on multivariate rayleigh and exponential distributions in this paper expressions for multivariate rayleigh and exponential probability density functions pdfs generated from correlated gaussian random variables are presented we first obtain a general integral form of the pdfs and then study the case when the complex gaussian generating vector is circular we consider two specific circular cases the exchangeable case when the variates are evenly correlated and the exponentially correlated case expressions for the multivariate pdf in these cases are obtained in integral form as well as in the form of a series of products of univariate pdfs we also derive a general expression for the multivariate exponential characteristic function cf in terms of determinants in the exchangeable and exponentially correlated cases cf expressions are obtained in the form of a series of products of univariate gamma cfs the cf of the sum of exponential variates in these cases is obtained in closed form finally the bivariate case is presented mentioning its main features while the integral forms of the multivariate pdfs provide a general analytical framework the series and determinant expressions for the exponential cfs and the series expressions for the pdfs can serve as a useful tool in the performance analysis of digital modulation over correlated rayleigh fading channels using diversity combining

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

nonparametric density estimation and detection in impulsive interference channels i estimators for pt i see ibid vol 42 no 2 4 p 1684 1697 1994 nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in part i the likelihood ratio test and the small signal locally optimum nonlinearity provide the basis for the formulation of these nonparametric detection schemes several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates in particular for the problem of detecting a known signal in impulsive noise two modifications to the standard likelihood ratio test are considered the first is adapted from robust statistics whereas the second the l sub 1 error based detector is specifically formulated for use with density estimates both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities from the merits of these two tests a new detection scheme that approximates the locally optimum nonlinearity is then developed this detector which uses the nonparametric density estimators developed in part i is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study this nonparametric density estimate based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise

projection method ii godunov ryabenki analysis this is the second of a series of papers on the subject of projection methods for viscous incompressible flow calculations the purpose of the present paper is to explain why the accuracy of the velocity approximation is not affected by 1 the numerical boundary layers in the approximation of pressure and the intermediate velocity field and 2 the noncommutativity of the projection operator and the laplacian this is done by using a godunov ryabenki type of analysis in a rigorous fashion by doing so we hope to be able to convey the message that normal mode analysis is basically sufficient for understanding the stability and accuracy of a finite difference method for the navier stokes equation even in the presence of boundaries as an example we analyze the second order projection method based on pressure increment formulations used by van kan and bell colella and glaz the leading order error term in this case is of o dt and behaves as high frequency oscillations over the whole domain compared with the o dt 1 2 numerical boundary layers found in the second order kim moin method

spurious transients of projection methods in microflow simulations the temporal behavior of projection methods for viscous incompressible lowreynolds number ows is adressed the methods considered result from algebraically splitting the linear system corresponding to each time step in such a way that the computation of velocity is segregated from that of pressure each method is characterized by two possibly equal approximate inverses b1 and b2 of the momentum equation velocity matrix plus a parameter which renders the method non incremental if 0 or incremental if 1 the classical rst order projection method together with more sophisticated methods perot s second order method yosida method pseudoexact factorization method and their incremental variants are put into the same algebraic form and their accuracy numerically tested splitting errors of rst

analysis of an exact fractional step method an exact fractional step or projection method for solving the incompressible navier stokes equations is analyzed the method is applied to both structured and unstructured staggered mesh schemes there are no splitting errors associated with the method it satisfies the incompressibility condition to machine precision and reduces the number of unknowns the exact projection technique is demonstrated on a two dimensional cavity flow and a multiply connected moving domain with a free surface its performance is compared directly to classic fractional step methods and shown to be roughly twice as efficient boundary conditions and the relationship of the method to streamfunction vorticity methods are discussed

analysis of an explicit and matrix free fractional step method for incompressible flows in this paper we present the analysis of an explicit and matrix free fractional step method for incompressible flows the presented method can be employed in either conservation or non conservation form the stabilization convergence and conservation aspects of the presented method are discussed a procedure for eliminating the first order error in time introduced by the split is proposed some benchmark steady and unsteady state examples are presented to demonstrate the proposed new aspects of the matrix free scheme

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

opportunistic group antenna selection in spatial modulation systems this paper proposes an opportunistic spatial modulation osm scheme where the transmit antennas are divided into k geq 1 equal groups and the best antenna from each group is selected to form a k transmit antenna subset for implementing spatial modulation sm thus the activation of one antenna from the subset to transmit one of the m ary modulation symbols achieves a data rate of log 2 k log 2 m bits per channel use notably special cases of osm include conventional sm and pure single transmit antenna selection to characterize and comparatively evaluate osm we first consider phase shift keying modulation and derive a closed form improved union bound of symbol error probability sep with a single antenna receiver explicit expressions for the sep in the high signal to noise ratio regime are also presented extensions to quadrature amplitude modulation analysis and simulations of multiple antenna reception case are also provided simulation results corroborate the analytical results and reveal the interesting interplay between the signal and spatial constellation diagrams for a given number of transmit antennas and targeted data rate asymptotically the sep can be minimized by using only one antenna group and the largest size of signal constellation as this configuration achieves the full diversity order

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

a new class of truly consistent splitting schemes for incompressible flows a new class of splitting schemes for incompressible flows is introduced the new schemes are based on a weak form of the pressure poisson equation and at each time step only require to solve a set of helmholtz type equations for the velocity and a poisson equation in the weak form for the pressure just as pressure correction and velocity correction schemes however unlike pressure correction and velocity correction schemes the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure

a coarse grid projection method for accelerating incompressible flow computations we present a coarse grid projection cgp method for accelerating incompressible flow computations which is applicable to methods involving poisson equations as incompressibility constraints the cgp methodology is a modular approach that facilitates data transfer with simple interpolations and uses black box solvers for the poisson and advection diffusion equations in the flow solver after solving the poisson equation on a coarsened grid an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid a particular version of the method is applied here to the vorticity stream function primitive variable and vorticity velocity formulations of incompressible navier stokes equations we compute several benchmark flow problems on two dimensional cartesian and non cartesian grids as well as a three dimensional flow problem the method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid a linear acceleration rate is obtained for all the cases we consider due to the linear cost elliptic poisson solver used with reduction factors in computational time between 2 and 42 the computational savings are larger when a suboptimal poisson solver is used we also find that the computational savings increase with increasing distortion ratio on non cartesian grids making the cgp method a useful tool for accelerating generalized curvilinear incompressible flow solvers

on the utility of laguerre series for the envelope pdf in multipath fading channels it is well known that multipath fading significantly affects the performance of communication systems in order to incorporate the impact of this random phenomenon on system analysis and design in many cases we need to calculate the probability density function pdf of the received signal envelope in multipath fading channels in this paper we consider a general multipath fading channel with arbitrary number of paths where the amplitudes of multipath components are arbitrary correlated positive random variables independent of phases whereas the phases are independent and identically distributed random variables with uniform distributions since the integral form of the envelope pdf for such a general channel model is too complicated to be used for analytic calculations we propose two infinite expansions for the pdf a laguerre series and a power series based on the tight uniform upper bounds on the truncation error of these two infinite series we show that the laguerre series is superior to the power series due to the fact that for a fixed number of terms it yields a smaller truncation error this laguerre series with a finite number of terms which expresses the envelope pdf just in terms of simple polynomial exponential kernels is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments where the number of strong multipath components is small

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

a discrete splitting finite element method for numerical simulations of incompressible navier stokes flows the presence of the pressure and the convection terms in incompressible navier stokes equations makes their numerical simulation a challenging task the indefinite system as a consequence of the absence of the pressure in continuity equation is ill conditioned this difficulty has been overcome by various splitting techniques but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity whenever introduced we present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions the non linear convection term can be treated by four different approaches and here we present a new linear implicit time scheme these two new techniques are implemented with a finite element method and numerical verifications are made copyright 2005 john wiley sons ltd

high order accurate solution of the incompressible navier stokes equations high order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation with this goal in mind the incompressible navier stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid the equations are integrated in time by a second order semi implicit method stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions the method is extended to three dimensions by a fourier expansion in every time step a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning the convergence properties of the iterative method are analyzed the order of accuracy of the method is demonstrated in numerical experiments the method is used to compute the flow in a channel the driven cavity and a constricted channel

algebraic fractional step schemes with spectral methods for the incompressible navier stokes equations the numerical investigation of a recent family of algebraic fractional step methods for the solution of the incompressible time dependent navier stokes equations is presented these methods are improved versions of the yosida method proposed in a quarteroni f saleri a veneziani factorization methods for the numerical approximation of navier stokes equations comput methods appl mech engrg 188 1 3 2000 505 526 a quarteroni f saleri a veneziani j math pures appl 9 78 5 1999 473 503 and one of them the yosida4 method is proposed in this paper for the first time they rely on an approximate lu block factorization of the matrix obtained after the discretization in time and space of the navier stokes system yielding a splitting in the velocity and pressure computation in this paper we analyze the numerical performances of these schemes when the space discretization is carried out with a spectral element method with the aim of investigating the impact of the splitting on the global accuracy of the computation

a class of fully second order accurate projection methods for solving the incompressible navier stokes equations in this paper a continuous projection method is designed and analyzed the continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the navier stokes n s equations in each time interval of a given time discretization the local truncation error lte analysis is applied to the continuous projection methods which yields a sufficient condition for the continuous projection methods to be temporally second order accurate based on this sufficient condition a fully second order accurate discrete projection method is proposed a heuristic stability analysis is performed to this projection method showing that the present projection method can be stable the stability of the present scheme is further verified through numerical experiments the second order accuracy of the present projection method is confirmed by several numerical test cases

distribution of the sum of two sine waves and gaussian noise the cumulative distribution of the envelope of the sum of two sine waves and narrowband gaussian noise the difference of the phases of the sine waves being uniformly distributed over 0 2 pi is expressed as an integral that is evaluated by numerical quadrature approximation for the distribution valid in the limit of large signal to noise ratio are derived the probability density function of the envelope is similarly treated

on the error estimates for the rotational pressure correction projection methods in this paper we study the rotational form of the pressure correction method that was proposed by timmermans minev and van de vosse we show that the rotational form of the algorithm provides better accuracy in terms of the h1 norm of the velocity and of the l2 norm of the pressure than the standard form

the equivalence of weak strong and complete convergence in l_1 for kernel density estimates theorem 1 let k be a nonnegative borel measurable function on rd with f k x dx 1 then the following conditions are equivalent i j 0 in probability as n oo some f ii jn o 0 in probability as n s oo all f iii jn s 0 almost surely as n oo all f iv jn 0 exponentially as n oc i e for all e 0 there exist r no 0 such that p jne no all f v lim0h 0 and limnnhd oo also v implies iv when k is merely absolutely integrable and f k x dx 1 0

boundary conditions for a divergence free velocity pressure formulation of the navier stokes equations new sets of boundary conditions for the velocity pressure formulation of the incompressible navier stokes equations are derived the boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution moreover the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure numerical experiments support the theoretical conclusions

numerical methods based on additive splittings for hyperbolic partial differential equations we derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds these techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales some of which are sometimes treated exactly the efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator this is analyzed and a technique is discussed for reducing this error through a simple change of variables a procedure for generating the appropriate boundary data for the intermediate solutions is also presented

projection method i convergence and numerical boundary layers this is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations the purpose of these papers is to provide a thorough understanding of the

parameter estimation for middleton class a interference processes the problem of estimating the parameters of the middleton class a interference model is considered on the assumption of the availability of a set of independent samples from class a envelope distribution the asymptotic performances of several estimation procedures are explored from this analysis estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient whereas more efficient likelihood based estimators are seen to be computationally unwieldy however an estimator that initiates likelihood iteration with the method of moments estimates is seen to overcome these difficulties in its asymptotic performance unfortunately simulation of this third estimator for practical sample sizes reveals poor performance under these conditions to overcome this lack of small sample efficiency a similar estimator that initiates likelihood iteration with physically motivated but nonoptimal estimates is also proposed simulation of this latter estimator for practical sample sizes indicates that near optimal performance is attained by this technique

on the pdf of the sum of random vectors there are various cases in physics and engineering sciences especially communications where one requires the envelope probability density function pdf of the sum of several random sinusoidal signals according to the correspondence between a random sinusoidal signal and a random vector the sum of random vectors can be considered as an abstract mathematical model for the above sum now it is desired to obtain the pdf of the length of the resulting vector considering the common and reasonable assumption of uniform distributions for the angles of the vectors many researchers have obtained the pdf of the length of the resulting vector only for special cases however in this paper the pdf is obtained for the most general case in which the lengths of vectors are arbitrary dependent random variables this pdf is in the form of a definite integral which may be inappropriate for analytic manipulations and numerical computations so an appropriate infinite laguerre expansion is also derived finally the results are applied to solve a typical example in computing the scattering cross section of random scatterers

on the accuracy of a numerical method for linear interfacial motion we present a new method to compute two dimensional linear interfacial motion which is governed by the unsteady stokes equations together with linearized interfacial conditions the method achieves second order accuracy for both the velocity and pressure in both fluids the order of accuracy is analytically verified by performing a normal mode analysis and numerically confirmed through a computational experiment

dual algorithms for fast calculation of the fourier bessel transform this paper presents a new procedure for the fast calculation of the fourier bessel transform the computation is performed in a dual mode and involves two matched algorithms the first of which provides the lower order components while the second yields intermediate and higher order samples of the transform the first algorithm is based on the fourier selection summation fss method derived in a previous study while the second relies on the bessel function large argument asymptotic expansion it is shown that the dual procedure constructed along these lines requires a computation time which is about four times that needed by a single n point fast fourier transform

an unconditionally stable rotational velocity correction scheme for incompressible flows we present an unconditionally stable splitting scheme for incompressible navier stokes equations based on the rotational velocity correction formulation the main advantages of the scheme are i it allows the use of time step sizes considerably larger than the widely used semi implicit type schemes the time step size is only constrained by accuracy ii it does not require the velocity and pressure approximation spaces to satisfy the usual inf sup condition in particular the equal order finite element spectral element approximation spaces can be used iii it only requires solving a pressure poisson equation and a linear convection diffusion equation at each time step numerical tests indicate that the computational cost of the new scheme for each time step under identical time step sizes is even less expensive than the semi implicit scheme with low element orders therefore the total computational cost of the new scheme can be significantly less than the usual semi implicit scheme

accurate error rate performance analysis of ofdm on frequency selective nakagami m fading channels error rates of orthogonal frequency division multiplexing ofdm signals in multipath slow fading nakagami m fading channels are considered the exact probability density function of a sum of nakagami m random phase vectors is used to derive a closed form expression for the error rates of ofdm signals the precise error rate analysis is extended to a system using multichannel reception with maximal ratio combining an asymptotic error rate analysis is also provided for a two tap channel with finite values of nakagami m fading parameters our analysis and numerical results show that the asymptotic error rate performance of an ofdm signal is similar to that of a single carrier signal transmitted over a rayleigh fading channel on the other hand our analysis further shows that a frequency selective channel that can be represented by two constant taps has similar asymptotic error rate performance to that of a one sided gaussian fading channel it is observed that depending on the number of channel taps the error rate performance does not necessarily improve with increasing nakagami m fading parameters

on the stationarity of signal scattering by two dimensional slightly rough random surfaces we present statistical properties of signal scattering by two dimensional slightly rough random surface the work concerns the intermediate field zone calculations are carried out within the framework of the first order small perturbation method the surface is assumed to be ergodic and stationary and the height distribution to be gaussian under an oblique incidence we demonstrate that the first order scattered field is not wide sense stationary for a given altitude under the normal incidence the scattered field is a strictly stationary random process by using the stationary phase method we show that the scattered field becomes asymptotically a strictly stationary random process when increasing the altitude of the observation point we also define the condition that must be satisfied by an antenna transfer function so that the measured scattered field becomes stationary and ergodic

efficient estimation of class a noise parameters via the em algorithm the class a middleton noise model is a commonly used statistical physical parametric model for non gaussian interference superimposed on a gaussian background in this study the problem of efficient estimation of the class a parameters for small sample sizes is considered the proposed estimator is based on the em algorithm a two step iterative estimation technique that is ideally suited for the class a estimation problem since the observations can be readily treated as incomplete data for the single parameter estimation problem a closed form expression for the estimator is obtained furthermore for the single parameter estimation problem it is shown that the sequence of estimates obtained via the em algorithm converges and a characterization of the point to which the sequence converges is given in particular it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest then it must be a stationary point of the traditional likelihood function in addition for both the single parameter and two parameter estimation problems the small sample size performance of the proposed em algorithm is examined via an extensive simulation study

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

bayes error estimation using parzen and k nn procedures the use of k nearest neighbor k nn and parzen density estimates to obtain estimates of the bayes error is investigated under limited design set conditions by drawing analogies between the k nn and parzen procedures new procedures are suggested and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k nn and parzen procedures we show that by varying the decision threshold many of the biases associated with the k nn or parzen density estimates may be compensated and successful error estimation may be performed in spite of these biases experimental results are given which demonstrate the effect of kernel size and shape parzen the size of k k nn and the number of samples in the design set

comments on statistics of the scattering cross section of small number of random scatterers with reply for original paper see ieee trans antennas propag vol 43 p 773 83 1995 august the present comment discusses the use of a recursive method and an orthonormal laguerre polynomial representation in the original paper a reply is given by the original authors

on the co polarized phase difference of rough layered surfaces formulae derived from the small perturbation method we determine the statistical distribution of the co polarized phase difference of fields scattered from a stack of two two dimensional rough interfaces in the incidence plane the electromagnetic fields are represented by rayleigh expansions and a perturbation method is used to solve the boundary value problem and to determine the first order scattering amplitudes for slightly rough interfaces with infinite length and gaussian height distributions we show that the probability density function is only a function of two parameters for a sand layer on a granite surface in backscattering configurations we study the influence of the incidence angle the layer thickness the cross spectral density and the wave frequency upon both parameters of the probability law

recursive algorithms for identification of impulse noise channels the class a middleton model is a widely accepted statistical physical parameteric model for impulsive interference superimposed on a gaussian background in the present work a recursive decision directed estimator for online identification of the parameters of the class a model is proposed this estimator is based on an adaptive bayesian classification of each of a sequence of class a envelope samples as an impulsive sample or as a background sample as each sample is so classified recursive updates of the estimates of the second moment of the background component of the interference envelope density the second moment of the impulsive component of the interference envelope density and the probability with which the impulsive component occurs are readily obtained from these estimates estimates of the parameters of the class a model follow straightforwardly since closed form expressions for the parameters exist in terms of these quantities the performance characteristics of this algorithm are investigated and an appropriately modified version is found to yield a recursive algorithm with excellent global performance

some statistical and spatial properties of signal scattering by 2 d slightly rough random surfaces within the framework of the first order small perturbation method spm we establish some statistical and spatial properties of signal scattering by 2 d slightly rough random surfaces the work concerns the total field within the intermediate field zone for an ergodic and stationary gaussian surface under illumination by a monochromatic plane wave for infinite extension surfaces we obtain the probability density functions pdfs for the modulus and phase of the total field components the modulus pdf is expressed as an infinite sum of modified bessel functions while the phase pdf is expressed in terms of the error function under oblique illumination the total field is not wide sense stationary from a spatial point of view for a given elevation and under all incidences we show that the total field is ergodic to the second order under oblique incidence the spatial distribution of the total field modulus is a rayleigh law and the phase is uniform under normal incidence we establish that the spatial and statistical distributions are interchangeable

statistics of the scattering cross section of a small number of random scatterers complex radar targets are often modeled as a number of individual scattering elements randomly distributed throughout the spatial region containing the target while it is known that as the number of scatterers grows large the distribution of the scattered signal power or intensity is asymptotically exponential this is not true for a small number of scatterers the authors study the statistics of measured power or intensity and hence scattering cross section resulting from a small number of constant amplitude scatterers each having a random phase they derive closed form expressions for the probability density function pdf of the scattered signal intensity for one two and three scatterers having arbitrary amplitudes for n 3 scatterers they derive expressions for the pdf when the individual scatterers have identical constant amplitudes and independent random phases these expressions are gram charlier type expansions with weighting functions determined by the asymptotic form of the intensity pdf for a large number of scatterers n the kolmogorov smirnov goodness of fit test is used to show that the series expansions are a good fit to empirical pdfs computed using monte carlo simulation of targets made up of a small number of constant amplitude scatterers with random phase

on the probability density function of the squared envelope of a sum of random phase vectors a recursive solution is presented for the probability density function of the sum of n independent random phase vectors the recursion parameter is n the number of vectors in the sum this approach allows one to rapidly compute a complete set of these density functions for values of n 2 3 n max where n max typically corresponds to the total number of system users in a multiuser fhma mfsk application or one plus the total number of jamming tones in an fh mfsk spread spectrum application such evaluations are necessary for exact calculation of the average error probability performance of such systems

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

asymptotically robust detection and estimation for very heavy tailed noise the asymptotically robust detection of signals and the analogous problem of estimation of location are considered for noise distributions with heavier than exponential tails the solution to both problems is identical and is obtained when using efficacy or asymptotic variance as the performance measure the density of the noise is assumed to belong to a e contamination class where the contaminant is either 1 from the class of unimodal densities 2 from the class of densities limited in support to an interval about the mode of the nominal density or 3 a mixture of a member of 1 with a member of 2 the robust detector or estimator is similar to a censored version of the nonlinearity used for maximum likelihood estimation or locally optimal detection in the presence of noise with the nominal distribution

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

a note on the l_1 consistency of variable kernel estimates 1 introduction most consistent nonparametric density estimates have a built in smoothing parameter numerous schemes have been proposed see e g references found in rudemo 1982 or devroye and penrod 1984 for selecting the smoothing parameter as a function of the data only a process called automatization and for introducing locally adaptable smoothing parameters in this note we give conditions which insure that estimators of the form

posbist reliability behavior of typical systems with two types of failure abstract the posbist reliability theory is based on the possibility assumption and the binary state assumption in this paper we study the posbist reliability behavior in the presence of two failure modes for various classes of typical systems including series systems parallel systems k out of n systems series parallel systems and parallel series systems it is shown that for each typical system the posbist system reliability is bounded by the minimum and the maximum of the posbist component reliabilities

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

ray chaotic footprints in deterministic wave dynamics a test model with coupled floquet type and ducted type mode characteristics ray chaos manifested by the exponential divergence of trajectories in an originally thin ray bundle can occur even in linear electromagnetic propagation environments due to the inherent nonlinearity of ray tracing maps in this paper we present a novel two dimensional test example of such an environment which embodies intimately coupled refractive wave trapping and periodicity induced multiple scattering phenomenologies and which is amenable to explicit full wave analysis though strictly nonchaotic it is demonstrated that under appropriate conditions which are inferred from a comprehensive parametric database generated via the above noted rigorous reference solution the high frequency wave dynamics exhibits trends toward irregularity and other peculiar characteristics these features can be interpreted as ray chaotic footprints and they are usually not observed in geometries characterized by regular ray behavior in this connection known analogies from other disciplines particularly quantum physics are briefly reviewed and related to the proposed test configuration moreover theoretical implications and open issues are discussed and potential applications are conjectured

three dimensional fully adaptive simulations of phase field fluid models we present an efficient numerical methodology for the 3d computation of incompressible multi phase flows described by conservative phase field models we focus here on the case of density matched fluids with different viscosity model h the numerical method employs adaptive mesh refinements amr in concert with an efficient semi implicit time discretization strategy and a linear multi level multigrid to relax high order stability constraints and to capture the flow s disparate scales at optimal cost only five linear solvers are needed per time step moreover all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of amr in a conservative phase field setting we validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation kelvin helmholtz instability and flow induced drop coalescence

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

a parallel block multi level preconditioner for the 3d incompressible navier stokes equations the development of robust and efficient algorithms for both steady state simulations and fully implicit time integration of the navier stokes equations is an active research topic to be effective the linear subproblems generated by these methods require solution techniques that exhibit robust and rapid convergence in particular they should be insensitive to parameters in the problem such as mesh size time step and reynolds number in this context we explore a parallel preconditioner based on a block factorization of the coefficient matrix generated in an oseen nonlinear iteration for the primitive variable formulation of the system the key to this preconditioner is the approximation of a certain schur complement operator by a technique first proposed by kay loghin and wathen siam j sci comput 2002 and silvester elman kay and wathen j comput appl math 128 2001 261 the resulting operator entails subsidiary computations solutions of pressure poisson and convection diffusion subproblems that are similar to those required for decoupled solution methods however in this case these solutions are applied as preconditioners to the coupled oseen system one important aspect of this approach is that the convection diffusion and poisson subproblems are significantly easier to solve than the entire coupled system and a solver can be built using tools developed for the subproblems in this paper we apply smoothed aggregation algebraic multigrid to both subproblems previous work has focused on demonstrating the optimality of these preconditioners with respect to mesh size on serial two dimensional steady state computations employing geometric multi grid methods we focus on extending these methods to large scale parallel three dimensional transient and steady state simulations employing algebraic multigrid amg methods our results display nearly optimal convergence rates for steady state solutions as well as for transient solutions over a wide range of cfl numbers on the two dimensional and three dimensional lid driven cavity problem

stability of approximate projection methods on cell centered grids projection methods are a popular class of methods for solving the incompressible navier stokes equations if a cell centered grid is chosen in order to use high resolution methods for the advection terms performing the projection exactly is problematic an attractive alternative is to use an approximate projection in which the velocity is required to be only approximately discretely divergence free the stability of the cell centered approximate projection is highly sensitive to the method used to update the pressure and compute the pressure gradient this is demonstrated by analyzing a model problem and conducting numerical simulations of the navier stokes equations

on arbitrarily slow rates of global convergence in density estimation let a density f on rd be estimated by fn x x1 xn where x rd fn is a borel measurable function of its arguments and x1 xn are independent random vectors with common density f let p 1 be a constant one of the main results of this note is that for every sequence fn and for every positive number sequence an satisfying lim an 0 there exists an f such that e left smallint f n left x right f left x right p dx right a n infinitely often

the immersed boundary method a projection approach a new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion like previous methods a boundary force is applied at the immersed surface to satisfy the no slip constraint this extra constraint can be added to the incompressible navier stokes equations by introducing regularization and interpolation operators the current method gives prominence to the role of the boundary force acting as a lagrange multiplier to satisfy the no slip condition this role is analogous to the effect of pressure on the momentum equation to satisfy the divergence free constraint the current immersed boundary method removes slip and non divergence free components of the velocity field through a projection the boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger cfl numbers compared to some past methods symmetry and positive definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field examples show that the current formulation achieves second order temporal accuracy and better than first order spatial accuracy in l 2 norms for one and two dimensional test problems results from two dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory

an orthonormal laguerre expansion yielding rice s envelope density function for two sine waves in noise through an orthonormal laguerre expansion expressions are derived for a lesser known rician probability distribution the probability density function pdf of the envelope of two fixed amplitude randomly phased sine waves in narrowband gaussian noise and for the integral of the density the cumulative distribution function cdf the principal formula derived has been checked analytically numerically and approximately graphically analytically the moment generating function for the pdf of the square of the envelope has been found to be a three term product of elementary functions times an i sub 0 bessel function and thus to be in closed form in confirmation the same result has been secured via another more direct route

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel

parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters this paper proposes a procedure to construct the membership functions of the system characteristics of a repairable system with two primary units one standby unit and one repair facility when switching to standby may fail failure times of primary and standby units are assumed to follow fuzzified exponential distributions and repair times of the failed units are also assumed to have a fuzzified exponential distribution the a cut approach is used to extract from the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics determined with a set of parametric nonlinear programs using their membership functions a numerical example is solved successfully to illustrate the practicality of the proposed approach because the system characteristics are governed by the membership functions more information is provided for use by designers and practitioners the successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications