the fast calculation of certain characteristics such as the transfer behavior over a range of excitation frequencies especially for highly resonant systems and the generation of macromodels such as equivalent circuits simplifying coupled simulations in the first case the computational cost of the method is of main interest while in the second one the size of the reduced model as well as the conservation of stability and passivity plays a major role the considered methods partial realization moment matching and modal extraction are well known and have been investigated for about two decades now however their efficiency appears in a different light if the number of unknowns reaches hundreds of thousands or even millions this paper compares the suitability and efficiency of the mentioned methods for lossless or weakly lossy structures discretized by the finite integration theory fit close relations and even transitions between the algorithms are shown finally some specific properties of fit enable the application of a method called two step lanczos tsl a successive application of partial realization and moment matching which is highly efficient in both computation time and model size while preserving the passivity of the reduced models tsl allows to compute the broadband transfer behavior of systems with hundreds of thousands of unknowns within minutes on a standard pc additionally the resulting model can easily be implemented as a physical electric equivalent circuit

the impact of connection density on scale free distribution in random networks abstract preferential attachment is considered as a fundamental mechanism that contributes to the scale free characteristics of random networks which include growth and non growth networks there exist some situations of non growth random networks particularly for very sparse or dense networks where preferential attachments cannot consequentially result in true scale free features but only in scale free like appearances this phenomenon implies that a close relationship exists between the connection density p and the scaling in this study we propose a self organized model with constant network size to study the phenomenon we show analytically and numerically that there exists a certain critical point p c only when p p c the random network evolves into steady scale free state otherwise the network exhibits a steady scale free like state the closer the p approximates p c the closer the scale free like distribution approximates the true scale free distribution our results show that in random network lack of growth a preferential scheme does not necessarily lead to a scale free state and a formation of scale free is a consequence of two mechanisms i a preferential scheme and ii appropriate connection density

a realization approach to stochastic model reduction the problem of discrete time stochastic model reduction approximation is considered using the canonical correlation analysis approach of akaike 1975 a new order reduction algorithm is developed furthermore it is shown that the inverse of the reduced order realization is asymptotically stable next an explicit relationship between canonical variables and the linear least squares estimate of the state vector is established using this a more direct approach for order reduction is presented and also a new design for reduced order kalman filters is developed finally the uniqueness and symmetry properties for the new realization the balanced stochastic realization along with a simulation result are presented

quasistatic scale free networks the nodal degree distribution function of a scale free net work sfn has a power law tail 1 empirical data obtainedfor several social biological and computational networkshave con rmed the existence of such probability distribu tions decaying as power laws 2 4 for example the world wide web 5 which is a network of web pages and the hy perlinks among various pages and the internet network 6 ofrouters or autonomous systems follow power laws as p k k

note on the relation between pole zero location and input output behaviour of siso systems and its influence on controller design linear time invariant completely controllable and observable systems can be described for example by state equations transfer functions or time responses due to specific test signals all these descriptions are uniquely related for a given system where different state representations are possible by use of equivalence transformations however a whole class of different systems characterized by an infinite number of different pole zero patterns exhibits the same input output behaviour within drawing accuracy i e the plots coincide to the point of indistinguishability this effect is demonstrated and it may have implications on such fields as system modelling model order reduction and controller design

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

discontinuous galerkin methods with plane waves for time harmonic problems a general framework for discontinuous galerkin methods in the frequency domain with numerical flux is presented the main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element the method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two dimensional linearized euler equations it is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high order drp schemes in addition the conditioning of the method is found to be high but not critical in practice it is shown that the ultra weak variational formulation is in fact a subset of the present discontinuous galerkin method a special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles aeroacoustic problems with non uniform flows are also considered and results are presented for the sound radiated from a two dimensional jet

frequency domain prediction of turbofan noise radiation this paper describes a frequency domain numerical method for predicting noise radiation from ducted fans including acoustic treatment and non uniform background flow effects the method solves the euler equations linearized about a mean flow in the frequency domain a pseudo time derivative term is added to the frequency domain equations so that a time marching technique can be employed to drive the acoustic field to steady state explicitly this approach makes distributed parallel computing more viable for equations of this type and will allow for future use of well known convergence acceleration techniques such as multigrid to obtain the solutions efficiently simulations of the jt15d static test inlet are performed including the effects of liners and the results are compared with experimental data a generic engine geometry is used for demonstrating further the prediction capability of the code calculating the attenuation effects of different liner impedances and liner installation locations on the radiated sound fields

exact integration scheme for planewave enriched partition of unity finite element method to solve the helmholtz problem in this paper we present an exact integration scheme to compute highly oscillatory integrals that appear in the solution of the two dimensional helmholtz problem using the planewave enriched partition of unity finite element method in the proposed scheme such oscillatory integrals are computed by a recursive application of the divergence theorem eventually expressing the integrals in terms of evaluations of the corresponding integrands at the nodes of the finite element mesh the number of such function evaluations is independent of the wave number kk which permits the scheme to be used for arbitrary high values of kk we consider finite element meshes with unstructured triangular and structured rectangular elements and present numerical results for three canonical benchmark helmholtz problems to demonstrate the accuracy and efficacy of the method

lamb wave propagation in elastic waveguides with variable thickness the problem of lamb wave propagation in waveguides with varying height is treated by a multimodal approach the technique is based on a rearrangement of the equations of elasticity that provides a new system of coupled mode equations preserving energy conservation these coupled mode equations avoid the usual problem at the cut offs with zero wavenumber thereafter we define an impedance matrix that is governed by a riccati equation yielding a stable numerical computation of the solution incidentally the versatility of the multimodal method is exemplified by treating analytically the case of slowly varying guide and by showing how to get easily the green tensor in any geometry the method is applied for a waveguide whose height is described by a gaussian function and the energy conservation in verified numerically we determine the green tensor in this geometry

frequency response computation via trigonometric continued fraction an efficient algorithm for computing the frequency response of discrete time systems described by rational transfer functions is presented the algorithm is simple fast recursive and can be used for equally or unequally spaced frequencies based on an initial expansion of the system transfer function to a novel jacobi type trigonometric continued fraction the algorithm proposed permits all operations to be performed by real arithmetic guarantees real results saves a number of operations and produces accurate results the algorithm is easily programmable and needs only 2nn real multiplications divisions for evaluating the frequency response of an nth order system at n different frequencies

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

dispersion analysis of plane wave discontinuous galerkin methods summary the plane wave dg pwdg method for the helmholtz equation was introduced and analyzed in gittelson c hiptmair r and perugia i plane wave discontinuous galerkin methods analysis of the h version math model numer anal 43 2009 297 331 as a generalization of the so called ultra weak variational formulation see o cessenat and b despres application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz equation siam j numer anal 35 1998 pp 255 299 the method relies on trefftz type local trial spaces spanned by plane waves of different directions and links cells of the mesh through numerical fluxes in the spirit of dg methods we conduct a partly empirical dispersion analysis of the method in a discrete translation invariant setting by studying the mismatch of wave numbers of discrete and continuous plane waves traveling in the same direction we find agreement of the wave numbers for directions represented in the local trial spaces for other directions the pwdg methods turn out to incur both phase and amplitude errors this manifests itself as a pollution effect haunting the h version of the method our dispersion analysis allows a quantitative prediction of the strength of this effect and its dependence on the wave number and number of plane waves copyright 2014 john wiley sons ltd

the partition of unity finite element method for short wave acoustic propagation on non uniform potential flows a novel numerical method is proposed for modelling time harmonic acoustic propagation of short wavelength disturbances on non uniform potential flows the method is based on the partition of unity finite element method in which a local basis of discrete plane waves is used to enrich the conventional finite element approximation space the basis functions are local solutions of the governing equations they are able to represent accurately the highly oscillatory behaviour of the solution within each element while taking into account the convective effect of the flow and the spatial variation in local sound speed when the flow is non uniform many wavelengths can be included within a single element leading to ultra sparse meshes results presented in this article will demonstrate that accurate solutions can be obtained in this way for a greatly reduced number of degrees of freedom when compared to conventional element or grid based schemes numerical results for lined uniform two dimensional ducts and for non uniform axisymmetric ducts are presented to indicate the accuracy and performance which can be achieved numerical studies indicate that the pollution effect associated with cumulative dispersion error in conventional finite element schemes is largely eliminated

special short wave elements for flow acoustics a numerical formulation based on the partition of unity method pum is proposed for modelling the propagation of short acoustic waves on irrotational mean flows the method seeks to reduce the pollution error which exists in conventional fe schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected helmholtz equation initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging diverging duct with mean flow next a simple two dimensional model of a straight duct with uniform flow is considered in both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and mach number characteristic of aero engine bypass ducts

a unified derivation and critical review of modal approaches to model reduction six of the most commonly used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables in this representation the derivation and the cross comparison of the various methods are greatly facilitated each method is then analysed to determine key characteristics i e i steady state agreement ii initial value agreement iii independence of the reduced model on the choice of retained state variables and inputs and iv eigen vector orientation realistic large scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically these studies reveal some important and often unrecognized weaknesses of several traditional techniques and confirm the strength of the newly developed technique of litz

scale free networks via attaching to random neighbors abstract preferential attachment is considered one of the key factors in the formation of scale free networks however complete random attachment without a preferential mechanism can also generate scale free networks in nature such as protein interaction networks in cells this article presents a new scale free network model that applies the following general mechanisms i networks expand continuously by the addition of new vertices and ii new vertices attach to random neighbors of random vertices that are already well connected the proposed model does not require global based preferential strategies and utilizes only the random attachment method theoretical analysis and numerical simulation results denote that the proposed model has steady scale free network characteristics and random attachment without a preferential mechanism may generate scale free networks

self organized scale free networks growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale free feature in complex networks as characterized by an algebraic degree distribution there are situations particularly in biological networks where growth is absent or not important yet some of these networks still exhibit the scale free feature with a small degree exponent here we propose two classes of models to account for this phenomenon we show analytically and numerically that in the first model a spectrum of algebraic degree distributions with a small exponent can be generated the second model incorporates weights for nodes and it is able to generate robust scale free degree distribution with larger algebraic exponents our results imply that it is natural for a complex network to self organize itself into a scale free

fingerprinting networks correlations of local and global network properties in complex networks a common task is to identify the most important or central nodes there are several definitions often called centrality measures which often lead to different results here we introduce fingerprints of networks which we define as correlation plots of local and global network properties we show that these fingerprints are suitable tools for characterizing networks beyond single quantity distributions in particular we study the correlations between four local and global measures namely the degree the shortest path betweenness the random walk betweenness and the subgraph centrality on different random network models like erd s renyi small world and barabasi albert as well as on different real networks like metabolic pathways social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models the correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world

an improved partition of unity finite element model for diffraction problems the partition of unity finite element method pufem is explored and improved to deal with practical diffraction problems efficiently the use of plane waves as an external function space allows an efficient implementation of an approximate exterior non reflective boundary condition improving the original proposed by higdon for general diffraction problems a virtually analytical integration procedure is introduced for multi dimensional high frequency problems which exhibits a dramatic decrease in the number of operations for a given error compared with standard integration methods suitable conjugate gradient type solvers for the whole range of wavenumbers are used including such cases in which pufem can produce nearly singular matrices caused by round off limits copyright 2001 john wiley sons ltd

non reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow we consider a time harmonic acoustic scattering problem in a 2d infinite waveguide with walls covered with an absorbing material in the presence of a mean flow assumed uniform far from the source to make this problem suitable for a finite element analysis the infinite domain is truncated this paper concerns the derivation of a non reflecting boundary condition on the artificial boundary by means of a dirichlet to neumann dtn map based on a modal decomposition compared with the hard walled guide case several difficulties are raised by the presence of both the liner and the mean flow in particular acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft walled guide however an accurate approximation of the dtn map can be derived using some bi orthogonality relations valid asymptotically for high order modes numerical validations show the efficiency of the method the influence of the liner with or without mean flow is illustrated

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

transfer function synthesis using frequency response data various linear least squares methods for transfer function synthesis from frequency response data are presented in a unified format solutions are derived from householder transformations and recursive least squares an alternative formulation derived from a time domain error criterion is also shown to be of the linear least squares type the comparative performance of the various methods is illustrated by several examples

a three dimensional hybrid finite element spectral analysis of noise radiation from turbofan inlets this paper describes a new three dimensional 3d analysis of tonal noise radiated from non axisymmetric turbofan inlets the novelty of the method is in combining a standard finite element discretisation of the acoustic field in the axial and radial coordinates with a fourier spectral representation in the circumferential direction the boundary conditions at the farfield fan face and acoustic liners are treated using the same spectral representation the resulting set of discrete acoustic equations are solved employing the well established bicgstab or qmr iterative algorithms and a very effective specialised preconditioner based on the axisymmetric mean geometry and flow field numerical examples demonstrate the suitability of the new method to engine configurations with realistic 3d features such as relatively large degrees of asymmetry and spliced acoustic liners the examples also illustrate the two advantages of the new method over a traditional 3d finite element approach the new method requires a significantly smaller number of unknowns as relatively few circumferential fourier modes in the spectral solution ensure an accurate field representation also due to the effective preconditioner the spectral linear solver benefits from stable iterations at a high rate of convergence

improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow we present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment the method relies on a variational formulation of the problem which allows to derive a multimodal formulation within a rigorous mathematical framework notably to properly account for the boundary conditions on the walls being locally the myers condition and the neumann condition otherwise also the method uses an enriched basis with respect to the usual cosine basis able to absorb the less converging part of the modal series and thus to improve the convergence of the method using the cosine basis the modal method has a low convergence 1 n with n the order of truncation using the enriched basis the improvement in the convergence is shown to depend on the mach number from 1 n5 to roughly 1 n1 5 for m 0 to m close to unity the case of a continuously varying wall impedance is considered and we discuss the limiting case of piecewise constant impedance which defines pressure edge conditions at the impedance discontinuities

exact solution for the time evolution of network rewiring models we consider the rewiring of a bipartite graph using a mixture of random and preferential attachment the full mean field equations for the degree distribution and its generating function are given the exact solution of these equations for all finite parameter values at any time is found in terms of standard functions it is demonstrated that these solutions are an excellent fit to numerical simulations of the model we discuss the relationship between our model and several others in the literature including examples of urn backgammon and balls in boxes models the watts and strogatz rewiring problem and some models of zero range processes our model is also equivalent to those used in various applications including cultural transmission family name and gene frequencies glasses and wealth distributions finally some voter models and an example of a minority game also show features described by our model

identification of linear dynamic systems using piecewise constant excitations use misuse and alternatives abstract time domain identification of linear dynamic systems using discrete time models relies heavily on the use of piecewise constant excitation signals zoh assumption if this assumption is not met severe errors can be generated and the results can be useless in this article we study the implications of the zoh assumption and an alternative is formulated this leads to frequency domain identification methods based on the band limited assumption that the signals obey the shannon sampling theory the theory and practical aspects of both approaches are compared finally it will be shown that periodic excitations or perturbation signals can offer significant advantages in both approaches

a comparison of wave based discontinuous galerkin ultra weak and least square methods for wave problems several numerical methods using non polynomial interpolation have been proposed for wave propagation problems at high frequencies the common feature of these methods is that in each element the solution is approximated by a set of local solutions they can provide very accurate solutions with a much smaller number of degrees of freedom compared to polynomial interpolation there are however significant differences in the way the matching conditions enforcing the continuity of the solution between elements can be formulated the similarities and discrepancies between several non polynomial numerical methods are discussed in the context of the helmholtz equation the present comparison is concerned with the ultra weak variational formulation uwvf the least squares method lsm and the discontinuous galerkin method with numerical flux dgm an analysis in terms of trefftz methods provides an interesting insight into the properties of these methods second the uwvf and the lsm are reformulated in a similar fashion to that of the dgm this offers a unified framework to understand the properties of several non polynomial methods numerical results are also presented to put in perspective the relative accuracy of the methods the numerical accuracies of the methods are compared with the interpolation errors of the wave bases

a comparison of two trefftz type methods the ultraweak variational formulation and the least squares method for solving shortwave 2 d helmholtz problems trefftz methods for the numerical solution of partial differential equations pdes on a given domain involve trial functions which are defined in subdomains are generally discontinuous and are solutions of the governing pde or its adjoint within each subdomain the boundary conditions and matching conditions between subdomains must be enforced separately an interesting novel result presented in this paper is that the least squares method lsm and the ultraweak variational formulation two methods already established for solving the helmholtz equation can be derived in the framework of the trefftz type methods in the first case the boundary conditions and interelement continuity are enforced by means of a least squares procedure in the second a galerkin type weighted residual method is used another goal of the work is to assess the relative efficiency of each method for solving shortwave problems in acoustics and to study the stability of each method the numerical performance of each scheme is assessed with reference to two 2 d test problems acoustic propagation in an uniform soft walled duct and propagation in an l shaped domain the latter involving singular behaviour at a sharp corner

numerical experiments on acoustic reciprocity in compressible potential flows in ducts a reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with acoustically hard walls or with acoustically absorbing walls has been given in a companion publication it was found that for a source at a specified end of the duct suitably scaled reflection matrices in direct and reverse flow have a reciprocal relationship scaled transmission matrices obtained for direct flow and reversed flow with simultaneous switching of source location from one end to the other also have a reciprocal relationship a reverse flow theorem for the equivalent one dimensional propagation model which is a good approximation to the three dimensional model at low frequencies was also obtained in this case using reciprocity and acoustic power conservation arguments it is additionally found that the acoustic power transmission coefficient is the same for a source at either end of the duct for a given flow direction this result leads to an invariance theorem which relates acoustic power propagated due to sources of equal pressure amplitude at the two ends of the duct a numerical verification of these reciprocal relationships is given here for propagation in axially symmetric circular and annular ducts with multi modal propagation and at low frequencies when a one dimensional model is appropriate

frequency response computation via rational interpolation a simple rational interpolation method is given for estimating a frequency response matrix the method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms when coupled with a pole cancellation method the resulting interpolation algorithm is accurate and efficient the error in this procedure has the form of a modified response matrix which means that the interpolation algorithm can be used to approximate both the response matrix and the error

comparison of a finite element model with a multiple scales solution for sound propagation in varying ducts with swirling flows a multiple scales ms solution is proposed to study sound propagation in slowly varying ducts with mean swirling flows instead of the standard linearized euler equations the ms method is applied to the so called galbrun s equation this equation is based on an eulerian lagrangian description and corresponds to a wave equation written only in terms of the lagrangian perturbation of the displacement this yields simpler differential equations to solve for the ms model as well as simpler boundary conditions in this paper galbrun s equation is also solved by a mixed pressure displacement finite element method fem the proposed fem model has already been tested in authors previous papers this model is quite general and is extended here to arbitrary mean flows including compressibility and swirling flow effects some ms and fem solutions are then compared in order to validate both models

a generalized theory of preferential linking abstract there are diverse mechanisms driving the evolution of social networks a key open question dealing with understanding their evolution is how do various preferential linking mechanisms produce networks with different features in this paper we first empirically study preferential linking phenomena in an evolving online social network find and validate the linear preference we propose an analyzable model which captures the real growth process of the network and reveals the underlying mechanism dominating its evolution furthermore based on preferential linking we propose a generalized model reproducing the evolution of online social networks and present unified analytical results describing network characteristics for 27 preference scenarios we study the mathematical structure of degree distributions and find that within the framework of preferential linking analytical degree distributions can only be the combinations of finite kinds of functions which are related to rational logarithmic and inverse tangent functions and extremely complex network structure will emerge even for very simple sublinear preferential linking this work not only provides a verifiable origin for the emergence of various network characteristics in social networks but bridges the micro individuals behaviors and the global organization of social networks

on longitudinal acoustic propagation in convergent and divergent nozzle flows abstract the longitudinal propagation of sound in quasi one dimensional low mach number nozzle flow is considered in section 1 the solution in the ray approximation section 2 1 is used to transform the wave equation into a schrodinger form which is studied for the family of power law ducts including as a particular case the conical nozzle it is shown that the coincidence of flow sources sinks with sound sources can lead to appearance of essential singularities section 2 2 which can be removed by using a riccati transformation section 2 4 the exact solutions of the acoustic equations for the parabolic figure 1 and hyperbolic figure 2 nozzles are obtained in terms of bessel functions section 2 3 respectively of complex order and argument the general formulas together with limiting forms in the compactness ray and asymptotic approximations section 3 1 are used to establish properties of the acoustic velocity and pressure section 3 2 kinetic and compression energies and energy flux and wave action section 3 3 for example it is shown that the equipartition of energies for moderate variations in cross section gives way table 2 to a predominance of kinetic compression energies respectively near blockages openings the effects of non uniform mean flow table 1 are discussed by comparing horns with nozzles section 3 4 e g it is shown that the duality principle in three alternative forms does not extend from horn to nozzles and the acoustic equations have no elementary solutions for the latter in contrast with the former

a numerical integration scheme for special finite elements for the helmholtz equation the theory for integrating the element matrices for rectangular triangular and quadrilateral finite elements for the solution of the helmholtz equation for very short waves is presented a numerical integration scheme is developed samples of maple and fortran code for the evaluation of integration abscissae and weights are made available the results are compared with those obtained using large numbers of gauss legendre integration points for a range of testing wave problems the results demonstrate that the method gives correct results which gives confidence in the procedures and show that large savings in computation time can be achieved

bilinear transformation and generalized singular perturbation model reduction a new general bilinear relationship is found between continuous and discrete generalized singular perturbation reduced order models this result is applied to the problem of deriving discrete analogs of continuous singular perturbation and direct truncation model reduction and leads to a new definition of discrete nyquist model reduction also unit circle bilinear transformations are used to relate several known facts about continuous and discrete balanced model reduction and incorporate them into a symmetrical unified framework

bloch waves in periodic multi layered acoustic waveguides the band spectrum and associated floquet bloch eigensolutions arising in acoustic and electromagnetic waveguides which have periodic structure along the guide while remaining of finite width are found homogeneous dirichlet or neumann conditions along the guide walls or an alternation of them are taken importantly in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes geometric defects in the structured waveguide also create these modes numerical and asymptotic techniques identify dispersion curves and trapped modes some cases demonstrate maxima and minima of the spectral edges within the brillouin zone and also allow for ultraslow light or sound imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

scale free networks with a large to hypersmall world transition abstract recently there has been a tremendous interest in models of networks with a power law distribution of degree so called scale free networks it has been observed that such networks normally have extremely short path lengths scaling logarithmically or slower with system size as an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale free networks with linearly scaling distances furthermore by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances apparently slower than log log n which we call a hypersmall world regime we characterize the degree degree correlation and clustering properties of this class of networks

multicommunity weight driven bipartite network model community structure and rewiring phenomena exist in many complex networks particularly in bipartite networks we construct a model for the degree distribution of the rewiring problem in a multicommunity weight driven bipartite network mcwbn the network consists of many interconnected communities each of which holds a bipartite graph the bipartite graph consists of two sets of nodes we name each node in one set a producer and each node in the other set a consumer a weight value matrix defining the trade barrier between any two communities is used to characterize the structure of the communities which ensures the higher preferential attachment probability in intracommunity than in intercommunity the size of one producer is defined as the number of consumers connected to it we find that the nonlinear dynamics of the scale of production or the total size of all producers in each community is dependent only on the initial scale of production in each community and independent of the distribution of the producer size furthermore if the nonlinear system of the scale of production in each community is at an equilibrium state the distribution of the producer size in each community of the mcwbn model is equivalent to that in a one community model

numerical evaluation of the two dimensional partition of unity boundary integrals for helmholtz problems there has been considerable attention given in recent years to the problem of extending finite and boundary element based analysis of helmholtz problems to higher frequencies one approach is the partition of unity method which has been applied successfully to boundary integral solutions of helmholtz problems providing significant accuracy benefits while simultaneously reducing the required number of degrees of freedom for a given accuracy these benefits accrue at the cost of the requirement to perform some numerically intensive calculations in order to evaluate boundary integrals of highly oscillatory functions in this paper we adapt the numerical steepest descent method to evaluate these integrals for two dimensional problems the approach is successful in reducing the computational effort for most integrals encountered the paper includes some numerical features that are important for successful practical implementation of the algorithm

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

well posed boundary condition for acoustic liners in straight ducts with flow doi 10 2514 1 j050723 the myers boundary condition for acoustics within flow over an acoustic lining has been shown to be ill posed leading to numerical stability issues in the time domain and mathematical problems with stability analyses this paper gives a modification for flat or cylindrical straight ducts to make the myers boundary condition well posed and indeed more accurate by accounting for a thin inviscid boundary layer over the lining and correctly deriving the boundary condition to first order in the boundary layer thickness the modification involves two integraltermsovertheboundarylayer the firstmaybewrittenintermsofthemass momentum andkinetic energy thicknessesoftheboundarylayer whichareshownto physicallycorrespondtoamodifiedboundarymass modified grazingvelocity andatensionalongtheboundary thesecondintegral termisrelatedtothecriticallayerwithinthe boundary layer a time domain version of the new boundary condition is proposed although not implemented the modified boundary condition is validated against high fidelity numerical solutions of the pridmore brown equation for sheared inviscid flow in a cylinder absolute instability boundaries are given for certain examples though convective instabilities appear to always be present at certain frequencies for any boundary layer thickness

cluster growth poised on the edge of break up size distributions with small exponent power laws abstract in many naturally occurring growth processes cluster size distributions of power law form n s s with small exponents 0 1 are observed we suggest here that such distributions emerge naturally from cluster growth where size dependent aggregation is counterbalanced by size dependent break up the model used in the study is a simple reaction kinetic model including only monomer cluster processes it is shown that under such conditions power law size distributions with small exponents are obtained therefore the results suggest that the ubiquity of small exponent power law distributions is related to the growth process where aggregation driven cluster growth is poised on the edge of cluster break up

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

network evolution by different rewiring schemes many real world networks such as social networks are characterized by rearrangements of the links between nodes rewiring indeed very few natural networks are static in time and it is therefore important to study the properties of networks in which rewiring occurs in this paper two different rewiring schemes are formulated and compared using a general ordinary differential equation ode model the equilibrium distributions are analytically derived it is found that by uniformly choosing a node and a link connected to it rewiring from different ends of the link yields different equilibrium degree distributions rewiring from the neighbor generally produces more high degree nodes the equilibrium distributions of the ode model are compared with simulation results of the corresponding stochastic process for rewiring conditions are discussed under which our ode provides a good approximation for the mean of the corresponding stochastic process

the partition of unity finite element method for elastic wave propagation in reissner mindlin plates this paper reports a numerical method for modelling the elastic wave propagation in plates the method is based on the partition of unity approach in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment the technique is general such that it can be applied to the lagrangian family of finite elements with specific waveform enrichment schemes depending on the dominant modes of wave propagation in the physical system a four noded element for the reissner mindlin plate is derived in this paper which is free of shear locking such a locking free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain as a result the frequency dependent stiffness matrix and the mass matrix are obtained which capture the higher frequency response with even coarse meshes accurately the steps involved in the numerical implementation of such element are discussed in details numerical studies on the performance of the proposed element are reported by considering a number of cases which show very good accuracy and low computational cost copyright 2006 john wiley sons ltd

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

a method for linear model reduction using the input independent equation error the paper deals with the order reduction problem for single input single output linear dynamical systems combining the uniform approximation approach with the equation error formulation a simplification method is proposed which leads to input independent optimal models by a relatively simple calculation procedure

a mapped finite and infinite partition of unity method for convected acoustic radiation in axisymmetric domains a mapped infinite partition of unity method is developed to solve frequency domain acoustic applications for convected radiation in axisymmetric domains the paper presents the formulation and the discretization technique the partition of unity method is coupled with infinite elements based on the astley leis conjugated formulation the performances of the method are analysed on two applications convected propagation in an uniform duct and dipole radiation the aim of such a method compared to the classical finite element method is to solve shortwave applications with a respectable level of accuracy

analysis of high order finite elements for convected wave propagation in this paper we examine the performance of high order finite element methods fem for aeroacoustic propagation based on the convected helmholtz equation a methodology is presented to measure the dispersion and amplitude errors of the p fem including non interpolating shape functions such as bubble shape functions a series of simple test cases are also presented to support the results of the dispersion analysis the main conclusion is that the properties of p fem that make its strength for standard acoustics e g exponential p convergence low dispersion error remain present for flow acoustics as well however the flow has a noticeable effect on the accuracy of the numerical solution even when the change in wavelength due to the mean flow is accounted for and an approximation of the dispersion error is proposed to describe the influence of the mean flow also discussed is the so called aliasing effect which can reduce the accuracy of the solution in the case of downstream propagation this can be avoided by an appropriate choice of mesh resolution

a reverse flow theorem and acoustic reciprocity in compressible potential flows in ducts a reverse flow theorem for acoustic propagation in compressible potential flow has been obtained directly from the field equations without recourse to energy conservation arguments a reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with either acoustically rigid walls or acoustically absorbing walls follows it is found that for a source at a specific end of the duct suitably scaled reflection matrices in direct and reverse flow have a reciprocal relationship scaled transmission matrices obtained for direct flow and reversed flow with simultaneous switching of source location from one end to the other also have a reciprocal relationship a related reverse flow theorem specialized to one dimensional acoustic propagation has also been obtained reciprocity relationships for the scattering coefficients for propagation are derived and are found to be similar though much simpler than in the case of multi mode propagation in one dimensional flow reciprocal relations and power conservation arguments are used to show that scaled power reflection and transmission coefficients are invariant to flow reversal and switching of source location from one end of the duct to the other numerical verification of the reciprocal relationships is given in a companion paper

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

higher order distributions and nongrowing complex networks without multiple connections we study stochastic processes that generate nongrowing complex networks without self loops and multiple edges simple graphs the work concentrates on understanding and formulation of constraints which keep the rewiring stochastic processes within the class of simple graphs to formulate these constraints a different concept of wedge distribution paths of length 2 is introduced and its relation to degree degree correlation is studied the analysis shows that the constraints together with edge selection rules do not even allow the formulation of a closed master equation in the general case we also introduce a particular stochastic process which does not contain edge selection rules but which we believe can provide some insight into the complexities of simple graphs